tag:theconversation.com,2011:/ca-fr/topics/statistics-1430/articlesStatistics – La Conversation2024-03-28T12:51:38Ztag:theconversation.com,2011:article/2263792024-03-28T12:51:38Z2024-03-28T12:51:38ZFor over a century, baseball’s scouts have been the backbone of America’s pastime – do they have a future?<figure><img src="https://images.theconversation.com/files/584862/original/file-20240327-28-o25sx.jpg?ixlib=rb-1.1.0&rect=952%2C15%2C4129%2C2834&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Texas Rangers scout Brian Williams takes notes at Roberto Clemente Stadium in Carolina, Puerto Rico.</span> <span class="attribution"><span class="source">H. James Gilmore and Tracy Halcomb</span>, <a class="license" href="http://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA</a></span></figcaption></figure><p>Former MLB executive <a href="https://baseballhall.org/hall-of-famers/gillick-pat">Pat Gillick</a> won three World Series titles and served as general manager of four baseball teams from the 1970s to 2000s. </p>
<p>But when we interviewed him for our documentary “<a href="https://filmfreeway.com/FieldingDreamsACelebrationofBaseballScouts183">Fielding Dreams: A Celebration of Baseball Scouts</a>,” he deflected praise.</p>
<p>“I wouldn’t be in the Hall of Fame if it wasn’t for the people in scouting,” he said. “Those are the people that deserve all the credit, not me.”</p>
<p>Even though they scour the world for talent, often working on year-to-year contracts and spending weeks away from their families, there are no scouts in the <a href="https://baseballhall.org/">National Baseball Hall of Fame</a>.</p>
<p>Their recent run of tough luck has also gone largely unnoticed. The profession has been under siege on a number of fronts, whether it’s facing competition and dismissal from analytics advocates, or experiencing <a href="https://www.bostonherald.com/2020/09/04/red-sox-lay-off-nine-employees-from-scouting-player-development-staffs/">mass</a> <a href="https://www.baseballamerica.com/stories/scouting-industry-endures-most-brutal-offseason-in-recent-memory/">layoffs</a> during the COVID-19 pandemic. </p>
<h2>A draft demands an army of evaluators</h2>
<p>In the first half of the 20th century, scouting was a free-for-all. </p>
<p>Team owners willing to spend the money could send scouts to go out and sign whomever they wanted, with contracts often written out by hand and players signing on the spot. When Iowa teen phenom Bob Feller was signed by Cleveland Indians scout <a href="https://sabr.org/bioproj/person/cy-slapnicka/">Cy Slapnicka</a> in 1935, Slapnicka simply took out a pen, wrote out a contract and had Feller and his father sign it, because Feller was underage.</p>
<p>The terms of the contract? <a href="https://case.edu/ech/articles/f/feller-robert">One dollar and an autographed ball</a>.</p>
<p>Major League Baseball <a href="https://sabr.org/journal/article/the-history-and-future-of-the-amateur-draft/">held its first draft in 1965</a>, in part to help level the playing field between wealthier teams, like the New York Yankees and St. Louis Cardinals, and everybody else.</p>
<p>The advent of the draft made scouts all the more important: Each team now had <a href="https://www.baseball-almanac.com/draft/baseball-draft.php?yr=1965">a massive pool of players</a> to interview, evaluate and rank.</p>
<p>The draft only includes U.S. amateur players. International players are not subject to the draft, so some teams have built training facilities in countries like <a href="https://theconversation.com/the-promise-and-peril-of-the-dominican-baseball-pipeline-113242">the Dominican Republic</a> and <a href="https://www.mlb.com/news/mlb-opens-new-academy-in-mexico-c215291168">Mexico</a>, where their international scouts find and sign promising young players. </p>
<h2>Strength in crunching the numbers?</h2>
<p>But since the turn of the century, some journalists and executives have questioned the value of scouts.</p>
<p>In 2003, author Michael Lewis published “<a href="https://wwnorton.com/books/9780393324815">Moneyball</a>,” in which he documented the success of the 2002 Oakland Athletics and the team’s <a href="https://sabr.org/sabermetrics">embrace of sabermetrics</a>, the statistical analysis of baseball data.</p>
<p>The Athletics were consistently winning with one of the lowest payrolls in baseball, and other team owners took notice. </p>
<p>Could data analytics exploit inefficiencies and produce better results than scouts? Could teams save money by trimming the ranks of old-school professionals and all of the human bias that they brought to evaluating talent?</p>
<p>The embrace of sabermetrics changed who got drafted. With raw data becoming increasingly important, college players – with a longer track record of statistics – became more attractive than high school athletes.</p>
<figure class="align-center ">
<img alt="Middle-aged man sitting on a metal bench with his legs crossed as he tugs on the brim of his baseball cap." src="https://images.theconversation.com/files/584559/original/file-20240326-16-7haf2s.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/584559/original/file-20240326-16-7haf2s.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=465&fit=crop&dpr=1 600w, https://images.theconversation.com/files/584559/original/file-20240326-16-7haf2s.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=465&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/584559/original/file-20240326-16-7haf2s.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=465&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/584559/original/file-20240326-16-7haf2s.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=584&fit=crop&dpr=1 754w, https://images.theconversation.com/files/584559/original/file-20240326-16-7haf2s.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=584&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/584559/original/file-20240326-16-7haf2s.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=584&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Oakland Athletics General Manager Billy Beane ushered in an era that emphasized the use of analytics to evaluate talent and construct rosters.</span>
<span class="attribution"><a class="source" href="https://newsroom.ap.org/detail/ATHLETICSSPRINGTRAINING/0fab9501d4e4da11af9f0014c2589dfb/photo?Query=billy%20beane&mediaType=photo&sortBy=arrivaldatetime:asc&dateRange=Anytime&totalCount=116&currentItemNo=5">AP Photo/Eric Risberg</a></span>
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<p>The shift to data-informed decision-making has had some unintended consequences. </p>
<p>In order for high school players to get recognized in today’s environment, <a href="https://www.americamagazine.org/politics-society/2022/05/19/catholic-youth-sports-little-league-club-baseball-243016">they turn to travel teams</a>, an expensive option that allows a player to participate in more games and accumulate more experience, more footage of their play and more exposure. </p>
<p>Players from lower-income families often can’t afford to participate – and that includes young Black athletes, <a href="https://www.povertycenter.columbia.edu/news-internal/2022/black-white-child-poverty-gap">who are disproportionately more likely to grow up in poverty</a>. <a href="https://apnews.com/article/baseball-diversity-study-black-players-5d0d1766536f1385ee673c68be55d89a">A recent study</a> found that Black athletes represented just 6.2% of MLB players on 2023 opening day rosters, down from 18% in 1991. </p>
<p>As retired Black utility player <a href="https://www.baseball-reference.com/players/c/collilo01.shtml">Lou Collier</a> told us: “A kid like me, today, never would have had an opportunity. … If I wasn’t able to afford any of these events, you never would have heard of Lou Collier. But back when I was coming up, the scouts found the Lou Colliers.” </p>
<h2>‘Moneyball’ or makeup?</h2>
<p>Scouts will also tell you that analytics is nothing new.</p>
<p>“We evaluated the player,” says former Atlanta Braves scouting director <a href="https://www.mlb.com/royals/team/front-office/roy-clark">Roy Clark</a>. “And when our scouts said, ‘We think this guy can play in the big leagues,’ the next thing we did is we gathered all the information we could – analytics. But then we emphasized makeup.”</p>
<p>It is a grasp of this concept – “makeup,” or a player’s character, drive and grit – that scouts say differentiates their work from data-driven evaluations.</p>
<p>“It comes down to the people who have a really good head on their shoulders,” says Matt O’Brien, a scout for the Toronto Blue Jays. </p>
<p>And the scouts will tell you that there is both on-field and off-field makeup. </p>
<p>“You’ve got to talk to his school counselor, you’ve got to talk to his coach, you’ve got to talk to his teammates, you’ve got to try and talk to other students,” explains Gillick. “Is he a good baseball player, and is he a good human being?” </p>
<p>This personalized approach, one that focuses on a player’s heart and mind, has kept scouting relevant. Even with the rise of analytics, the number of MLB scouts had stayed remarkably consistent into the 21st century. It seemed as if the fear generated by “Moneyball” was unfounded. </p>
<p>That all changed in 2020.</p>
<figure class="align-center ">
<img alt="Black and white photo of smiling man seated at a table. Behind him is another man standing next to a board with sheets of paper affixed to it." src="https://images.theconversation.com/files/584514/original/file-20240326-18-7daslm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/584514/original/file-20240326-18-7daslm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=448&fit=crop&dpr=1 600w, https://images.theconversation.com/files/584514/original/file-20240326-18-7daslm.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=448&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/584514/original/file-20240326-18-7daslm.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=448&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/584514/original/file-20240326-18-7daslm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=563&fit=crop&dpr=1 754w, https://images.theconversation.com/files/584514/original/file-20240326-18-7daslm.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=563&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/584514/original/file-20240326-18-7daslm.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=563&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Hall of Fame executive Pat Gillick during the 1983 MLB draft, when he served as vice president of baseball operations for the Toronto Blue Jays. Behind him is scout Bob Prentice.</span>
<span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/news-photo/pat-gillick-right-blue-jays-vice-president-of-baseball-news-photo/502315001?adppopup=true">Jeff Goode/Toronto Star via Getty Images</a></span>
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<h2>The costs of COVID-19</h2>
<p>COVID-19 didn’t just shorten the 2020 baseball season, winnowing it down from 162 games to 60. It also shrank baseball’s scouting ranks. </p>
<p>USA Today reported that <a href="https://www.usatoday.com/story/sports/mlb/columnist/bob-nightengale/2021/03/11/baseball-scouts-return-covid-pandemic/4645174001/?utm_source=feedblitz&utm_medium=FeedBlitzRss&utm_campaign=usatodaycomsports-topstories">about 20% of scouts were laid off in 2020</a>. Many of them weren’t hired back. </p>
<p>“It was just the most uneasy feeling,” recalled MLB Scouting Bureau’s Christie Wood, <a href="https://www.nytimes.com/2016/03/29/sports/baseball/a-harder-look-at-female-scouts-shows-more-in-the-job-than-thought.html">one of the few female scouts in the game</a>.</p>
<p>According to the magazine Baseball America, by 2021 <a href="https://www.baseballamerica.com/stories/scouting-industry-endures-most-brutal-offseason-in-recent-memory/">seven teams had reduced their scouting staff by double digits</a>. </p>
<p>The Tampa Bay Rays and Milwaukee Brewers cut 10 scouts apiece. The Los Angeles Dodgers and San Francisco Giants had 13 fewer on their payrolls. The Chicago Cubs were down 20, while the Los Angeles Angels and Seattle Mariners each reduced their scouting ranks by 23. </p>
<p>At the beginning of the 2019 season, teams employed 1,909 scouts across their amateur, professional and international departments. By 2021, that number was down to 1,756. And most of the scouts that were laid off were older, more experienced scouts making higher salaries.</p>
<p>In June 2023, 17 former scouts <a href="https://www.espn.com/mlb/story/_/id/37893641/ex-scouts-file-age-discrimination-lawsuit-major-league-baseball">sued MLB for age discrimination</a>. They claimed that the league and its teams acted intentionally to prevent the employment of older scouts after the pandemic.</p>
<h2>A big win for the scouts</h2>
<p>The state of scouting today is a mixed bag.</p>
<p>Some teams seem to be prioritizing analytics. But other organizations – the Pittsburgh Pirates, Toronto Blue Jays, Houston Astros, Minnesota Twins and Texas Rangers – have actually added scouts to their payrolls since 2019.</p>
<p>The Rangers organization opened their doors to our documentary crew over the past four years, allowing us into the inner sanctum. We were able to see, firsthand, the organization’s emphasis on scouting, and witness the relationships the team’s scouts built with prospects and their families.</p>
<p>When the Rangers won the World Series in 2023, baseball scouts around the league rejoiced: The team’s success confirmed that an emphasis on personal touch and people could still pay off. </p>
<p>“I’m just proud of all the scouts that are here and who have worked so hard,” Texas Rangers scout Demond Smith told us during one playoff game. “At the end of the day, it’s baseball. It’s Little League from the beginning, and then you are dreaming. And here we are.”</p><img src="https://counter.theconversation.com/content/226379/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The authors do not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Even with teams’ embrace of analytics, the number of scouts employed by MLB teams had stayed remarkably consistent. That all changed with the COVID-19 pandemic.H. James Gilmore, Visiting Filmmaker, Flagler CollegeTracy Halcomb, Professor of Communication, Flagler CollegeLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2260212024-03-21T06:12:11Z2024-03-21T06:12:11ZSocial media apps have billions of ‘active users’. But what does that really mean?<figure><img src="https://images.theconversation.com/files/583295/original/file-20240321-26-3vpdrd.jpg?ixlib=rb-1.1.0&rect=628%2C519%2C4539%2C2925&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://unsplash.com/photos/group-of-people-standing-on-brown-floor-HN6uXG7GzTE">Creative Christians/Unsplash</a></span></figcaption></figure><p>Our digital world is bigger and more connected than ever. Social media isn’t just a daily habit – <a href="https://wearesocial.com/au/blog/2024/01/digital-2024-5-billion-social-media-users/">with more than 5 billion users globally</a>, it’s woven into the very fabric of our existence.</p>
<p>These platforms offer entertainment, connection, information and support, but they’re also battlegrounds for misinformation and online harassment. </p>
<p>Platforms like Facebook, YouTube, Instagram and TikTok vie for our attention, each boasting user counts in the billions. But what do these numbers actually tell us, and should we care?</p>
<h2>What is an active user or a unique user?</h2>
<p>Behind the impressive statistics lies a complex reality. While global social media usership has hit the 5 billion mark, representing <a href="https://datareportal.com/reports/digital-2024-global-overview-report">about 62% of the world’s population</a>, these figures mask the intricacies of online participation.</p>
<p>In Australia, the average person juggles <a href="https://www.genroe.com/blog/social-media-statistics-australia/13492">nearly seven social media accounts</a> across multiple platforms. This challenges the assumption that user counts equate to unique individuals.</p>
<p>It is also important to differentiate between accounts and active users. Not all accounts represent actual engagement in the platform’s community.</p>
<p>An “active user” is typically someone who has logged into a platform within a specific timeframe, such as the past month, indicating engagement with the platform’s content and features. They’re measured with analytics tools provided by the platform itself, or with third-party software. </p>
<p>The tools track the number of unique users – that is, individual accounts – who have interacted with or been exposed to specific content, whether a post, story or advertising campaign. </p>
<p>Social media companies use these metrics to showcase the potential reach of their platform to marketers. It’s key to their business model, as advertising revenue is typically their main source of income. </p>
<p>However, the reliability of these statistics is debatable. Factors such as <a href="https://www.dw.com/en/fact-check-how-do-i-spot-fake-social-media-accounts-bots-and-trolls/a-60313035">bot accounts</a>, inactive accounts and duplicates can inflate numbers, offering a distorted view of a platform’s user base.</p>
<p>Moreover, the criteria for an “active user” vary across platforms. This makes it difficult to make comparisons between user bases and to truly understand online audiences.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/583298/original/file-20240321-22-ifb91e.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="A person holding up a smartphone at a busy nightclub." src="https://images.theconversation.com/files/583298/original/file-20240321-22-ifb91e.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/583298/original/file-20240321-22-ifb91e.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/583298/original/file-20240321-22-ifb91e.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/583298/original/file-20240321-22-ifb91e.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/583298/original/file-20240321-22-ifb91e.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/583298/original/file-20240321-22-ifb91e.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/583298/original/file-20240321-22-ifb91e.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
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<span class="caption">Sheer user numbers can make a social media platform influential, but there’s nuance in how we measure impact.</span>
<span class="attribution"><a class="source" href="https://unsplash.com/photos/a-person-taking-a-picture-with-a-cell-phone-D4kALj_9CEE">Michael Effendy/Unsplash</a></span>
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<h2>User count isn’t always relevance</h2>
<p><a href="https://datareportal.com/reports/digital-2024-global-overview-report">TikTok boasts a staggering 1.5 billion users globally</a>. This doesn’t even include users on its Chinese counterpart, Douyin. It is also often at the centre of <a href="https://theconversation.com/tiktok-has-a-startling-amount-of-sexual-content-and-its-way-too-easy-for-children-to-access-216114">controversies</a> and <a href="https://medium.com/datasociety-points/the-politics-and-optioncs-of-the-tiktok-ban-d88bdcb532d">geopolitical tensions</a>.</p>
<p>For example, <a href="https://theconversation.com/attempts-to-ban-tiktok-reveal-the-hypocrisy-of-politicians-already-struggling-to-relate-to-voters-225870">TikTok has repeatedly faced threats of bans</a> in significant markets such as the United States, raising questions about future access. But with such a vast user base, TikTok’s impact on culture and trends – particularly among young people – is clear and far-reaching.</p>
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<em>
<strong>
Read more:
<a href="https://theconversation.com/if-tiktok-is-banned-in-the-us-or-australia-how-might-the-company-or-china-respond-225889">If TikTok is banned in the US or Australia, how might the company – or China – respond?</a>
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<p>However, the true impact of platforms is further muddied by algorithms – the complex formulas that dictate the content we see and engage with. Designed to keep us scrolling and interacting, they significantly shape our online experiences.</p>
<p>They also complicate how “active” a user might appear. Someone could seem more engaged simply because the algorithm promotes content they interact with more often.</p>
<p>So, while a high active-user count might indicate a platform’s popularity and reach, it doesn’t fully capture its influence or social relevance. True engagement goes beyond numbers, delving into the depth of user interaction, the quality of the content, and the cultural impact these platforms wield.</p>
<h2>Different strokes for different ages</h2>
<p>When we look at the users’ demographics, we see <a href="https://wearesocial.com/au/blog/2024/01/digital-2024-5-billion-social-media-users/">distinct preferences across age groups</a>. </p>
<p>Among the younger crowd, specifically Gen Z, <a href="https://wearesocial.com/au/blog/2024/01/digital-2024-5-billion-social-media-users/">TikTok vastly outpaces Instagram</a> with <a href="https://explodingtopics.com/blog/tiktok-demographics">one in four users under the age of 20</a>. </p>
<p>Meanwhile, <a href="https://sproutsocial.com/insights/new-social-media-demographics/">Snapchat and Instagram</a> are the preferred platforms for people aged 18–29. </p>
<p>Facebook, with its massive user base of more than 3 billion and a <a href="https://datareportal.com/essential-facebook-stats">median user age of 32</a>, is the platform of choice for millennials, Gen X and boomers.</p>
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<strong>
Read more:
<a href="https://theconversation.com/ok-boomer-how-a-tiktok-meme-traces-the-rise-of-gen-z-political-consciousness-165811">'OK Boomer': how a TikTok meme traces the rise of Gen Z political consciousness</a>
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<p>People in their 30s and older <a href="https://datareportal.com/reports/digital-2024-global-overview-report">tend to use LinkedIn</a> and X (formerly Twitter) more than platforms like Snapchat.</p>
<p>But all these social media platforms tend to vary in their primary focus, from news and professional connections (like LinkedIn) to predominantly serving entertainment (like TikTok).</p>
<p>This means demographic trends also reveal how each platform impacts users differently, catering to varied content preferences – whether it’s for entertainment, staying updated on news and events, or connecting with friends and family. </p>
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<a href="https://images.theconversation.com/files/583296/original/file-20240321-30-s182sm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="A group of women at a nice restaurant taking a selfie together." src="https://images.theconversation.com/files/583296/original/file-20240321-30-s182sm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/583296/original/file-20240321-30-s182sm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/583296/original/file-20240321-30-s182sm.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/583296/original/file-20240321-30-s182sm.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/583296/original/file-20240321-30-s182sm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/583296/original/file-20240321-30-s182sm.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/583296/original/file-20240321-30-s182sm.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Ultimately, social media really is about community, not global relevance.</span>
<span class="attribution"><a class="source" href="https://unsplash.com/photos/3-women-smiling-and-standing-near-table-_3Pyr85zcE8">Rendy Novantino/Unsplash</a></span>
</figcaption>
</figure>
<h2>User count isn’t what matters</h2>
<p>For content creators and news media, delving into user statistics is crucial if they want to reach their target audiences.</p>
<p>However, despite headlines often focusing on vast user numbers, do these figures actually matter to the everyday social media user? <a href="https://apo.org.au/node/322860">Research I’ve done with colleagues</a> suggests they don’t.</p>
<p>For individuals navigating these digital spaces, it’s not about which platform boasts the highest user count and is therefore deemed “important”.</p>
<p>Instead, the focus is on maintaining connections within their social circles. This preference is rooted in cultural practices, meaning it aligns with the habits, preferences and values of their own community or cultural group.</p>
<p>In other words, people are drawn to social media platforms that are popular or widely accepted among their family, friends, social allies and broader cultural community. This suggests the essence of social media lies in the quality of interactions rather than the platform’s global standing.</p>
<p>Whether for staying informed, being entertained, or nurturing relationships, people gravitate to spaces where their community or “tribe” gathers. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/its-hard-to-imagine-better-social-media-alternatives-but-scuttlebutt-shows-change-is-possible-190351">It's hard to imagine better social media alternatives, but Scuttlebutt shows change is possible</a>
</strong>
</em>
</p>
<hr>
<img src="https://counter.theconversation.com/content/226021/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Milovan Savic receives funding from Australian Research Council </span></em></p>Platforms like Facebook, Instagram and TikTok vie for our attention and boast billions of users. Ultimately, what matters is connection.Milovan Savic, Research Fellow, ARC Centre of Excellence for Automated Decision-Making and Society, Swinburne University of TechnologyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2235092024-03-01T13:40:34Z2024-03-01T13:40:34ZThe ‘average’ revolutionized scientific research, but overreliance on it has led to discrimination and injury<figure><img src="https://images.theconversation.com/files/578352/original/file-20240227-22-rs4i9u.jpg?ixlib=rb-1.1.0&rect=0%2C0%2C5591%2C3722&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">The average can tell you a lot about a dataset, but not everything. </span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/photos/bell-curve?assettype=image&alloweduse=availableforalluses&agreements=pa%3A174132&family=creative&phrase=bell%20curve&sort=best">marekuliasz/iStock via Getty Images Plus</a></span></figcaption></figure><p>When analyzing a set of data, one of the first steps many people take is to compute an average. You might compare your height against the average height of people where you live, or brag about your favorite baseball player’s batting average. But while the average can help you study a dataset, it has important limitations. </p>
<p>Uses of the average that ignore these limitations have led to serious issues, such as <a href="https://www.routledge.com/The-Disability-Studies-Reader/Davis/p/book/9781138930230">discrimination</a>, <a href="https://www.gao.gov/products/gao-23-105595">injury</a> and even life-threatening accidents. </p>
<p>For example, the U.S. Air Force used to design its planes for “the average man,” but abandoned the practice when pilots <a href="https://www.youtube.com/watch?v=4eBmyttcfU4&pp=ygURdG9kZCByb3NlIGF2ZXJhZ2U%3D">couldn’t control their aircraft</a>. The average has many uses, but it doesn’t tell you anything about the variability in a dataset.</p>
<p>I am a <a href="https://scholar.google.com/citations?user=zEYYuIcAAAAJ&hl=en">discipline-specific education researcher</a>, meaning I study how people learn, with a focus on engineering. My research includes study of how engineers use averages in their work.</p>
<h2>Using the average to summarize data</h2>
<p>The average has been around for a long time, with its use documented as early as the ninth or eighth century BCE. In an early instance, the Greek poet Homer <a href="https://www.penguinrandomhouse.com/books/292278/the-history-of-the-peloponnesian-war-by-thucydides-translated-by-rex-warner-introduction-and-notes-by-m-i-finley/">estimated the number of soldiers</a> on ships by taking an average.</p>
<p>Early astronomers wanted to predict future locations of stars. But to make these predictions, they first needed accurate measurements of the stars’ current positions. Multiple astronomers would take position measurements independently, but they often arrived at different values. Since a star has just one true position, these discrepancies were a problem.</p>
<p>Galileo in 1632 was the <a href="https://doi.org/10.1080/0025570X.2006.11953386">first to push for a systematic approach</a> to address these measurement differences. His analysis was the beginning of <a href="https://press.princeton.edu/books/paperback/9780691208428/the-rise-of-statistical-thinking-1820-1900">error theory</a>. Error theory helps scientists reduce uncertainty in their measurements.</p>
<h2>Error theory and the average</h2>
<p>Under error theory, researchers interpret a set of measurements as falling around a true value that is corrupted by error. In astronomy, a star has a true location, but early astronomers may have had unsteady hands, blurry telescope images and bad weather – all sources of error.</p>
<p>To deal with error, researchers often assume that measurements are unbiased. In statistics, this means they evenly distribute around a central value. Unbiased measurements still have error, but they can be combined to better estimate the true value.</p>
<p>Say three scientists have each taken three measurements. Viewed separately, their measurements may seem random, but when unbiased measurements are put together, they evenly distribute around a middle value: the average.</p>
<p>When measurements are unbiased, the average will tend to sit in the middle of all measurements. In fact, we can show mathematically that <a href="https://doi.org/10.1080/0025570X.2006.11953386">the average is closest</a> to all possible measurements. For this reason, the average is an excellent tool for dealing with measurement errors.</p>
<h2>Statistical thinking</h2>
<p>Error theory was, in its time, considered revolutionary. Other scientists admired the precision of astronomy and sought to bring the same approach to their disciplines. The 19th century scientist Adolphe Quetelet applied ideas from error theory to study humans and <a href="https://press.princeton.edu/books/paperback/9780691208428/the-rise-of-statistical-thinking-1820-1900">introduced the idea</a> of taking averages of human heights and weights.</p>
<p>The average helps make comparisons across groups. For instance, taking averages from a dataset of male and female heights can show that the males in the dataset are taller – on average – than the females. However, the average does not tell us everything. In the same dataset, we could likely find individual females who are taller than individual males.</p>
<p>So, you can’t consider only the average. You should also consider the spread of values by thinking statistically. <a href="https://doi.org/10.1111/j.1751-5823.1999.tb00442.x">Statistical thinking</a> is defined as thinking carefully about variation – or the tendency of measured values to be different.</p>
<p>For example, different astronomers taking measurements of the same star and recording different positions is one example of variation. The astronomers had to think carefully about where their variation came from. Since a star has one true position, they could safely assume their variation was due to error.</p>
<p>Taking the average of measurements makes sense when variation comes from sources of error. But researchers have to be careful when interpreting the average when there is real variation. For instance, in the height example, individual females can be taller than individual males, even if men are taller on average. Focusing on the average alone <a href="https://doi.org/10.1080/26939169.2024.2308119">neglects variation</a>, which has caused serious issues.</p>
<p>Quetelet did not just take the practice of computing averages from error theory. He also took the assumption of a single true value. He elevated an ideal of “the average man” and suggested that <a href="https://press.princeton.edu/books/paperback/9780691208428/the-rise-of-statistical-thinking-1820-1900">human variability was fundamentally error</a> – that is, not ideal. To Quetelet, there’s something wrong with you if you’re not exactly average height.</p>
<p>Researchers who study <a href="https://www.routledge.com/The-Disability-Studies-Reader/Davis/p/book/9781138930230">social norms</a> note that Quetelet’s ideas about “the average man” contributed the modern meaning of the word “normal” – normal height, as well as normal behavior.</p>
<p>These ideas have been used by some, such as <a href="https://theconversation.com/francis-galton-pioneered-scientific-advances-in-many-fields-but-also-founded-the-racist-pseudoscience-of-eugenics-144465">early statisticians</a>, to divide populations in two: people who are in some way superior and those who are inferior. </p>
<p>For instance, the <a href="https://www.genome.gov/about-genomics/fact-sheets/Eugenics-and-Scientific-Racism">eugenics movement</a> – a despicable effort to prevent “inferior” people from having children – <a href="https://www.routledge.com/The-Disability-Studies-Reader/Davis/p/book/9781138930230">traces its thinking</a> to these ideas about “normal” people.</p>
<p>While Quetelet’s idea of variation as error <a href="https://doi.org/10.1080/15017410600608491">supports practices of discrimination</a>, Quetelet-like uses of the average also have direct connections to modern engineering failures.</p>
<h2>Failures of the average</h2>
<p>In the 1950s, the U.S. Air Force designed its aircraft for “the average man.” It assumed that a plane designed for an average height, average arm length and the average along several other key dimensions <a href="https://www.youtube.com/watch?v=4eBmyttcfU4&pp=ygURdG9kZCByb3NlIGF2ZXJhZ2U%3D">would work for most pilots</a>.</p>
<p>This decision contributed to as many as <a href="http://www.toddrose.com/endofaverage">17 pilots crashing in a single day</a>. While “the average man” could operate the aircraft perfectly, real variation got in the way. A shorter pilot would have trouble seeing, while a pilot with longer arms and legs would have to squish themselves to fit. </p>
<p>While the Air Force assumed most of its pilots would be close to average along all key dimensions, it found that out of 4,063 pilots, <a href="https://books.google.com/books/about/The_Average_Man.html?id=NxmdHAAACAAJ">zero were average</a>.</p>
<p>The Air Force solved the problem by designing for variation – it designed adjustable seats to account for the real variation among pilots.</p>
<p>While adjustable seats might seem obvious now, this “average man” thinking still causes problems today. In the U.S., women experience <a href="https://doi.org/10.2105/AJPH.2011.300275">about 50% higher odds of severe injury</a> in automobile accidents.</p>
<p>The Government Accountability Office blames this disparity on crash-test practices, where female passengers are crudely represented using a <a href="https://www.gao.gov/products/gao-23-105595">scaled version of a male dummy</a>, much like the Air Force’s “average man.” The first female crash-test dummy <a href="https://www.npr.org/2022/11/01/1133375223/the-first-female-crash-test-dummy-has-only-now-arrived">was introduced in 2022</a> and has yet to be adopted in the U.S.</p>
<p>The average is useful, but it has limitations. For estimating true values or making comparisons across groups, the average is powerful. However, for individuals who exhibit real variability, the average simply doesn’t mean that much.</p><img src="https://counter.theconversation.com/content/223509/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Zachary del Rosario receives funding from the National Science Foundation, and has worked with Citrine Informatics and Toyota Research Institute.</span></em></p>The average might come in handy for certain data analyses, but is any one person really ‘average’?Zachary del Rosario, Assistant Professor of Engineering, Olin College of EngineeringLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2145762024-01-07T19:04:19Z2024-01-07T19:04:19ZHere’s why you should (almost) never use a pie chart for your data<figure><img src="https://images.theconversation.com/files/558554/original/file-20231109-25-j7ehuz.jpg?ixlib=rb-1.1.0&rect=810%2C436%2C4761%2C3377&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/lemon-pie-flat-lay-on-blue-1663719415">YesPhotographers/Shutterstock</a></span></figcaption></figure><p>Our lives are becoming increasingly data driven. Our phones monitor our time and internet usage and online surveys discern our opinions and likes. These data harvests are used for telling us how well we’ve slept or what we might like to buy. </p>
<p>Numbers are becoming more important for everyday life, yet people’s numerical skills are falling behind. For example, the percentage of Year 12 schoolchildren in Australia taking higher and intermediate mathematics <a href="https://amsi.org.au/?publications=year-12-participation-in-calculus-based-mathematics-subjects-takes-a-dive-2">has been declining for decades</a>. </p>
<p>To help the average person understand big data and numbers, we often use visual summaries, such as pie charts. But while non-numerate folk will avoid numbers, most numerate folk will avoid pie charts. Here’s why.</p>
<h2>What is a pie chart?</h2>
<p>A pie chart is a circular diagram that represents numerical percentages. The circle is divided into slices, with the size of each slice proportional to the category it represents. It is named because it resembles a sliced pie and can be “served” in many different ways. </p>
<p>An example pie chart below shows Australia’s two-party preferred vote before the last election, with Labor on 55% and the the Coalition on 45%. The two near semi-circles show the relatively tight race – this is a useful example of a pie chart. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/560670/original/file-20231121-23-sgp640.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="55% for labor, 45% for coalition on a red and blue pie chart" src="https://images.theconversation.com/files/560670/original/file-20231121-23-sgp640.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/560670/original/file-20231121-23-sgp640.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=360&fit=crop&dpr=1 600w, https://images.theconversation.com/files/560670/original/file-20231121-23-sgp640.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=360&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/560670/original/file-20231121-23-sgp640.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=360&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/560670/original/file-20231121-23-sgp640.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=452&fit=crop&dpr=1 754w, https://images.theconversation.com/files/560670/original/file-20231121-23-sgp640.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=452&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/560670/original/file-20231121-23-sgp640.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=452&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">A simple pie chart showing the percentages for the two major Australian parties in an opinion poll.</span>
<span class="attribution"><span class="source">Victor Oguoma</span></span>
</figcaption>
</figure>
<h2>What’s wrong with pie charts?</h2>
<p>Once we have more than two categories, pie charts can easily misrepresent percentages and become hard to read.</p>
<p>The three charts below are a good example – it is very hard to work out which of the five areas is the largest. The pie chart’s circularity means the areas lack a common reference point. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/556782/original/file-20231031-27-3dz8ta.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/556782/original/file-20231031-27-3dz8ta.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/556782/original/file-20231031-27-3dz8ta.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=208&fit=crop&dpr=1 600w, https://images.theconversation.com/files/556782/original/file-20231031-27-3dz8ta.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=208&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/556782/original/file-20231031-27-3dz8ta.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=208&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/556782/original/file-20231031-27-3dz8ta.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=261&fit=crop&dpr=1 754w, https://images.theconversation.com/files/556782/original/file-20231031-27-3dz8ta.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=261&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/556782/original/file-20231031-27-3dz8ta.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=261&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Three example pie charts, each with five similar categories. Can you quickly tell which colour is the largest in each pie?</span>
<span class="attribution"><a class="source" href="https://commons.wikimedia.org/wiki/File:Piecharts.svg">Schutz/Wikimedia Commons</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<p>Pie charts also do badly when there are lots of categories. For example, this chart from a study on data sources used for COVID data visualisation shows hundreds of categories in one pie. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/556770/original/file-20231031-19-uurqzu.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/556770/original/file-20231031-19-uurqzu.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/556770/original/file-20231031-19-uurqzu.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=340&fit=crop&dpr=1 600w, https://images.theconversation.com/files/556770/original/file-20231031-19-uurqzu.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=340&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/556770/original/file-20231031-19-uurqzu.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=340&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/556770/original/file-20231031-19-uurqzu.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=428&fit=crop&dpr=1 754w, https://images.theconversation.com/files/556770/original/file-20231031-19-uurqzu.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=428&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/556770/original/file-20231031-19-uurqzu.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=428&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">A pie chart with dozens of categories. Not every category has a label, it’s not clear what the total number of categories is and what the unlabelled slices refer to.</span>
<span class="attribution"><a class="source" href="https://doi.org/10.3390/informatics7030035">Trajkova et al., Informatics (2020)</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<p>The tiny slices, lack of clear labelling and the kaleidoscope of colours make interpretation difficult for anyone.</p>
<p>It’s even harder for a colour blind person. For example, this is a simulation of what the above chart would look like to a person with deuteranomaly or reduced sensitivity to green light. This is the most common type of colour blindness, affecting roughly <a href="https://wearecolorblind.com/articles/a-quick-introduction-to-color-blindness/">4.6% of the population</a>. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/558560/original/file-20231109-27-4714o0.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/558560/original/file-20231109-27-4714o0.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/558560/original/file-20231109-27-4714o0.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=449&fit=crop&dpr=1 600w, https://images.theconversation.com/files/558560/original/file-20231109-27-4714o0.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=449&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/558560/original/file-20231109-27-4714o0.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=449&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/558560/original/file-20231109-27-4714o0.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=564&fit=crop&dpr=1 754w, https://images.theconversation.com/files/558560/original/file-20231109-27-4714o0.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=564&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/558560/original/file-20231109-27-4714o0.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=564&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">The same data chart as above, but run through a simulation filter to demonstrate what it would look like for someone with a common type of colour blindness.</span>
<span class="attribution"><a class="source" href="https://doi.org/10.3390/informatics7030035">Trajkova et al., Informatics (2020); modified.</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<p>It can get even worse if we take pie charts and make them three-dimensional. This can lead to egregious misrepresentations of data.</p>
<p>Below, the yellow, red and green areas are all the same size (one-third), but appear to be different based on the angle and which slice is placed at the bottom of the pie.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/556772/original/file-20231031-25-bdpq56.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/556772/original/file-20231031-25-bdpq56.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/556772/original/file-20231031-25-bdpq56.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=196&fit=crop&dpr=1 600w, https://images.theconversation.com/files/556772/original/file-20231031-25-bdpq56.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=196&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/556772/original/file-20231031-25-bdpq56.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=196&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/556772/original/file-20231031-25-bdpq56.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=246&fit=crop&dpr=1 754w, https://images.theconversation.com/files/556772/original/file-20231031-25-bdpq56.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=246&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/556772/original/file-20231031-25-bdpq56.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=246&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">A standard two-dimensional pie chart and two three-dimensional pie charts. In every chart the proportions are one-third but there appear to be differences between states in the three-dimensional versions.</span>
<span class="attribution"><span class="source">Victor Oguoma</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<h2>So why are pie charts everywhere?</h2>
<p>Despite the well known problems with pie charts, they are everywhere. They are in journal articles, PhD theses, political polling, books, newspapers and government reports. They’ve even been used by the Australian Bureau of Statistics.</p>
<p>While statisticians have criticised them for decades, it’s hard to argue with this logic: “if pie charts are so bad, why are there so many of them?”</p>
<p>Possibly they are popular because they are popular, which is a circular argument that suits a pie chart.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/556781/original/file-20231031-17-hfvpgr.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/556781/original/file-20231031-17-hfvpgr.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/556781/original/file-20231031-17-hfvpgr.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=395&fit=crop&dpr=1 600w, https://images.theconversation.com/files/556781/original/file-20231031-17-hfvpgr.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=395&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/556781/original/file-20231031-17-hfvpgr.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=395&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/556781/original/file-20231031-17-hfvpgr.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=496&fit=crop&dpr=1 754w, https://images.theconversation.com/files/556781/original/file-20231031-17-hfvpgr.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=496&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/556781/original/file-20231031-17-hfvpgr.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=496&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">A collection of terrible pie charts gathered from various open access sources, including ‘exploded’ pie charts and 3D pie charts.</span>
<span class="attribution"><span class="source">Adrian Barnett and Victor Oguoma</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<h2>What’s a good alternative to pie charts?</h2>
<p>There’s a simple fix that can effectively summarise big data in a small space and still allow creative colour schemes. </p>
<p>It’s the humble bar chart. Remember the brain-aching pie chart example above with the five categories? Here’s the same example using bars – we can now instantly see which category is the largest.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/556773/original/file-20231031-25-9vdsm4.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/556773/original/file-20231031-25-9vdsm4.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/556773/original/file-20231031-25-9vdsm4.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=430&fit=crop&dpr=1 600w, https://images.theconversation.com/files/556773/original/file-20231031-25-9vdsm4.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=430&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/556773/original/file-20231031-25-9vdsm4.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=430&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/556773/original/file-20231031-25-9vdsm4.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=541&fit=crop&dpr=1 754w, https://images.theconversation.com/files/556773/original/file-20231031-25-9vdsm4.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=541&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/556773/original/file-20231031-25-9vdsm4.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=541&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Three pie charts, each with five similar categories, and the same data presented using bar charts.</span>
<span class="attribution"><a class="source" href="https://commons.wikimedia.org/wiki/File:Piecharts.svg">Schutz/Wikimedia Commons</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<p>Linear bars are easier on the eye than the non-linear segments of a pie chart. But beware the temptation to make a humble bar chart look more interesting by adding a 3D effect. As you already saw, 3D charts distort perception and make it harder to find a reference point.</p>
<p>Below is a standard bar chart and a 3D alternative of the number of voters in the 1992 US presidential election split by family income (from under US$15K to over $75k). Using the 3D version, can you tell the number of voters for each candidate in the highest income category? Not easily. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/556775/original/file-20231031-17-dscfue.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/556775/original/file-20231031-17-dscfue.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/556775/original/file-20231031-17-dscfue.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=157&fit=crop&dpr=1 600w, https://images.theconversation.com/files/556775/original/file-20231031-17-dscfue.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=157&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/556775/original/file-20231031-17-dscfue.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=157&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/556775/original/file-20231031-17-dscfue.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=197&fit=crop&dpr=1 754w, https://images.theconversation.com/files/556775/original/file-20231031-17-dscfue.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=197&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/556775/original/file-20231031-17-dscfue.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=197&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">The same voter data presented as a standard two-dimensional bar chart and an unhelpful three-dimensional version.</span>
<span class="attribution"><span class="source">Victor Oguoma</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<h2>Is it ever okay to use a pie chart?</h2>
<p>We’ve shown some of the worst examples of pie charts to make a point. Pie charts can be okay when there are just a few categories and the percentages are dissimilar, for example with one large and one small category.</p>
<p>Overall, it is best to use pie charts sparingly, especially when there is a more “digestible” alternative – the bar chart.</p>
<p>Whenever we see pie charts, we think one of two things: their creators don’t know what they’re doing, or they know what they are doing and are deliberately trying to mislead.</p>
<p>A graphical summary aims to easily and quickly communicate the data. If you feel the need to spruce it up, you’re likely reducing understanding without meaning to do so.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/3-questions-to-ask-yourself-next-time-you-see-a-graph-chart-or-map-141348">3 questions to ask yourself next time you see a graph, chart or map</a>
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<img src="https://counter.theconversation.com/content/214576/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Adrian Barnett is a member of the Statistical Society of Australia.</span></em></p><p class="fine-print"><em><span>Victor Oguoma is a member of the Statistical Society of Australia.</span></em></p>They are popular because they are popular, which is a circular argument that suits a pie chart. But there are some serious downsides to using the humble pie.Adrian Barnett, Professor of Statistics, Queensland University of TechnologyVictor Oguoma, Senior Research Fellow, Poche Centre for Indigenous Health, The University of QueenslandLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2188022023-12-13T01:25:02Z2023-12-13T01:25:02Z20 people, 2.4 quintillion possibilities: the baffling statistics of Secret Santa<figure><img src="https://images.theconversation.com/files/565106/original/file-20231212-29-ba551n.jpeg?ixlib=rb-1.1.0&rect=87%2C21%2C7196%2C4739&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/secret-santa-smiling-man-unpacks-christmas-2378052273">Harbucks / Shutterstock</a></span></figcaption></figure><p>Christmas, we’re told, is the <a href="https://www.youtube.com/watch?v=AN_R4pR1hck&ab_channel=AndyWilliamsVEVO">most wonderful time of the year</a>. For many of us, however, it is preceded by one of the least wonderful times: the awkward social spectacle of the office <a href="https://en.wikipedia.org/wiki/Secret_Santa">Secret Santa</a> or Kris Kringle, where employees agree to purchase a gift for a randomly allocated colleague.</p>
<p>As you watch your co-workers unwrap their often wildly inappropriate gifts, each chosen by a office mate they barely know, cast your mind to the sheer statistical improbability of what you’re seeing. The odds of such a combination of these cheaply re-gifted photograph frames, inexplicably scented candles or unwanted <a href="https://metro.co.uk/2020/12/25/how-do-the-makers-of-lynx-feel-about-being-a-christmas-meme-13776264/">Lynx Africa gift sets</a> being passed around your office is, in its own way, truly a Christmas miracle.</p>
<h2>The 12! ways of Christmas?</h2>
<p>To work out how many possible pairings of buyers and recipients there are, you need to calculate the <a href="https://brilliant.org/wiki/permutations/">number of permutations</a> of the people involved.</p>
<p>Consider a workplace with four employees. If there is no rule to prevent people selecting their own names, there are four people who could be selected to buy the first person’s gift. </p>
<p>Once this is decided, there are three remaining choices for the second person, then two choices for the third person. Finally, there is one choice for the last person’s workplace Santa.</p>
<p>This means there are 4 × 3 × 2 × 1 = 24 possible permutations. Mathematicians write this as 4!, which is pronounced “four factorial”.</p>
<p><iframe id="tc-infographic-1006" class="tc-infographic" height="400px" src="https://cdn.theconversation.com/infographics/1006/695db8d722e320a72096762eabdfe31099bb09c6/site/index.html" width="100%" style="border: none" frameborder="0"></iframe></p>
<p>However, factorials soon get out of hand. Spare a thought for poor Santa himself. With <a href="https://www.saturdayeveningpost.com/2019/12/in-a-word-eight-er-nine-tiny-reindeer/">nine reindeer</a>, there are 9! = 362,880 ways these could be arranged, although perhaps <a href="https://en.wikipedia.org/wiki/Rudolph_the_Red-Nosed_Reindeer">on one foggy Christmas Eve</a>, this number is reduced by the requirement to have a red nose leading his sleigh.</p>
<p>Once the office workforce swells to 20, there are more than 2.4 quintillion permutations. To put this mind-boggling 20! figure into context, that’s more than three times current estimates of <a href="https://www.oklahoman.com/story/lifestyle/2019/02/05/more-stars-than-grains-of-sand-on-earth-you-bet/60474645007/">the number of grains of sand on Earth</a>.</p>
<h2>Yule buy for someone else</h2>
<p>Of course, nobody wants to draw themselves in a Secret Santa.</p>
<p>What a Secret Santa really wants is not a permutation of all employees, but instead what mathematicians call a <a href="https://brilliant.org/wiki/derangements/">derangement</a>. This is simply a permutation where no element remains in its original position, which means no employee has to buy their own gift.</p>
<p>The calculation is <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Hassani/hassani5.pdf">far from simple</a>, but the number of ways <em>n</em> employees can be assigned another unique co-worker is called the <em>n</em> th <a href="https://www.sciencedirect.com/science/article/abs/pii/S0096300322004155">de Montmort number</a>.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/the-mathematics-of-christmas-a-review-of-the-indisputable-existence-of-santa-claus-88508">The mathematics of Christmas: A review of the Indisputable Existence of Santa Claus</a>
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<p>Amazingly, this is equal to <em>n</em>!/<em>e</em> , rounded to the nearest whole number. The <em>e</em> here is one of the most famous numbers in mathematics, <a href="https://www.investopedia.com/terms/e/eulers-constant.asp">Euler’s number, approximately equal to 2.71828</a>, and the bane of anyone whose schooldays involved logarithm tables.</p>
<p>In the 24 permutations of four employees illustrated, there are 9 derangements, which is equal to 24/<em>e</em> rounded to the nearest whole number. For large numbers, approximately 63.2% of possible permutations are not derangements and so would be excluded.</p>
<p>For a 20-employee situation, this cuts the over 2.4 quintillion permutations to a mere 895 quadrillion or so. (This is still more than 100 million times the current global population.)</p>
<h2>Uniquely self-Santa-ed?</h2>
<p>Another surprising feature of a Secret Santa arises from the number of people who will, on average, be assigned their own name in a random draw.
It doesn’t matter if you have one person (although that is a terribly un-secret and desperately sad Secret Santa) or a billion people, the expected number of people to be allocated to buy their own gift is the same – just one person.</p>
<p>A full proof is a little more complicated than this, but think what happens if you double the number of employees. With twice as many gifts to buy, everybody’s chance of selecting themselves is halved. Twice as many people, each with half the chance of matching, then gives an unchanged average.</p>
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<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/how-to-play-and-win-the-gift-stealing-game-bad-santa-according-to-a-mathematician-196483">How to play and win the gift-stealing game Bad Santa, according to a mathematician</a>
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<p>For example, of the 24 permutations of four people illustrated, one involves four self-matches, none involve three self-matches, six involve two self matches and eight involve a single self-match. In total, this gives 24 possible self-matches in the 24 permutations, so an average of one each.</p>
<h2>Ho Ho Hope for the best</h2>
<p>If you do find yourself trapped in the dystopian office whodunit of guessing which of your co-workers gifted a <a href="https://www.usmagazine.com/celebrity-news/pictures/australia-firefighters-pose-with-cute-animals-for-sexy-2024-calendar/">hunky shirtless firefighter calendar</a> to an elderly colleague from human resources, at least hope that the one-in-a-billion or one-in-trillion permutation that was drawn in your office lands you something useful.</p>
<p>Mariah Carey may have <a href="https://en.wikipedia.org/wiki/All_I_Want_for_Christmas_Is_You">assured us of more specific requests</a>, but all I want for Christmas is avoid getting dragged into a workplace Secret Santa in the first place.</p>
<p><a href="https://www.historyextra.com/period/victorian/why-we-say-bah-humbug-christmas-carol-scrooge-dickens-what-mean/">Bah humbug</a> indeed.</p><img src="https://counter.theconversation.com/content/218802/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Stephen Woodcock does not receive funding from Santa Claus or any other relevant external party. He has remained off Santa's Naughty List for over 40 years.</span></em></p>The annual ritual of buying a gift for a random recipient opens a window onto some fascinating mathematics.Stephen Woodcock, Associate Professor of Mathematical Sciences, University of Technology SydneyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2155602023-10-13T12:17:30Z2023-10-13T12:17:30ZSouth Africa’s 2022 census missed 31% of people - big data could help in future<p>No census is ever exact: as academics Tom Moultrie and Rob Dorrington at the University of Cape Town have <a href="https://www.un.org/development/desa/pd/sites/www.un.org.development.desa.pd/files/files/documents/2020/Oct/undesa_pd_tp_2020_tp_population_estimates.pdf#page=8">noted previously</a>:</p>
<blockquote>
<p>a census is not, in reality, a full and accurate count of the number of people in a country; rather, it is itself an estimate of the size of the population at a moment in time. </p>
</blockquote>
<p>South Africa has announced the results of its fourth census as a democracy – <a href="https://www.statssa.gov.za/?p=16711">Census 2022</a>. I have been involved in the process for the last four years as chair of South Africa’s National Statistics Council. As outgoing chair, my last task was to <a href="https://www.statssa.gov.za/?p=15192">take part</a> in the release of Census 2022.</p>
<p>The census found that the national population has grown to <a href="https://www.statssa.gov.za/?p=16711">62 million</a>, up 10.3 million from the last census <a href="https://www.statssa.gov.za/publications/P03014/P030142011.pdf">in 2011</a>. Gauteng is now clearly the most populous province in the country, with 15.1 million people, overtaking KwaZulu-Natal (12.4 million). The Western Cape jumped from fifth to being the third largest province, with 7.4 million people. These figures are important because they inform resource allocation by government.</p>
<p>What is perhaps most striking about Census 2022 is the very high <a href="https://www.statssa.gov.za/publications/P03015/P030152022.pdf#page=11">undercount</a> – 31% of people and 30% of households were missed (or chose not to self-enumerate, either online or via zero-rated telephone methods). This is the highest undercount of any post-apartheid census; sadly, it may set a new international record. </p>
<p>A census is immediately followed by a <a href="https://www.statssa.gov.za/publications/P03015/P030152022.pdf">Post Enumeration Survey</a>, which identifies where the census missed people. This allows Statistics SA to develop adjustment factors, or weights, so that the final data represents an adjusted final tally. The Post Enumeration Survey is used to manage the undercount. Census undercounts are the norm, <a href="https://www.un.org/development/desa/pd/sites/www.un.org.development.desa.pd/files/files/documents/2020/Oct/undesa_pd_tp_2020_tp_population_estimates.pdf#page=8">not the exception</a>. But it is safe to assume that with weighting on this scale – adjusting for an undercount of 31.06% – analysts may identify some confounding results. </p>
<p>At aggregate level, <a href="https://census.statssa.gov.za/#/">Census 2022</a> is robust. At sub-national – and especially sub-provincial – levels, however, it may be less so. Only time and data analysis will tell.</p>
<p>The census confirmed the global trend of <a href="https://www.icf.com/insights/health/declining-survey-response-rate-problem">declining survey response rates</a>. People are less and less inclined to be involved in the process. This raises the question: does a fieldwork-based census have a future? Given the challenges that faced Census 2022, I believe the census may need to be re-imagined as a very different exercise. This requires <a href="https://www.statssa.gov.za/">Statistics South Africa</a>, which conducts the census, to fully engage with big data to bring the process into the 21st century.</p>
<h2>The process</h2>
<p>South Africa’s National Statistics Council, an independent body of experts that advises the statistician-general and the minister in the presidency regarding statistics, had secured a number of local and international experts – as had Stats SA – to stress test the census and the Post Enumeration Survey. Council never has prior sight of the data: its job is to focus on methods and process.</p>
<p>The experts do engage with the data and flagged only a few variables (mortality data, and some service and asset questions which had too many non-responses to be reliable) as requiring a cautionary note. Council engaged vigorously with the experts and Stats SA, and with no red flag raised by any, we declared the census <a href="https://census.statssa.gov.za/#/">“fit for purpose”</a>.</p>
<p>It is notable that Stats SA routinely conducts a post enumeration survey. Many countries do not, even when there is systematic undercounting of particular groups (often young men, children and minorities). Moreover, Stats SA will make available both the weighted and the raw data for analysts to examine in detail. This transparency should be welcomed, given that (as previously noted by the <a href="https://unstats.un.org/unsd/demographic/sources/census/wphc/QA.htm">United Nations Statistics Division</a>) issues of undercounting affect all countries, and estimating the undercount and whether to adjust the data is a political issue “throughout the world”. The undercount was high, but not as a result of any lack of effort or commitment from Stats SA.</p>
<h2>Why the undercount</h2>
<p>The undercount is the result of many factors. </p>
<p>First, the context matters. This time round it was as bad as it could be, with the COVID-19 pandemic affecting training and supply chains for equipment. The pandemic also generated anxiety in a populace that had been avoiding contact with strangers as part of social distancing. Census planning usually starts three or four years prior to fieldwork. Training about 100,000 enumerators is a major effort in its own right, combined with the shift to digital platforms for the first time. All were affected by the pandemic.</p>
<p>The fieldwork took place after the devastating <a href="https://theconversation.com/south-africas-deadly-july-2021-riots-may-recur-if-theres-no-change-186397">July 2021 insurrection</a>, and after the hard-fought <a href="https://www.elections.org.za/pw/Elections-and-results/Municipal-Elections-2021">local elections</a>. The process also coincided with xenophobic violence meted out by the anti-migrant pressure group-<a href="https://www.theguardian.com/global-development/2023/sep/26/south-africa-anti-migrant-vigilante-operation-dudula-registers-as-party-2024-elections">turned-political party</a> <a href="https://theconversation.com/rising-vigilantism-south-africa-is-reaping-the-fruits-of-misrule-179891">Operation Dudula</a> in Johannesburg. Taken together, the effect was a deep-seated reluctance to open doors to strangers, particularly those asking lots of questions.</p>
<p>A second factor that affected the gathering of data was the fact that there is <a href="https://www.afrobarometer.org/wp-content/uploads/migrated/files/publications/Dispatches/ad474-south_africans_trust_in_institutions_reaches_new_low-afrobarometer-20aug21.pdf">very low trust in the government</a>. Although the census is conducted by Stats SA, which is an independent entity, it is seen as “government”. This label didn’t make it easy to persuade people to allow an enumerator into their dwellings and answer questions. </p>
<p>People in the Western Cape, the only province not run by the African National Congress, were particularly resistant to being enumerated or self-enumerating. This was true even after the provincial premier and Cape Town mayor made public calls for people to comply. The undercount in the Western Cape stands at 35.58% of people and 36.3% of households. In the Free State, by comparison, the undercount is 20.95% of people and 17.93% of households.</p>
<p>A third factor was that response rates have been getting consistently lower over at least the last decade. This has been true for Stats SA and other entities undertaking primary research. The decision to go digital was an attempt to open different avenues for people to complete the questionnaire online, or by phone, to improve response rates.</p>
<p>People appear to be sick and tired of being polled by everyone, from their local supermarket to endless tele-marketers and others. They also appear much more wary of sharing their data. What, then, is the future for the census?</p>
<h2>Enter big data</h2>
<p>Countries around the world are facing the same challenge of low response rates. </p>
<p>The advent of big data opens intriguing possibilities. </p>
<p>A first step would be to harvest data from the records kept by government departments (assuming they are run well). In addition, data could be unlocked if a working relationship was developed with private sector entities, such as suppliers and banks. </p>
<p>Becoming far more tech-savvy, and encouraging people to engage with Stats SA digitally, could be combined with other options to compile a national population dataset. It would also represent a significant cost-saving. This approach – harvesting data rather than gathering it directly – is being considered by many countries, but has not yet been attempted, and Stats SA needs to carefully consider this option.</p>
<p>Stats SA needs to fully engage with the world of big data, and the key players in that data ecosystem. It has convening authority, and should be engaging all key players, whether they are academic, private sector or others. </p>
<p>At the very least, an alternative way of conducting the next census in 2032 must be rigorously examined and tested. </p>
<p>Big data is not the answer to all the challenges that faced Census 2022, but it may be a key enabler for gathering reliable national data in the future.</p><img src="https://counter.theconversation.com/content/215560/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>David Everatt does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Big data is not the answer to all the challenges that faced Census 2022, but it may be a key enabler for gathering reliable national data in the future.David Everatt, Professor of Urban Governance, University of the WitwatersrandLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2142612023-09-26T02:31:46Z2023-09-26T02:31:46ZFrom stock markets to brain scans, new research harmonises hundreds of scientific methods to understand complex systems<figure><img src="https://images.theconversation.com/files/550140/original/file-20230926-25-q3h0fe.jpeg?ixlib=rb-1.1.0&rect=5%2C32%2C3589%2C3190&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-vector/orchestra-instruments-set-designed-using-colorful-1921758500">Shutterstock</a></span></figcaption></figure><p>Complexity is all around us, from the daily fluctuations of financial markets to the intricate web of neurons in our brains. </p>
<p>Understanding how the different components of these systems interact with each other is a fundamental challenge for scientists trying to predict their behaviour. Piecing together these interactions is like deciphering a code from an intricate set of clues. </p>
<p>Scientists have developed hundreds of different methods for doing this, from engineers studying noisy radio channels to neuroscientists studying firing patterns in networks of interacting neurons. Each method captures a unique aspect of the interactions within a complex system – but how do we know which method is right for any given system sitting right in front of us?</p>
<p>In <a href="https://doi.org/10.1038/s43588-023-00519-x">new research</a> published in Nature Computational Science, we have developed a unified way to look at hundreds of different methods for measuring interaction patterns in complex systems – and working out which ones are most useful for understanding a given system.</p>
<h2>A scientific orchestra</h2>
<p>The science of complex systems can be, well, complex. And the science of comparing and combining different ways of studying these systems even more so.</p>
<p>But one way to think about what we’ve done is to imagine each scientific method is a different musical instrument playing in a scientific orchestra. Different instruments are playing different melodies with different tones and in different styles.</p>
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Read more:
<a href="https://theconversation.com/fireflies-brain-cells-dancers-new-synchronisation-research-shows-natures-perfect-timing-is-all-about-connections-212708">Fireflies, brain cells, dancers: new synchronisation research shows nature's perfect timing is all about connections</a>
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<p>We wanted to understand which of our scientific instruments are best suited to solving which types of problems. We also wanted to know whether we could conduct all of the instruments to form a harmonious whole.</p>
<p>By presenting these methods as a full orchestra for the first time, we hoped we would find new ways of deciphering patterns in the world around us.</p>
<h2>Hundreds of methods, more than 1,000 datasets</h2>
<p>To develop our orchestra, we undertook the mammoth task of analysing more than 200 methods for computing interactions from as many datasets as we could get our hands on. These covered a huge range of subjects, from stock markets and climate to brain activity and earthquakes to river flow and heart beats.</p>
<p>In total, we applied our 237 methods to more than 1,000 datasets. By analysing how these methods behave when applied to such diverse scientific systems, we found a way for them to “play in harmony” for the first time.</p>
<p>In the same way that instruments in an orchestra are usually organised as strings, brass, woodwind and percussion, scientific methods from areas like engineering, statistics and biophysics also have their traditional groupings.</p>
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<a href="https://images.theconversation.com/files/549963/original/file-20230925-23-e9842u.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/549963/original/file-20230925-23-e9842u.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/549963/original/file-20230925-23-e9842u.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=287&fit=crop&dpr=1 600w, https://images.theconversation.com/files/549963/original/file-20230925-23-e9842u.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=287&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/549963/original/file-20230925-23-e9842u.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=287&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/549963/original/file-20230925-23-e9842u.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=361&fit=crop&dpr=1 754w, https://images.theconversation.com/files/549963/original/file-20230925-23-e9842u.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=361&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/549963/original/file-20230925-23-e9842u.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=361&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
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<span class="caption">Applying different methods to more than 1,000 datasets from a wide range of fields revealed surprising similarities and differences.</span>
<span class="attribution"><a class="source" href="https://doi.org/10.1038/s43588-023-00519-x">Cliff et al. / Nature Computational Science</a>, <a class="license" href="http://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA</a></span>
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<p>But when we organised our scientific orchestra, we found that the scientific instruments grouped together in a strikingly different way to this traditional organisation. Some very different methods behaved in surprisingly similar ways to one another.</p>
<p>This was a bit like discovering that the tuba player’s melody was surprisingly similar to that of the flute, but no one had noticed it before.</p>
<p>Our weird and wonderful new orchestral layout (which sometimes places cello and trumpet players next to the piccolo player), represents a more “natural” way of grouping methods from all across science. This opens exciting new avenues for cross-disciplinary research.</p>
<h2>The orchestra in the real world</h2>
<p>We also put our full scientific orchestra to work on some real-world problems to see how it would work. One of these problems was using motion data from a smartwatch to classify activities like “badminton playing” and “running”; another was distinguishing different activities from brain-scan data.</p>
<p>Properly orchestrated, the full ensemble of scientific methods demonstrated improved performance over any single method on its own.</p>
<p>To put it another way, virtuosic solos are not always the best approach! You can get better results when different scientific methods work cooperatively as an ensemble.</p>
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Read more:
<a href="https://theconversation.com/electricity-flow-in-the-human-brain-can-be-predicted-using-the-simple-maths-of-networks-new-study-reveals-200831">Electricity flow in the human brain can be predicted using the simple maths of networks, new study reveals</a>
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<p>The scientific ensemble introduced in this work provides a deeper understanding of the interacting systems that shape our complex world. And its implications are widespread – from understanding how brain communication patterns break down in disease, to developing improved detection algorithms for smartwatch sensor data. </p>
<p>Time will tell what new music scientists will make as they step up to conduct our new scientific orchestra that simultaneously incorporates diverse ways of thinking about the world.</p><img src="https://counter.theconversation.com/content/214261/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Ben Fulcher receives funding from the National Health and Medical Research Council.</span></em></p>There are hundreds of ways to analyse interactions in a complex system. A new study shows how they can all work together.Ben Fulcher, Senior Lecturer, School of Physics, University of SydneyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2133592023-09-18T20:03:42Z2023-09-18T20:03:42ZTests that diagnose diseases are less reliable than you’d expect. Here’s why<figure><img src="https://images.theconversation.com/files/548709/original/file-20230918-27-xhsztq.jpg?ixlib=rb-1.1.0&rect=0%2C0%2C3583%2C2376&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://unsplash.com/photos/OZcQIhidMTw">CDC / Unsplash</a></span></figcaption></figure><p>You feel unwell, and visit your doctor. They ask some questions and take some blood for testing; a few days later they call to say you have been diagnosed with a disease.</p>
<p>What are the chances you <em>actually have</em> the disease? For some common diagnostic tests, the answer is surprisingly low.</p>
<p>Few medical tests are 100% accurate. Part of the reason is that people are inherently variable, but many tests are also built on limited or biased samples of patients – and our own work has shown researchers may <a href="https://bmcmedicine.biomedcentral.com/articles/10.1186/s12916-023-03048-6">deliberately exaggerate</a> the effectiveness of new tests.</p>
<p>None of this means we should stop trusting diagnostic tests, but a better understanding of their strengths and weaknesses is essential if we want to use them wisely. </p>
<h2>People are variable</h2>
<p>An example of a widely used imperfect test is prostate-specific antigen (PSA) screening, which measures the level of a particular protein in the blood as an indicator of prostate cancer. </p>
<p>The test catches an estimated 93% of cancers – but it has a very high false positive rate, as around 80% of men with a positive result do not actually have cancer. For those in the 80%, the result <a href="https://theconversation.com/prostate-cancer-testing-has-the-bubble-burst-82260">creates unnecessary stress</a> and likely further testing including painful biopsies.</p>
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Read more:
<a href="https://theconversation.com/prostate-cancer-testing-has-the-bubble-burst-82260">Prostate cancer testing: has the bubble burst?</a>
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<p>Rapid antigen tests for COVID-19 are another widely used imperfect test. A <a href="https://www.cochrane.org/CD013705/INFECTN_how-accurate-are-rapid-antigen-tests-diagnosing-covid-19">review of these tests</a> found that, of people without symptoms but with a positive test result, only 52% actually had COVID. </p>
<p>Among people with COVID symptoms and a positive result, the accuracy of the tests rose to 89%. This shows how a test’s performance cannot be summarised by a single number and depends on individual context.</p>
<p>Why aren’t diagnostic tests perfect? One key reason is that people are variable. A high temperature for you, for example, might be perfectly normal for someone else. For blood tests, many extraneous factors can influence the results, such as the time of day or how recently you have eaten.</p>
<p>Even the ubiquitous blood pressure test <a href="https://www.ama-assn.org/delivering-care/hypertension/4-big-ways-bp-measurement-goes-wrong-and-how-tackle-them">can be inaccurate</a>. Results can vary depending on whether the cuff is a good fit for your arm, if you have your legs crossed, and if you’re talking when the test is done. </p>
<h2>Small samples and statistical skullduggery</h2>
<p>There’s an enormous amount of research on new diagnostic models. New models frequently make the headlines as “medical breakthroughs”, such as how your <a href="https://www.jpost.com/health-and-science/handwriting-assessment-can-be-used-for-early-detection-of-parkinsons-disease-325798">handwriting could detect Parkinson’s disease</a>, how your pharmacy loyalty card could <a href="https://www.theguardian.com/society/2023/jan/26/loyalty-card-data-could-help-spot-ovarian-cancer-cases-sooner">detect ovarian cancer earlier</a>, or how <a href="https://www.abdn.ac.uk/news/4602/">eye movements could detect schizophrenia</a>.</p>
<p>But living up to the headlines is often a different story.</p>
<p>Many diagnostic models are developed based on small sample sizes. <a href="https://www.bmj.com/content/332/7550/1127.long">A review</a> found half of diagnostic studies used just over 100 patients. It is hard to get a true picture of the accuracy of a diagnostic test from such small samples. </p>
<p>For accurate results, the patients who use the test should be similar to those who were used to develop the test. For example, the widely used Framingham Risk Score for identifying people at high risk of heart disease was developed in the United States and is known to <a href="https://pubmed.ncbi.nlm.nih.gov/28749178/">perform poorly</a> in Aboriginal and Torres Strait Islander people. </p>
<p>Similar disparities in accuracy have been found for “polygenic risk scores”. These combine information on thousands of genes to predict disease risk, but were developed in European populations and <a href="https://www.nature.com/articles/s41588-019-0379-x">perform poorly in non-European populations</a>. </p>
<p>Recently, we identified another important problem: researchers have exaggerated <a href="https://bmcmedicine.biomedcentral.com/articles/10.1186/s12916-023-03048-6">the accuracy of some models</a> to gain journal publications. </p>
<p>There are many ways to exaggerate the performance of a test, such as dropping hard-to-predict patients from the sample. Some tests are also not truly predictive, as they include information from the future, such as a <a href="https://www.statnews.com/2021/09/27/epic-sepsis-algorithm-antibiotics-model/">predictive model of infection</a> that includes whether the patient had been prescribed antibiotics.</p>
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Read more:
<a href="https://theconversation.com/elizabeth-holmes-theranos-scandal-has-more-to-it-than-just-toxic-silicon-valley-culture-114102">Elizabeth Holmes: Theranos scandal has more to it than just toxic Silicon Valley culture</a>
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<p>Perhaps the most extreme example of exaggerating the power of a diagnostic test was the <a href="https://theconversation.com/elizabeth-holmes-theranos-scandal-has-more-to-it-than-just-toxic-silicon-valley-culture-114102">Theranos scandal</a>, in which a finger-prick blood test supposed to diagnose multiple health conditions attracted hundreds of millions of dollars from investors. This was too good to be true – and the mastermind has now been convicted of fraud. </p>
<h2>Big data can’t make tests perfect</h2>
<p>In the era of precision medicine and big data, it seems appealing to combine tens or hundreds of pieces of information about a patient – perhaps using machine learning or artificial intelligence – to provide highly accurate predictions. However, the promise is so far outstripping the reality. </p>
<p>One <a href="https://osf.io/preprints/4txc6/">study</a> estimated 80,000 new prediction models were published between 1995 and 2020. That’s around 250 new models every month. </p>
<p>Are these models transforming healthcare? We see no sign of it – and if they really were having a big impact, surely we wouldn’t need such a steady stream of new models. </p>
<p>For many diseases there are data problems that no amount of sophisticated modelling can fix, such as measurement errors or missing data that make accurate predictions impossible. </p>
<p>Some diseases or illnesses are likely inherently random, and involve complex chains of events which a patient cannot describe and no model could predict. Examples might include injuries or previous illnesses that happened to a patient decades ago, which they cannot recall and are not in their medical notes. </p>
<p>Diagnostic tests will never be perfect. Acknowledging their imperfections will enable doctors and their patients to have an informed discussion about what a result means – and most importantly, what to do next.</p><img src="https://counter.theconversation.com/content/213359/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The authors do not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Many diagnostic tests are far from 100% accurate – and even in the era of big data and machine learning, they never will be.Adrian Barnett, Professor of Statistics, Queensland University of TechnologyNicole White, Senior Research Fellow - Statistics, Queensland University of TechnologyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2099252023-08-21T13:01:08Z2023-08-21T13:01:08ZThe order in which you acquire diseases could affect your life expectancy – new research<figure><img src="https://images.theconversation.com/files/542634/original/file-20230814-15-6ly3wb.jpg?ixlib=rb-1.1.0&rect=47%2C0%2C5310%2C3497&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Almost two-thirds of UK adults aged 65 and over possess two or more long-term health conditions.</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/elderly-couple-tourists-sea-resort-1596444508">EvgL/Shutterstock</a></span></figcaption></figure><p><a href="https://doi.org/10.1016/S0140-6736(12)60240-2">More than 25%</a> of adults in the UK have two or more long-term health conditions. This increases to 65% for people older than 65 years, and to almost 82% for those aged 85 or older. </p>
<p><a href="https://doi.org/10.1016/S2468-2667(23)00098-1">Our study</a> assessed how a number of multiple long-term health conditions (<a href="https://www.nhs.uk/mental-health/conditions/psychosis/overview/">psychosis</a>, diabetes and congestive heart failure) develop over time, and what effect this can have on life expectancy. We chose these conditions because, together, they can lead to substantial reductions in how long someone lives.</p>
<p>We analysed the development of these conditions over a 20-year period for more than 1.6 million adults aged 25 and over. We used data held within the <a href="https://saildatabank.com/">SAIL databank</a>, which provides secure access to routinely collected anonymous health and administrative records for the population of Wales.</p>
<p>We also worked with patients and the public from across the UK to understand their experience of living with multiple long-term conditions. </p>
<p>Using statistical models, we examined the order and timing of developing psychosis, diabetes and congestive heart failure in patients of the same age, sex and area-level deprivation – and the related impact on their life expectancy. </p>
<h2>The impact of disease order</h2>
<p>We found that the order in which people developed these diseases had an important impact on their life expectancy. People who developed diabetes, psychosis and congestive heart failure, in that order, had the largest loss in life expectancy (approximately 13 years, on average).</p>
<p>People who developed the same conditions in a different order were less affected. So, for example, a 50-year-old man in an area of average deprivation could experience a difference in his life expectancy of more than 10 years, depending on the order in which he developed the three diseases. </p>
<p>Our research also identified that people who first developed diabetes, then psychosis and finally congestive heart failure carried a higher risk of developing the next long-term health condition, or dying within five years of their last diagnosis. </p>
<p>However, the development of further conditions is not always life-limiting. For example, people diagnosed with psychosis and diabetes – in any order – had a higher life expectancy than those diagnosed with psychosis alone. While this was a surprising finding, we expect people with diabetes to have more regular contact with health professionals through diabetic clinics, for example, which may improve their overall health. </p>
<p>Our study also found that congestive heart failure on its own, and in combination with psychosis (in any order), had a similar effect on life expectancy to the “worst case” combination of diabetes, psychosis and congestive heart failure (in that order). </p>
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<img alt="An empty bed in a hospital surrounded with medical equipment" src="https://images.theconversation.com/files/542796/original/file-20230815-25-8wyoa2.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/542796/original/file-20230815-25-8wyoa2.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=450&fit=crop&dpr=1 600w, https://images.theconversation.com/files/542796/original/file-20230815-25-8wyoa2.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=450&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/542796/original/file-20230815-25-8wyoa2.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=450&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/542796/original/file-20230815-25-8wyoa2.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=566&fit=crop&dpr=1 754w, https://images.theconversation.com/files/542796/original/file-20230815-25-8wyoa2.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=566&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/542796/original/file-20230815-25-8wyoa2.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=566&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<span class="caption">The application of this research could lead to improved outcomes for the NHS.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/national-health-service-uk-19th-march-608498993">Imran Khan's Photography/Shutterstock</a></span>
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<p>This is the first study to examine how the order of developing multiple long-term conditions affects a person’s life expectancy. This research could be used to inform patients, healthcare providers and decision-makers on the appropriate identification of diseases and management of patient care. In turn, this could lead to improved outcomes for patients and the NHS. </p>
<p>Our research also helps to support healthcare delivery by looking at the factors that may increase a person’s risk of developing disease, as well as identifying potential opportunities for disease screening and earlier intervention.</p>
<h2>Applying our research</h2>
<p>Future research could evaluate the impact of screening programmes and interventions in delaying the development of further long-term conditions and extending life.</p>
<p>However, it is important to note that our research used information from routinely collected health records, which are not always accurate – some diagnoses may be missing or delayed. Also, diagnoses are not always accurately described. These are all important factors in being able to accurately estimate the impact of multiple long-term conditions on life expectancy. </p>
<p><a href="https://phenotypes.healthdatagateway.org/">Further research funded by Health Data Research UK</a>, the national institute for health data science, aims to harmonise how this data is collected and reported. Over time, this will improve the quality of information obtained from routinely collected health records for research. </p>
<p>While our study examined the development of one group of multiple long-term conditions, this approach could be replicated for any other combination of conditions – including the development of long-term health conditions following COVID-19 infection (known as long COVID), and the impact this has on quality of life.</p>
<p>Those living with multiple long-term conditions often experience increased use of healthcare services and medications, as well as greater difficulty with day-to-day tasks. This leads to a reduced quality of life as well as reduced life expectancy. </p>
<p>Our research has shown that the combination of long-term conditions and order in which you develop them may both have a substantial impact on your life expectancy. However, this relationship can be complex, and the development of further disease does not always reduce life expectancy.</p><img src="https://counter.theconversation.com/content/209925/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Rhiannon Owen receives funding from the Academy of Medical Sciences (AMS), Health and Care Research Wales (HCRW), Heath Data Research UK (HDRUK), Medical Research Council (MRC), and the National Institute for Health and Care Research (NIHR). She is affiliated with the National Institute for Health and Care Excellence (NICE). </span></em></p>People who developed diabetes, psychosis and congestive heart failure, in that order, experienced the largest reduction in life expectancyRhiannon Owen, Professor of Statistics, Swansea UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2089192023-08-01T00:49:01Z2023-08-01T00:49:01ZBazball by the numbers: what the stats say about English cricket’s ambitious but risky change of pace<p>The leisurely sport of Test cricket, in which matches last for several days, has been around for almost 150 years. Over the course of that century and a half, cricket has been reshaped by a few crucial events: the “bodyline” era of the 1930s, the invention of one-day matches and World Series Cricket in the 1970s, and the introduction of the even faster-paced Twenty20 cricket in 2005. </p>
<p>We may be living through another pivotal moment in the history of Test cricket: the advent of “Bazball”, a freewheeling, attacking style of play developed by England coach Brendon “Baz” McCullum. </p>
<p>The aggressive approach is seen as carrying high risk and high reward, with the goal of scoring runs quickly and forcing a conclusive result in a game that often ends in draws when time runs out.</p>
<p>Bazball is only about a year old, and some debate its merits and even its very existence. As statisticians, we can’t determine whether Bazball will transform the sport or fade away – but we’ve crunched the numbers and found evidence England’s new approach does represent a genuine break with the history of Test cricket.</p>
<h2>What is Bazball?</h2>
<p>After a lacklustre 4-0 loss to Australia in the Ashes series two summers ago, England sacked head coach Chris Silverwood. His replacement was the relatively untested McCullum, a former captain of the New Zealand team known for his fast scoring as a batsman.</p>
<p>McCullum only retired from playing in 2019. He is the first international head coach to have played the majority of his career in the era of the frenetic, high-scoring Twenty20 cricket format. </p>
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Read more:
<a href="https://theconversation.com/the-ashes-how-england-crickets-head-coach-brendon-mccullum-developed-his-bazball-style-207949">The Ashes: how England cricket's head coach Brendon McCullum developed his 'Bazball' style</a>
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<p>With this appointment, England has adopted an extremely attacking style dubbed “<a href="https://open.spotify.com/episode/2kHhXVRPCrT1Qap1fG6sWW">Bazball</a>” by Cricinfo editor Andrew Miller. The name has taken off in discussions of the stark shift in England’s play, which has attracted attention among cricket fans around the world.</p>
<p>So what is Bazball? McCullum himself recently <a href="https://www.espncricinfo.com/story/england-test-cricket-brendon-mccullum-i-don-t-really-like-that-silly-term-bazball-1323779">told</a> a Perth radio show “I don’t have any idea what ‘Bazball’ is”.</p>
<h2>Run rates</h2>
<p>To understand what Bazball is, and whether it even exists, we turned to the voluminous statistical history of the game.</p>
<p>At the conclusion of the first Test of this Ashes series, 2,507 <a href="https://stats.espncricinfo.com/ci/engine/stats/index.html?class=1;filter=advanced;orderby=matches;spanmax1=16+Jun+2023;spanval1=span;template=results;type=aggregate">matches</a> of Test cricket had been played and nearly 2,500,000 runs scored. Across all those matches, the average number of runs scored per six-ball over (known as the “run rate”) has been remarkably stable. </p>
<p>From 1910 to 1919, on average, 3.03 runs were scored every six balls. By the 1950s this had fallen a little to 2.32 runs per six balls, but it has been slowly increasing ever since. </p>
<p>Over the past 20 years, the run rate has averaged 3.29 runs per over, the highest in Test cricket’s history. </p>
<p>What kind of numbers have we seen in Bazball matches?</p>
<h2>Comparing Bazball to the past</h2>
<p>It might be tempting to compare run rates directly, but run rates can be affected by many factors, such as the total number of runs scored in an innings and the pitch conditions. </p>
<p>For example, an innings with a larger run total will tend to correspond to more runs per over, as there are a limited number of overs. As a result, there is less variety in run rates for innings with larger totals.</p>
<p><iframe id="AYHSw" class="tc-infographic-datawrapper" src="https://datawrapper.dwcdn.net/AYHSw/2/" height="400px" width="100%" style="border: none" frameborder="0"></iframe></p>
<p>We built a statistical model to predict, and capture the variability of, run rates in Test matches. The model took into account the innings total, the year of play, and the location where the match was played. </p>
<p>We fitted the model to the data for run rate per innings. We only included data since 2000, which we define loosely as “modern cricket”. </p>
<p>Further, we excluded data where the innings total was less than 200, as it can be easier to maintain a very high run rate for a shorter innings. This left a total of 2,659 innings for analysis.</p>
<p><iframe id="oJ9Rb" class="tc-infographic-datawrapper" src="https://datawrapper.dwcdn.net/oJ9Rb/4/" height="400px" width="100%" style="border: none" frameborder="0"></iframe></p>
<p><iframe id="IJ4Cx" class="tc-infographic-datawrapper" src="https://datawrapper.dwcdn.net/IJ4Cx/2/" height="400px" width="100%" style="border: none" frameborder="0"></iframe></p>
<p>As the charts above show, the model does well at capturing how the mean and variance of run rates changes with year and innings total. </p>
<h2>Putting Bazball in context</h2>
<p>Next, we can measure how far a given innings deviates from the model’s prediction with a number we call the “run rate score”. If the model represents business as usual, the run rate score shows how “unusual” the innings is.</p>
<p>We are interested in high run rates, so we focused on data points larger than what the model predicts (that is, the highest positive run rate scores). We used a statistical approach that can also capture the estimated uncertainty in the run rate scores.</p>
<p><iframe id="z5Rei" class="tc-infographic-datawrapper" src="https://datawrapper.dwcdn.net/z5Rei/3/" height="400px" width="100%" style="border: none" frameborder="0"></iframe></p>
<p>In the chart above, you can see the top 30 estimated run rate scores. There are some uncertainties in estimating a run rate score, so these are shown by the shaded areas. As you can see by the highlighted bars, there are eight Bazball innings in the top 30. This is quite remarkable, given there are only 20 Bazball innings altogether in our data set of 2,659 innings.</p>
<p>This demonstrates strong evidence that Bazball is a very real phenomenon. Whether Brendon McCullum knows it or not, his team is up to something very unusual </p>
<p>So now that Bazball has faced its toughest challenge yet – the Australian pace attack – and seemingly survived, the final hurdle will be an away series in India in February next year. For now, we will be keeping a close eye on whether other teams follow suit in this revolutionary style of cricket.</p><img src="https://counter.theconversation.com/content/208919/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Christopher Drovandi is a Professor of Statistics at the Queensland University of Technology (QUT), and is an Investigator in the QUT Centre for Data Science. He receives funding from the Australian Research Council.</span></em></p><p class="fine-print"><em><span>Tim Newans does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Statistics show how a change of approach by England’s team marks a dramatic break with the history of Test cricket.Tim Newans, Lecturer, Griffith UniversityChristopher Drovandi, Professor of Statistics, Queensland University of TechnologyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2011472023-04-18T12:43:34Z2023-04-18T12:43:34ZIf 1% of COVID-19 cases result in death, does that mean you have a 1% chance of dying if you catch it? A mathematician explains the difference between a population statistic and your personal risk<figure><img src="https://images.theconversation.com/files/521327/original/file-20230417-22-5x3idt.jpg?ixlib=rb-1.1.0&rect=0%2C0%2C2078%2C1440&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">The risk of dying from COVID-19 varies from person to person.</span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/photo/covid-19-statistics-graph-royalty-free-image/1347040093">Jasmin Merdan/Moment via Getty Images</a></span></figcaption></figure><p>As of April 2023, <a href="https://covid19.who.int/">about 1% of people</a> who contracted COVID-19 ended up dying. Does that mean you have a 1% chance of dying from COVID-19? </p>
<p>That 1% is what epidemiologists call the <a href="https://www.cdc.gov/foodnet/reports/data/case-fatality.html">case fatality rate</a>, calculated by dividing the number of confirmed COVID-19 deaths by the number of confirmed cases. The case fatality rate is a <a href="https://mathworld.wolfram.com/Statistic.html">statistic</a>, or something that is calculated from a data set. Specifically, it is a type of statistic called a <a href="https://mathworld.wolfram.com/SampleProportion.html">sample proportion</a>, which measures the proportion of data that satisfies some criteria – in this case, the proportion of COVID-19 cases that ended with death.</p>
<p>The goal of calculating a statistic like case fatality rate is normally to estimate an unknown proportion. In this case, if every person in the world were infected with COVID-19, what proportion would die? However, some people also use this statistic as a guide to estimate personal risk as well.</p>
<p>It is natural to think of such a statistic as a <a href="https://mathworld.wolfram.com/Probability.html">probability</a>. For example, popular statements that you are <a href="https://doi.org/10.1080/09546553.2018.1530662">more likely to get struck by lightning</a> than die in a terrorist attack, or <a href="https://www.cleveland19.com/story/38100144/how-likely-are-you-to-die-on-a-plane-these-statistics-may-ease-your-fears/">die driving to work</a> than get killed in a plane crash, are based on statistics. But is it accurate to take these statements literally?</p>
<p>I’m a <a href="https://scholar.google.com/citations?user=qPNQSR5AWokC&hl=en">mathematician who studies probability theory</a>. During the pandemic, I watched health statistics become a national conversation. The public was inundated with ever-changing data as research unfolded in real time, calling attention to specific risk factors such as preexisting conditions or age. However, using these statistics to accurately determine your own personal risk is <a href="https://theconversation.com/its-impossible-to-determine-your-personal-covid-19-risks-and-frustrating-to-try-but-you-can-still-take-action-182287">nearly impossible</a> since it varies so much from person to person and depends on intricate physical and biological processes. </p>
<h2>The mathematics of probability</h2>
<p>In <a href="https://www.britannica.com/science/probability-theory">probability theory</a>, a process is considered random if it has an unpredictable outcome. This unpredictability could simply be due to difficulty in getting the necessary information to accurately predict the outcome. Random processes have observable events that can each be assigned a probability, or the tendency for that process to give that particular result.</p>
<p>A typical example of a random process is flipping a coin. A coin flip has two possible outcomes, each assigned a probability of 50%. Even though most people might think of this process as random, knowing the precise force applied to the coin can allow an observer to <a href="https://www.youtube.com/watch?v=AYnJv68T3MM">predict the outcome</a>. But a coin flip is still considered random since measuring this force is not practical in real-life settings. A slight change can result in a different outcome for the coin flip.</p>
<figure>
<iframe width="440" height="260" src="https://www.youtube.com/embed/AYnJv68T3MM?wmode=transparent&start=0" frameborder="0" allowfullscreen=""></iframe>
<figcaption><span class="caption">You could predict the outcome of a coin toss if you had the right information.</span></figcaption>
</figure>
<p>A common way to think about the probability of heads being 50% is that, when a coin is flipped several times, you would expect 50% of those flips to be heads. For a large number of flips, in fact, very close to 50% of the flips will be heads. A mathematical theorem called the <a href="https://www.britannica.com/science/law-of-large-numbers">law of large numbers</a> guarantees this, stating that running proportion of outcomes will get closer and closer to the actual probability when the process is repeated many times. The more you flip the coin, the running percentage of flips that are heads will get closer and closer to 50%, essentially with certainty. This depends on each repeated coin flip happening in essentially identical conditions, though. </p>
<p>The 1% case fatality rate of COVID-19 can be thought of as the running percentage of COVID-19 cases that have resulted in death. It doesn’t represent the true average probability of death, though, since the virus, and the global population’s immunity and behavior, have changed so much over time. The conditions are not constant. </p>
<p>Only if the virus stopped evolving, everyone’s immunity and risk of death were identical and unchanging over time, and there were always people available to become infected, then, by the law of large numbers, would the case fatality rate get closer to the true average probability of death over time.</p>
<h2>A 1% chance of dying?</h2>
<p>The biological process of a disease leading to death is complex and uncertain. It is unpredictable and <a href="https://theconversation.com/cancer-evolution-is-mathematical-how-random-processes-and-epigenetics-can-explain-why-tumor-cells-shape-shift-metastasize-and-resist-treatments-199398">therefore random</a>. Each person has a real physical risk of dying from COVID-19, though this risk varies over time and place and between individuals. So, at best, 1% could be the average probability of death within the population.</p>
<p>Health risks vary among demographic groups, too. For example, elderly individuals have a much <a href="https://www.statnews.com/2020/03/30/what-explains-coronavirus-lethality-for-elderly/">higher risk of death</a> than younger individuals. Tracking COVID-19 infections and how they end for a large number of people that are demographically similar to you would give a better estimate of personal risk. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/521375/original/file-20230417-974-45tk2h.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Pedestrian crosses street in front of cars" src="https://images.theconversation.com/files/521375/original/file-20230417-974-45tk2h.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/521375/original/file-20230417-974-45tk2h.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=425&fit=crop&dpr=1 600w, https://images.theconversation.com/files/521375/original/file-20230417-974-45tk2h.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=425&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/521375/original/file-20230417-974-45tk2h.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=425&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/521375/original/file-20230417-974-45tk2h.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=535&fit=crop&dpr=1 754w, https://images.theconversation.com/files/521375/original/file-20230417-974-45tk2h.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=535&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/521375/original/file-20230417-974-45tk2h.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=535&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">You have a much smaller chance of dying from a car accident if you aren’t near any roads or cars.</span>
<span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/photo/crossing-in-moab-royalty-free-image/1177654681">georgeclerk/E+ via Getty Images</a></span>
</figcaption>
</figure>
<p>Case fatality rate is a probability, but only when you look at the specific data set it was directly calculated from. If you were to write the outcome of every COVID-19 case in that data set on a strip of paper and randomly select one from a hat, you have a 1% chance of selecting a case that ended in death. Doing this only for cases from a particular group, such as a group of older adults with a higher risk or young children with a lower risk, would cause the percentage to be higher or lower. This is why 1% may not be a great estimate of personal risk for every person across all demographic groups. </p>
<p>We can apply this logic to car accidents. The chance of getting into a car crash on a 1,000-mile road trip is about <a href="https://www.news9.com/story/5e6fca6cf86011d4820c3f2d/what-are-your-chances-of-getting-into-a-car-accident">1 in 366</a>. But if you are never anywhere near roads or cars, then you would have a 0% chance. This is really a probability only in the sense of drawing names from a hat. It also applies unevenly across the population – say, due to differences in driving behavior and local road conditions.</p>
<p>Although a population statistic is not the same thing as a probability, it might be a good estimate of it. But only if everyone in the population is demographically similar enough so that the statistic doesn’t change much when calculated for different subgroups.</p>
<p>The next time you’re confronted with such a population statistic, recognize what it actually is: It’s just the percent of a particular population that satisfies some criteria. Chances are, you’re not average for that population. Your own personal probability could be higher or lower.</p><img src="https://counter.theconversation.com/content/201147/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Joseph Stover does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>It’s not entirely accurate to say that you’re more likely to die in a car accident than in a plane crash. Chances are, you’re not the average person.Joseph Stover, Associate Professor of Mathematics, Gonzaga UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2029492023-04-02T11:46:46Z2023-04-02T11:46:46ZBest time to play Tim Hortons’ Roll up to Win? The middle of the night dramatically increases your odds<figure><img src="https://images.theconversation.com/files/518865/original/file-20230401-16-sk7jdj.jpg?ixlib=rb-1.1.0&rect=31%2C7%2C5145%2C3437&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">A professor of statistics has used game data from Tim Hortons Roll up to Win to figure out the best time to play.</span> <span class="attribution"><span class="source">(Shutterstock)</span></span></figcaption></figure><iframe style="width: 100%; height: 100px; border: none; position: relative; z-index: 1;" allowtransparency="" allow="clipboard-read; clipboard-write" src="https://narrations.ad-auris.com/widget/the-conversation-canada/best-time-to-play-tim-hortons--roll-up-to-win-the-middle-of-the-night-dramatically-increases-your-odds" width="100%" height="400"></iframe>
<p>Tim Hortons’ iconic Roll up the Rim contest began in 1985 and went largely unaltered for 25 years. The format was simple: buy a coffee, roll up the rim of the paper cup and see if you’ve won a prize. But this all changed in 2020.</p>
<p>Amid the emergence of a global pandemic, the game went digital. Buying Tim Hortons products still earned you entries to the contest, but these were now stored on the company’s loyalty app. It was then up to you when to play these so-called “digital rolls.” Because players no longer roll up an actual coffee cup rim, the contest is now called Roll up to Win.</p>
<p>Last week I made national news as “<a href="https://kitchener.ctvnews.ca/meet-the-ontario-stats-prof-who-claims-he-can-t-stop-beating-roll-up-to-win-1.6332975">the stats prof who cracked Roll up to Win”</a>. I boosted my odds in Tim Hortons’ annual coffee contest to 80 per cent and then shared my strategy with the nation. </p>
<p>My approach sounds simple — play when other people aren’t — but it took data, determination and drinking a lot of coffee to find the optimal approach.</p>
<p>Here’s the story of the statistics behind the headlines.</p>
<h2>Digital element changes odds</h2>
<p><a href="https://theconversation.com/heres-how-i-cracked-roll-up-the-rim-and-won-almost-every-time-136939">As I explained in 2020</a>, “digital rolls” introduced an element of strategy to the game. There’s one major trick to increasing your odds: play when other people aren’t.</p>
<p>So when are the fewest people playing?</p>
<p>On the surface this seems simple: play in the middle of the night when most Canadians are asleep. But in a country spanning six time zones, finding the single best time is a challenging calculation.</p>
<p>In previous contests I made an educated guess that 4:30 a.m. Eastern was the sweet spot: not too late and not too early. But an educated guess is still a guess, and if I wanted to find the true Goldilocks zone of free coffee I’d need data.</p>
<p>This year, that’s exactly what Tim Hortons gave me.</p>
<figure class="align-right ">
<img alt="A screenshot of the Tim Hortons app showing More than 2,520,293 prizes already awarded!" src="https://images.theconversation.com/files/518854/original/file-20230401-16-as76wk.png?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/518854/original/file-20230401-16-as76wk.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=1085&fit=crop&dpr=1 600w, https://images.theconversation.com/files/518854/original/file-20230401-16-as76wk.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=1085&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/518854/original/file-20230401-16-as76wk.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=1085&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/518854/original/file-20230401-16-as76wk.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1364&fit=crop&dpr=1 754w, https://images.theconversation.com/files/518854/original/file-20230401-16-as76wk.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1364&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/518854/original/file-20230401-16-as76wk.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1364&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">A screenshot of the Tim Hortons app showing how many prizes have been awarded.</span>
<span class="attribution"><span class="source">Tim Hortons</span></span>
</figcaption>
</figure>
<h2>Getting data from the app</h2>
<p>Logging in to the app on the first day of the contest on March 6, a large message grabbed my attention: “More than 308,619 prizes already awarded!” This is an enticement to play — so many winners already! — but it’s also a valuable piece of information.</p>
<p>I waited five minutes and refreshed the page. The message changed: “More than 309,949 prizes already awarded!” Another 1,330 prizes had been won.</p>
<p>This gave me an idea.</p>
<p>I periodically refreshed the page, logging the time and number of prizes awarded. My theory: the number of prizes won should correlate with the number of people playing. By tracking these data I could build a model of Roll up to Win player behaviour and, by extension, calculate exactly when I should play.</p>
<p>Tracking online data is common in scientific research and often employs software to download information automatically. Automated procedures are usually against the rules of contests like this, however, and Roll up to Win was no exception. So I gathered the data manually.</p>
<p>Refreshing the page myself throughout the day — and night — I was able to approximately track the prizes. But I did have other things to do, so there were gaps in my logs. In statistical terms, I had what’s known as missing data.</p>
<figure class="align-center ">
<img alt="A graph showing total prizes awarded over time. The line is steepest during daytime hours, plateauing during the night. Red circles highlight areas with missing data." src="https://images.theconversation.com/files/518855/original/file-20230401-14-zc2kou.jpeg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/518855/original/file-20230401-14-zc2kou.jpeg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=346&fit=crop&dpr=1 600w, https://images.theconversation.com/files/518855/original/file-20230401-14-zc2kou.jpeg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=346&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/518855/original/file-20230401-14-zc2kou.jpeg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=346&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/518855/original/file-20230401-14-zc2kou.jpeg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=435&fit=crop&dpr=1 754w, https://images.theconversation.com/files/518855/original/file-20230401-14-zc2kou.jpeg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=435&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/518855/original/file-20230401-14-zc2kou.jpeg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=435&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">During this two-day period the number of prizes awarded continued to climb, with the win rate slowing during the nighttime hours. Gaps in the data can also be seen. All times Eastern.</span>
<span class="attribution"><span class="source">(author provided)</span></span>
</figcaption>
</figure>
<p>Missing data are common in real-world analysis. Examples include unreturned or incomplete surveys, patients missing medical appointments or even misplaced or corrupted data files.</p>
<h2>Statistical challenges</h2>
<p>This can present statistical challenges depending on how — and why — we have gaps in our records. A patient might miss their appointment because they were too unwell to travel, or maybe just because their car wouldn’t start. These two scenarios provide different information, requiring different solutions.</p>
<p>My missing data problem was comparatively simple. My goal was to fill in the gaps that arose when I was sleeping, travelling or otherwise away from my keyboard.</p>
<p>Using the data I did have, I looked for patterns. The most prizes were being won between 9 a.m. and 1 p.m. Eastern, the fewest around 3 a.m. This repeated each day and I was able to use this to my advantage.</p>
<p>To map our mathematical models onto the real world, statisticians often make assumptions. I assumed that player behaviour patterns would be similar day-to-day. This was a fairly strong assumption — I had some evidence of a slightly later start on Sunday mornings — but it seemed a reasonable one for my problem.</p>
<h2>Weighting the data</h2>
<p>I could then combine each day’s data and employ <a href="https://www.scb.se/contentassets/ca21efb41fee47d293bbee5bf7be7fb3/weighting-methods.pdf">a technique known as weighting</a>. Days where I had logged more observations were given more importance — or weight — in my calculations. I was then able to use statistical methods to “join the dots” and map out the overall shape of player behaviour.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/518869/original/file-20230401-16-li9ktq.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/518869/original/file-20230401-16-li9ktq.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=341&fit=crop&dpr=1 600w, https://images.theconversation.com/files/518869/original/file-20230401-16-li9ktq.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=341&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/518869/original/file-20230401-16-li9ktq.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=341&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/518869/original/file-20230401-16-li9ktq.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=428&fit=crop&dpr=1 754w, https://images.theconversation.com/files/518869/original/file-20230401-16-li9ktq.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=428&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/518869/original/file-20230401-16-li9ktq.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=428&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Stats professor Michael Wallace has needed a lot of coffee to record his data on the Roll up to Win game.</span>
<span class="attribution"><span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>With this, my educated guess of previous years became a data-driven estimate. The best time to play was 3:16 a.m. Eastern — over an hour earlier than I was playing in the past — and the worst was 11:46 a.m. There is always some statistical uncertainty in an analysis, but playing around these times should give you the highest and lowest chances of winning.</p>
<p>There was one last step: I had to test my results. My analysis was predicated on another assumption: that the number of available prizes was consistent through the day. Maybe fewer people were winning at 3 a.m. because there were fewer prizes, not fewer players. Luckily, this was an assumption I could test.</p>
<h2>3:16 a.m. is the golden hour</h2>
<p>I racked up 60 rolls and split them in half, playing 30 around the 3:16 a.m. mark and the rest just before lunchtime. I won 23 times in the early hours compared to just five times later on. No big prizes — mostly a lot of free coffee — but I got the result I was hoping for: statistically strong evidence that my theory was correct.</p>
<p>I reached out to a local journalist who’d worked with me in the past. I thought this might be a fun little story about applying statistics to the real world, with a hint of local colour as a University of Waterloo professor. Then things snowballed. By the end of the week I’d appeared on countless radio stations and even nationally broadcast television shows including CTV’s Your Morning and CBC’s The National.</p>
<figure>
<iframe width="440" height="260" src="https://www.youtube.com/embed/LGCfTZAOZMI?wmode=transparent&start=0" frameborder="0" allowfullscreen=""></iframe>
</figure>
<p>While the interviews were a great opportunity to showcase how stats can be more than just equations in a textbook, many outlets spotted a potential flaw. If everyone starts playing at 3:16 a.m., won’t the strategy change?</p>
<p>The short answer is yes, and it illustrates <a href="https://plato.stanford.edu/entries/game-theory/">a concept from another area of study: game theory</a>. Sometimes when everyone knows the best strategy it can turn into the worst strategy.</p>
<p>That said, I don’t think everyone will be getting up in the middle of the night to win a free coffee, so it should remain a good time to play. </p>
<p>I’ll be up in the early hours tracking the data for the last week of the contest — all entries must be played by April 9 — to see if the strategy needs updating. It’s a few more late nights, but I think I have enough caffeine for that.</p><img src="https://counter.theconversation.com/content/202949/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Michael Wallace does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Statistics have many real-world applications — including what’s the best time to play Tim Hortons’ Roll up to Win contest. A stats prof explains how he found the precise time with the best odds.Michael Wallace, Associate Professor, Department of Statistics and Actuarial Science, University of WaterlooLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2026912023-03-31T18:15:47Z2023-03-31T18:15:47ZDeclines in math readiness underscore the urgency of math awareness<figure><img src="https://images.theconversation.com/files/518595/original/file-20230330-1139-7yolln.jpg?ixlib=rb-1.1.0&rect=0%2C73%2C6134%2C4000&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Math scores plummeted during the COVID-19 pandemic. What will it take to raise them back up?</span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/photo/girl-solving-mathematical-addition-royalty-free-image/950609102?phrase=math%20classroom&adppopup=true">Ridofranz / iStock / Getty Images Plus</a></span></figcaption></figure><p>When President Ronald Reagan <a href="https://ww2.amstat.org/mam/98/what.is.maw.html">proclaimed the first National Math Awareness Week</a> in April 1986, one of the problems he cited was that too few students were devoted to the study of math.</p>
<p>“Despite the increasing importance of mathematics to the progress of our economy and society, enrollment in mathematics programs has been declining at all levels of the American educational system,” Reagan wrote in his proclamation.</p>
<p>Nearly 40 years later, the problem that Reagan lamented during the first National Math Awareness Week – which has since evolved to become “<a href="https://ww2.amstat.org/mathstatmonth/aboutmathstatmonth.html">Mathematics and Statistics Awareness Month</a>” – not only remains but has gotten worse.</p>
<p>Whereas 1.63%, or about <a href="https://nces.ed.gov/programs/digest/d21/tables/dt21_325.65.asp">16,000</a>, of the <a href="https://nces.ed.gov/programs/digest/d12/tables/dt12_310.asp">nearly 1 million</a> bachelor’s degrees awarded in the U.S. in the 1985-1986 school year went to math majors, in 2020, just 1.4%, or about <a href="https://nces.ed.gov/programs/digest/d21/tables/dt21_325.65.asp">27,000</a>, of the <a href="https://nces.ed.gov/programs/digest/d12/tables/dt12_310.asp">1.9 million</a> bachelor’s degrees were awarded in the field of math – a small but significant decrease in the proportion.</p>
<p>Post-pandemic data suggests the number of students majoring in math in the U.S. is likely to decrease in the future.</p>
<p>A key factor is the <a href="https://www.nytimes.com/2022/10/24/us/math-reading-scores-pandemic.html">dramatic decline in math learning</a> that took place during the lockdown. For instance, whereas 34% of eighth graders were proficient in math in 2019, test data shows the percentage <a href="https://www.nytimes.com/2022/10/24/us/math-reading-scores-pandemic.html">dropped to 26% after the pandemic</a>.</p>
<p>These declines will undoubtedly affect how much math U.S. students can do at the college level. For instance, in 2022, only <a href="https://www.act.org/content/dam/act/unsecured/documents/2022/2022-National-ACT-Profile-Report.pdf">31% of graduating high school seniors were ready for college-level math</a> – down from 39% in 2019.</p>
<p>These declines will also affect how many U.S. students are able to take advantage of the growing number of <a href="https://www.bls.gov/ooh/math/home.htm">high-paying math occupations</a>, such as <a href="https://www.bls.gov/ooh/math/data-scientists.htm">data scientists</a> and <a href="https://www.bls.gov/ooh/math/actuaries.htm">actuaries</a>. Employment in math occupations is projected to <a href="https://www.bls.gov/ooh/math/home.htm">increase by 29%</a> in the period from 2021 to 2031.</p>
<p>About <a href="https://www.bls.gov/ooh/math/home.htm">30,600 math jobs</a> are expected to open up per year from growth and replacement needs. That exceeds the 27,000 or so math graduates being produced each year – and <a href="https://www.bls.gov/ooh/field-of-degree/mathematics/mathematics-field-of-degree.htm">not all math degree holders</a> go into math fields. Shortages will also arise in several other areas, since math is a gateway to many STEM fields.</p>
<p>For all of these reasons and more, as a <a href="https://manilsuri.umbc.edu/">mathematician</a> who thinks deeply about the <a href="https://wwnorton.com/books/9781324007036">importance of math</a> and what it means to our world – and even to <a href="https://scholar.google.com/citations?view_op=view_citation&hl=en&user=lFWFsSkAAAAJ&sortby=pubdate&citation_for_view=lFWFsSkAAAAJ:j3f4tGmQtD8C">our existence as human beings</a> – I believe this year, and probably for the foreseeable future, educators, policymakers and employers need to take Mathematics and Statistics Awareness Month more seriously than ever before.</p>
<h2>Struggles with mastery</h2>
<p>Subpar math achievement has been endemic in the U.S. for a long time. </p>
<p>Data from the National Assessment of Educational Progress shows that <a href="https://www.nationsreportcard.gov/mathematics/nation/achievement/?grade=12">no more than 26% of 12th graders</a> have been rated proficient in math since 2005.</p>
<p>The pandemic <a href="https://www.nationsreportcard.gov/mathematics/nation/groups/?grade=4#nation-gaps-gaps">disproportionately affected</a> racially and economically disadvantaged groups. During the lockdown, these groups had <a href="https://www.nationsreportcard.gov/highlights/mathematics/2022/#student-experiences">less access to the internet and quiet studying spaces</a> than their peers. So securing Wi-Fi and places to study are key parts of the battle to improve math learning.</p>
<p>Some people believe math teaching techniques need to be revamped, as they were through the <a href="https://www.vox.com/2014/4/20/5625086/the-common-core-makes-simple-math-more-complicated-heres-why">Common Core</a>, a new set of educational standards that stressed alternative ways to solve math problems. Others want a return to more traditional methods. Advocates also argue there is a need for colleges to <a href="https://www.nctq.org/publications/Teacher-Prep-Review:-Building-Content-Knowledge">produce better-prepared teachers</a>.</p>
<p>Other observers believe the problem lies with the “<a href="https://www.penguinrandomhouse.com/books/44330/mindset-by-carol-s-dweck-phd/">fixed mindset</a>” many students have – where failure leads to the conviction that they can’t do math – and say the solution is to foster a <a href="https://www.frontiersin.org/articles/10.3389/feduc.2021.784393/full#B21">“growth” mindset</a> – by which failure spurs students to try harder.</p>
<p>Although all these factors are relevant, none address what in my opinion is a root cause of math underachievement: our nation’s ambivalent relationship with mathematics.</p>
<h2>Low visibility</h2>
<p>Many observers worry about how U.S. children fare in <a href="https://data.oecd.org/pisa/mathematics-performance-pisa.htm">international rankings</a>, even though math anxiety makes <a href="https://files.eric.ed.gov/fulltext/ED536509.pdf">many adults in the U.S.</a> steer clear of the subject themselves.</p>
<p>Mathematics is not like art or music, which people regularly enjoy all over the country by visiting museums or attending concerts. It’s true that there is a National Museum of Mathematics in New York, and some science centers in the U.S. devote exhibit space to mathematics, but these can be geographically inaccessible for many.</p>
<p>A 2020 study on media portrayals of math <a href="https://doi.org/10.29333/iejme/8260">found an overall “invisibility of mathematics</a>” in popular culture. Other findings were that math is presented as being irrelevant to the real world and of little interest to most people, while mathematicians are stereotyped to be singular geniuses or socially inept nerds, and white and male. </p>
<p>Math is tough and typically takes much discipline and perseverance to succeed in. It also calls for a <a href="https://doi.org/10.1088/1742-6596/947/1/012029">cumulative learning approach</a> – you need to master lessons at each level because you’re going to need them later. </p>
<p>While research in neuroscience shows almost everyone’s brain is <a href="https://blogs.ams.org/matheducation/2019/02/01/everyone-can-learn-mathematics-to-high-levels-the-evidence-from-neuroscience-that-should-change-our-teaching/">equipped to take up the challenge</a>, many students balk at putting in the effort when they don’t score well on tests. The <a href="https://www.frontiersin.org/articles/10.3389/feduc.2018.00026/full#B6">myth that math is just about procedures and memorization</a> can make it easier for students to give up. So can <a href="https://files.eric.ed.gov/fulltext/EJ1304392.pdf">negative opinions</a> about math ability conveyed by peers and parents, such as declarations of not being “<a href="https://www.nytimes.com/2017/04/24/well/family/fending-off-math-anxiety.html">a math person</a>.”</p>
<h2>A positive experience</h2>
<p>Here’s the good news. A 2017 Pew poll found that despite the bad rap the subject gets, <a href="https://www.pewresearch.org/social-trends/2018/01/09/many-americans-say-they-liked-math-and-science-in-school-thought-about-a-stem-career/">58% of U.S. adults enjoyed their school math classes</a>. It’s members of this legion who would make excellent recruits to help promote April’s math awareness. The initial charge is simple: Think of something you liked about math – a topic, a <a href="https://www.mathsisfun.com/puzzles/">puzzle</a>, a fun fact – and go over it with someone. It could be a child, a student, or just one of the many adults who have left school with a negative view of math.</p>
<figure class="align-center ">
<img alt="Three seashells are shown under the words " src="https://images.theconversation.com/files/518209/original/file-20230329-24-bfj94q.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/518209/original/file-20230329-24-bfj94q.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=430&fit=crop&dpr=1 600w, https://images.theconversation.com/files/518209/original/file-20230329-24-bfj94q.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=430&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/518209/original/file-20230329-24-bfj94q.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=430&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/518209/original/file-20230329-24-bfj94q.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=540&fit=crop&dpr=1 754w, https://images.theconversation.com/files/518209/original/file-20230329-24-bfj94q.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=540&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/518209/original/file-20230329-24-bfj94q.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=540&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Math exercise for shells can be downloaded at https://www.manilsuri.com/assets/shell_patterns.pptx.</span>
<span class="attribution"><span class="source">Manil Suri</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>Can something that sounds so simplistic make a difference? Based on my years of experience as a mathematician, I believe it can – if nothing else, for the person you talk to. The goal is to stimulate curiosity and convey that mathematics is much more about <a href="https://theconversation.com/pi-gets-all-the-fanfare-but-other-numbers-also-deserve-their-own-math-holidays-200046">exhilarating ideas that inform our universe</a> than it is about the school homework-type calculations so many dread.</p>
<p>Raising math awareness is a first step toward making sure people possess the basic math skills required not only for employment, but also to understand math-related issues – such as gerrymandering or climate change – well enough to be an informed and participating citizen. However, it’s not something that can be done in one month.</p>
<p>Given the decline in both math scores and the percentage of students studying math, it may take many years before America realizes the stronger relationship with math that President Reagan’s proclamation called for during the first National Math Awareness Week in 1986.</p><img src="https://counter.theconversation.com/content/202691/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Manil Suri does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Nearly four decades after President Ronald Reagan proclaimed the first National Math Awareness Week, math readiness and enrollment in college math programs continue to decline.Manil Suri, Professor of Mathematics and Statistics, University of Maryland, Baltimore CountyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2012992023-03-16T19:11:07Z2023-03-16T19:11:07ZRobodebt not only broke the laws of the land – it also broke laws of mathematics<p>Friday marked the end of the public hearings for the Royal Commission into the Robodebt Scheme. They painted a picture of a catastrophic program that was legally and <a href="https://theconversation.com/amateurish-rushed-and-disastrous-royal-commission-exposes-robodebt-as-ethically-indefensible-policy-targeting-vulnerable-people-201165">ethically indefensible</a> – an example of how technological overreach, coupled with dereliction of duty can amount to immense suffering for ordinary people.</p>
<p>The artificial intelligence (AI) algorithm behind Robodebt has been called “flawed”. But it was worse than that; it broke laws of mathematics. A mathematical law called Jensen’s inequality shows the Robodebt algorithm should have generated not only debts, but also credits.</p>
<h2>What was Robodebt?</h2>
<p>The Australian government’s Robodebt program was designed to catch people exploiting the Centrelink welfare system. </p>
<p>The system compared welfare recipients’ Centrelink-reported fortnightly income with their ATO-reported yearly income, the latter of which was averaged to provide fortnightly figures that could be lined up with Centrelink’s system.</p>
<p>If the difference showed an overpayment by Centrelink, a red flag was raised. The AI system then issued a debt notice and put the onus on the recipient to prove they weren’t exploiting the welfare system. </p>
<h2>A Robodebt victim</h2>
<p>To understand the extent of the failure, let’s consider a hypothetical case study. Will Gossett was a university student from 2017-2019. He was single, older than 18, and living at home with his parents.</p>
<p>Will received Centrelink payments according to his fortnightly income from a couple of casual jobs with highly variable work hours. In his first year at university his jobs didn’t pay much, so he received more Centrelink payments in the 2018 financial year than the year following.</p>
<p>The Robodebt algorithm took Will’s ATO yearly income records for both the 2018 and 2019 financial years and, for each year, averaged them into a series of fortnightly “robo” incomes.</p>
<p>Inside Robodebt’s AI world, his fortnightly incomes were then the same throughout the 2018 financial year, and the same throughout the 2019 financial year.</p>
<p>Will was honest with his claims, but was stunned to receive a debt notice for Centrelink overpayments made in the 2019 financial year – the year in which he actually received lower welfare payments. </p>
<p>The income-averaging algorithm gave Will an average fortnightly income for 2019 that was above the threshold that made him eligible for Centrelink payments. As far as the Robodebt system was concerned, Will shouldn’t have received any welfare payments that year.</p>
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Read more:
<a href="https://theconversation.com/amateurish-rushed-and-disastrous-royal-commission-exposes-robodebt-as-ethically-indefensible-policy-targeting-vulnerable-people-201165">'Amateurish, rushed and disastrous': royal commission exposes robodebt as ethically indefensible policy targeting vulnerable people</a>
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<h2>Jensen’s inequality</h2>
<p>The laws of mathematics tell us when two things are equal, but they can also tell us when one thing is bigger than another. This type of law is called an “inequality”. </p>
<p>To understand why and when Robodebt failed for Will, we need to understand a concept called Jensen’s inequality, credited to Danish mathematician Johan Jensen (1859-1925). </p>
<p>Jensen’s inequality explains how making a decision based on the averaging of numbers leads to either a negative bias or a positive bias under a “convexity condition”, which I’ll explain soon.</p>
<p>You’ll recall Will is a single university student, above 18, and living with his parents. Based on these factors, Centrelink has a fortnightly payment table for him, illustrated with the curve in the figure below. </p>
<p>The figure shows the more income Will earns from his jobs, the less welfare payment he receives, until a specific income, after which he receives none.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/515021/original/file-20230313-2477-qqk3ao.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/515021/original/file-20230313-2477-qqk3ao.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=359&fit=crop&dpr=1 600w, https://images.theconversation.com/files/515021/original/file-20230313-2477-qqk3ao.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=359&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/515021/original/file-20230313-2477-qqk3ao.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=359&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/515021/original/file-20230313-2477-qqk3ao.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=451&fit=crop&dpr=1 754w, https://images.theconversation.com/files/515021/original/file-20230313-2477-qqk3ao.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=451&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/515021/original/file-20230313-2477-qqk3ao.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=451&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">This graph, created from tables provided by Centrelink, shows how certain factors determine the amount of welfare payments Will can receive depending on his income.</span>
</figcaption>
</figure>
<p>The parts of the curve where Jensen’s inequality is relevant are highlighted by two red squares. In the square on the left, the curve bends downwards (concave), and in the square on the right it bends upwards (convex).</p>
<p>Because Will’s income was higher in 2019 and spread across the part where the payment curve is convex, Jensen’s inequality guarantees he would receive a Robodebt notice, even though there was no debt.</p>
<p>In 2018, however, Will’s income distribution was spread around smaller amounts where the curve is concave. So if Jensen’s inequality was adhered to, the AI algorithm should have issued him a “Robocredit” – but it didn’t.</p>
<p>It could be the algorithm contained a line of code that nullified Jensen’s inequality by instructing any credits be ignored. </p>
<h2>Big data and a bad algorithm</h2>
<p>The people responsible for the Robodebt system should have had a strong interest in keeping error rates low. Data scientists have a big red “stop” button when error rates of automated systems go beyond a few percent. </p>
<p>It’s straightforward to estimate error rates for an AI scheme. Experts do this by running simulations inside a virtual model called a “digital twin”. These can be used to carry out statistical evaluations, and expose conscious and unconscious biases in bad algorithms.</p>
<p>In Robodebt’s case, a digital twin could have been used to figure out error rates. This would have required running the Robodebt algorithm through representative incomes simulated under two different scenarios. </p>
<p>Under the first scenario, incomes are simulated assuming no debt is owed by anyone. Every time a result is returned saying a debt is owed, a Type 1 (or false-positive) error is recorded. Under the second scenario, incomes are simulated assuming everyone owes a debt (to varying degrees). If a no-debt result is returned, a Type 2 (false-negative) error rate is recorded. </p>
<p>Then an error rate is estimated by dividing the number of errors by the number of simulations, within each scenario. </p>
<h2>Eye-watering inaccuracies</h2>
<p>Although no consistently reliable error rates have been published for Robodebt, <a href="https://ministers.dss.gov.au/transcripts/10181#:%7E:text=The%20reported%20accuracy%20of%20the,stop%20Robodebt%20five%20years%20ago">a figure of</a> at least 27% was quoted in Parliament Question Time on February 7.</p>
<p>The reality was probably much worse. During the scheme, on the order of one million income reviews were performed, of <a href="https://www.theguardian.com/australia-news/2019/sep/27/centrelink-could-launch-more-than-a-million-new-robodebts-in-next-three-years">which 81% led</a> to a debt being raised. </p>
<p>Of these, <a href="https://www.theguardian.com/australia-news/2021/apr/07/federal-government-criticised-for-continuing-robodebt-after-admitting-it-was-unlawful">about 70%</a>
(roughly 567,000 debts) were raised through the use of income averaging in the Robodebt algorithm. </p>
<p>In 2020, the <a href="https://www.theguardian.com/australia-news/2020/may/29/robodebt-government-to-repay-470000-unlawful-centrelink-debts-worth-721m">government conceded</a> about 470,000 debts had been falsely raised, out of a total of about 567,000. </p>
<p>Back-of-the-envelope calculations give a Type 1 (false-positive) error rate on the order of 80% (470,000/567,000). Compared to the usual target of a few percent, this is an eye-wateringly large error rate. </p>
<p>If simulations had been run, or human intelligence used to check real cases, the “stop” button would have been hit almost immediately. </p>
<p>Jensen’s inequality establishes why and when income averaging will fail, yet income matching hasn’t gone away. It can be found in AI software used for official statistics, welfare programs, bank loans and so forth. </p>
<p>Deeper statistical theory for this “change of support” problem — for example, going from data on yearly support to fortnightly support — will be needed as AI becomes increasingly pervasive in essential parts of society. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/why-robodebts-use-of-income-averaging-lacked-basic-common-sense-201296">Why robodebt's use of 'income averaging' lacked basic common sense</a>
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</em>
</p>
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<img src="https://counter.theconversation.com/content/201299/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Noel Cressie does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>I crunched the numbers, and they suggest the Robodebt algorithm’s error rate was on the order of 80%.Noel Cressie, Distinguished Professor of Statistics, University of WollongongLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1995872023-02-09T19:10:48Z2023-02-09T19:10:48ZAustralia’s new pay equality law risks failing women – unless we make this simple fix<figure><img src="https://images.theconversation.com/files/509079/original/file-20230209-13-d2gtzv.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">shutterstock</span> </figcaption></figure><p>The Albanese government’s efforts to address the gender pay gap are laudable. Despite all the attention given to the issue over the past decade or so, sectoral pay discrimination is very real and <a href="https://danielle-li.github.io/assets/docs/PotentialAndTheGenderPromotionGap.pdf">workplace biases persist</a>.</p>
<p>But the federal government’s new tool to address the problem, the Workplace Gender Equality Amendment Bill, may not achieve much. </p>
<p>The <a href="https://parlinfo.aph.gov.au/parlInfo/download/legislation/bills/s1363_first-senate/toc_pdf/2300120.pdf;fileType=application%2Fpdf">amendment</a> to the <a href="https://www.legislation.gov.au/Details/C2016C00895">Workplace Gender Equality Act</a> (enacted by the Gillard Labor government in 2012) requires all companies with more than 100 employees to report their “gender pay gap”. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/how-the-jobs-summit-shifted-gender-equality-from-the-sidelines-to-the-mainstream-189869">How the jobs summit shifted gender equality from the sidelines to the mainstream</a>
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<hr>
<p>Much like the <a href="https://www.legislation.gov.au/Details/C2018A00153">Modern Slavery Act</a>, <a href="https://parlinfo.aph.gov.au/parlInfo/download/legislation/ems/s1363_ems_c828bc87-8341-420d-9641-981a45c43fc6/upload_pdf/EM_JC008778.pdf;fileType=application%2Fpdf">the idea</a> is that public reporting will concentrate employers’ attention on the problem, leading to greater gender equality.</p>
<p>But will it? </p>
<p>The problem is the type of data companies must report to the <a href="https://www.wgea.gov.au/">Workplace Gender Equality Agency</a>, which has been publishing pay-gap statistics since being established by the Workplace Gender Equality Act in 2012.</p>
<p>As with the other statistics the agency has published over the past decade, the <a href="https://parlinfo.aph.gov.au/parlInfo/download/legislation/bills/s1363_first-senate/toc_pdf/2300120.pdf">new amendment</a> requires only publishing simple aggregates:</p>
<blockquote>
<p>The Agency must publish aggregate information, for each relevant employer for each reporting period, for the purpose of showing the employer’s performance and progress in achieving gender equality in relation to remuneration for the employer’s workforce"</p>
</blockquote>
<p>This may seem like a positive step. But aggregate numbers – which in practice translates into reporting summary statistics – do not help us to either identify or understand the pay gap. Those aggregates also don’t help us come up with the right fixes. </p>
<p>To do that requires better data that enables more precise analysis for the factors affecting pay disparities. </p>
<h2>The problem with averages</h2>
<p>Averages are ubiquitous in statistics. They can serve a important service, such as identifying trends. I’ll even be using averages to illustrate a few points. </p>
<p>But their limitations should be understood. They are particularly problematic when it comes to areas of endemic inequality, such as income.</p>
<p>Consider a company with 101 employees, one being the founder and chief executive. The other 100 employees, split 50/50 between men and women, are all paid the same salary. </p>
<p>But suppose the chief executive pays himself ten times as much as the other employees. This isn’t ridiculous; the average CEO of a listed company in Australia is <a href="https://thenewdaily.com.au/finance/finance-news/2022/07/13/ceos-pay-2021/">paid 132 times</a> the average income. This creates a 17.6% gender pay gap. </p>
<p>Now consider a similar company, run by a “tech bro” who doesn’t draw a salary but does pay every woman 2% less than every man. The aggregate numbers will show no gender pay gap.</p>
<p>In the first case, where there’s no explicit gender discrimination, aggregate numbers can be misread as indicating there is. In the second case, actual gender discrimination is obscured. </p>
<hr>
<p><strong>The WGEA’s pay gap results</strong></p>
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<img alt="Workplace Gender Equality Agency's pay gap results, 2013-14 to 2021-22" src="https://images.theconversation.com/files/509108/original/file-20230209-28-a6yq1r.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/509108/original/file-20230209-28-a6yq1r.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=535&fit=crop&dpr=1 600w, https://images.theconversation.com/files/509108/original/file-20230209-28-a6yq1r.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=535&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/509108/original/file-20230209-28-a6yq1r.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=535&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/509108/original/file-20230209-28-a6yq1r.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=673&fit=crop&dpr=1 754w, https://images.theconversation.com/files/509108/original/file-20230209-28-a6yq1r.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=673&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/509108/original/file-20230209-28-a6yq1r.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=673&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<span class="caption"></span>
<span class="attribution"><a class="source" href="https://www.wgea.gov.au/publications/australias-gender-equality-scorecard">Workplace Gender Equality Agency</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<hr>
<h2>Poor data leads to poor analysis</h2>
<p>The widespread use of averages often skew our sense of things. If you compare your own income to the Australian average (<a href="https://www.abs.gov.au/statistics/labour/earnings-and-working-conditions/average-weekly-earnings-australia/may-2021">A$90,324 a year in 2021</a>), the probability is you’ll feel left behind. But if you compare yourself to the median income – the income at which half the population earns more, and half less – you’ll feel much better: it’s only $62,868 a year.</p>
<p>Bad data leads to bad analysis, and bad policy responses.</p>
<p>Here’s another scenario. Consider our first company again. The CEO is concerned about the publicity from reporting a 17% gender pay gap to the agency. So he employs his wife as deputy CEO, paying her five times the rest of the staff, and cuts his own salary by half. He no longer has a gender pay gap to report. </p>
<p>This is progress of a kind, but not the progress needed to address the complex causes of gender pay inequality for ordinary people. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/women-are-as-likely-as-men-to-accept-a-gender-pay-gap-if-they-benefit-from-it-151524">Women are as likely as men to accept a gender pay gap if they benefit from it</a>
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</em>
</p>
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<h2>How to fix this problem</h2>
<p>So how then to improve the reporting of gender pay statistics generally?</p>
<p>Reporting <em>median</em> statistics would help mitigate the skewing problem with averages. Unless the government demands this, the agency will more than likely keeping taking the same approach as over the past decade – relying on averages. </p>
<p>There’s also a case for companies to report other relevant factors that could influence pay, such as qualifications, skill, tenure, seniority and productivity. </p>
<p>This would enable the Workplace Gender Equality Agency to provide more sophisticated analysis, breaking down the factors contributing to the figures that get the headlines.</p>
<p>The agency <a href="https://www.wgea.gov.au/pay-equity">defines equal pay</a> as “men and women performing the same work are paid the same amount”. To achieve this, it is essential to ensure apples are being compared with apples. This is only possible if we control for the factors that can influence pay, and don’t lose the necessary nuance. </p>
<p>Blunt data does not properly inform us about the pay gap, why it arises, nor how to solve it. This risks policy responses that focus on the wrong issues and which achieve little. </p>
<p>Decision-makers, both in public and private sectors, risk making bad decisions on poor-quality data. The wrong fixes could even <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=4308670">make things worse</a>. We will not eradicate the gender pay gap using bad statistics.</p><img src="https://counter.theconversation.com/content/199587/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Mark Humphery-Jenner does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>We will not eradicate the gender pay gap using bad statistics. Here’s what we need to do instead.Mark Humphery-Jenner, Associate Professor of Finance, UNSW SydneyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1943142022-12-30T08:24:01Z2022-12-30T08:24:01ZA brief history of statistics in football: why actual goals remain king in predicting who will win<p>In 2017, BBC’s Match of the Day introduced a new statistic in their post-match summaries of Premier League matches. Expected goals, or xG, is designed to tell us how many goals a team should have scored based on the quality of the chances they created in a game. It is loved by amateur and professional statisticians alike who want to use data to analyse performance.</p>
<p>The BBC regularly uses xG in its Premier League coverage, but this metric was absent from both BBC and ITV coverage at the recent men’s World Cup. A brief look into what xG is and the history of using data to predict football matches may give us some insight into why they decided not to use it.</p>
<p>The concept of expected goals originally came from <a href="http://www.hockeyanalytics.com/Research_files/NHL-Expected-Goals-Brian-Macdonald.pdf">ice hockey</a> but is easily appliable to football. xG is calculated by looking at every shot that a team took in a match and assigning it a probability of being scored.</p>
<p>This probability is calculated by looking at shots from similar situations in historical matches and calculating what percentage of them resulted in a goal. By adding the probabilities together for all shots that a team takes, we get their expected goals for the entire game. </p>
<p>Consider the <a href="https://www.fotmob.com/match/3901079/matchfacts/tottenham-hotspur-vs-liverpool">Premier League</a> match between Tottenham and Liverpool in November 2022, which Liverpool won 2-1. Liverpool only achieved an xG of 1.18 from 13 shots in the match, while Tottenham managed an xG of 1.21 from their 14 shots.</p>
<p>In the <a href="https://www.skysports.com/football/news/11661/12736385/tottenham-1-2-liverpool-mohamed-salah-strikes-twice-before-harry-kane-sets-up-tense-finish">post-match interviews</a>, Tottenham manager Antonio Conte claimed that Tottenham were unlucky to lose given their performance. An xG score line of 1.21 vs 1.18 suggests a very even game and would seem to back up Conte’s point. </p>
<p>However, Liverpool manager Jürgen Klopp suggested that the quality of Mohamed Salah, who scored two goals from three shots with a combined xG of 0.67, was the difference in this match. This exposes one of the major weaknesses of xG. It takes no account of who the striker or goalkeeper is. But is this weakness enough to make xG unreliable as a resource for predicting future games?</p>
<h2>Football prediction before xG</h2>
<p>The obvious piece of data to use when analysing football is goals. Indeed, this was the only information used in the 1997 model of <a href="https://web.math.ku.dk/%7Erolf/teaching/thesis/DixonColes.pdf">Mark Dixon and Stuart Coles</a>, which predicts future football matches by assigning each team attacking and defensive rating.</p>
<p>The Dixon-Coles ratings are calculated using the number of goals scored and conceded in previous matches, taking account of the quality of the opposition. The ratings of two different teams, along with a home advantage boost, can them be combined to predict the score of an upcoming match between them.</p>
<p>Given the number of statistics available in football, a model that only uses goals to predict future games may seem remarkably simple, but its effectiveness lies in understanding what makes for good statistical analysis: high quality data, and lots of it.</p>
<p>Goals are the highest quality data available in football prediction, since they are the only thing that actually affects results. This explains why other traditional metrics such as number of shots or possession percentage are not used in the Dixon-Coles model. </p>
<p>A shot could be a penalty, which players expect to score, or a speculative effort from distance – yet both count equally as shots on goal. Similarly, a team could have lots of possession but not in an area of the pitch that gives them chances to score goals.</p>
<p>As far back as 1968, <a href="https://pdfslide.net/documents/reep-benjamin-1968-skill-and-chance-in-association-football.html?page=6">a statistical study</a> was unable to find any link between shots, possession or passing moves and the outcomes of football matches. This supports the idea that goals are the only factor worth considering.</p>
<h2>Why might xG be useful?</h2>
<p>The weakness of Dixon-Coles comes in the quantity of data. There were <a href="https://www.premierleague.com/news/2637865">1,071 goals scored</a> in the 2021/22 Premier League season, which may seem like a lot. However, this is only 2.82 goals per game. To counteract this lack of information per game, Dixon and Coles used three years’ worth of data to make their predictions, despite most teams going through wholesale changes in playing and management staff over this period.</p>
<p>Increasing the quantity of data over a shorter timescale is where xG data has an advantage over goals alone. Essentially, it is an attempt to find balance between the quality of goal data and the quantity of shot-based data. This is a classic conundrum in statistics known as the <a href="http://robotics.stanford.edu/%7Eronnyk/biasVar.pdf">bias-variance trade-off</a>.</p>
<p>Take the Liverpool vs Tottenham game mentioned earlier. The three goals scored are the only pieces of information that the Dixon-Coles model can extract from this match, whereas an xG-based model would get information from all 27 shots taken – with the added quality of having some indication of how likely those shots were to result in a goal. However, not taking account of who is involved in a shot does place a limit on the quality of this xG data. </p>
<p>Despite being 25 years old, the Dixon-Coles model is still the gold standard of football prediction, as found in <a href="https://ieeexplore.ieee.org/abstract/document/9795385">this 2022 study</a>. While xG provides good information about the balance of play in a single match, no xG model has been shown to be superior to Dixon-Coles in predicting the future. </p>
<p>Until that happens, doubts about its weaknesses will remain and actual goals must retain their place as the only truly reliable indicator of how good a team is.</p><img src="https://counter.theconversation.com/content/194314/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Laurence Shaw does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Despite being 25 years old, the Dixon-Coles model is still the gold standard of football predictionLaurence Shaw, Senior Lecturer in Mathematics, Nottingham Trent UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1939822022-12-15T15:36:51Z2022-12-15T15:36:51ZWorld Cup 2022: how injuries could affect the rest of the domestic and Champions League season<p>The World Cup in Qatar has seen many injuries. Arsenal striker Gabriel Jesus had to have <a href="https://www.skysports.com/football/news/11670/12761483/gabriel-jesus-arsenal-forward-undergoes-knee-surgery-after-injury-at-world-cup-with-brazil">surgery on his right knee</a> after being forced off during Brazil’s group stage match against Cameroon. And Paris Saint-Germain (PSG) players and Portugal teammates <a href="https://www.goal.com/en-gb/news/injured-psg-stars-danilo-nuno-mendes-leave-portugal-world-cup-squad/blte6ed70b91b14b9d5">Danilo and Nuno Mendes</a> were both unable to continue playing in the tournament after the former fractured three ribs and the latter injured his thigh.</p>
<p>There were even some fears that Argentina’s Lionel Messi (also a PSG player) might not appear in the World Cup final after he was seen <a href="https://www.theguardian.com/football/2022/nov/21/lionel-messi-feeling-good-before-last-chance-to-get-what-we-all-want-so-much">clutching his hamstring</a> during the semi-final against Croatia – but he has since confirmed he is fine.</p>
<p>With the tournament taking place in the middle of many domestic football seasons, club fans may be wondering what impact the injuries and fatigue will have on players when competitions such as the Premier League and Champions League resume.</p>
<p>Premier League fixtures in England restart on December 26, having been on hold for 42 days. While many of this league’s players competed in Qatar, the majority – including two of its biggest stars, Erling Haaland of Manchester City and Liverpool’s Mohamed Salah – have enjoyed a mid-season rest before resuming training with their clubs.</p>
<h2>What does the research say?</h2>
<p>There is a lot of research that can be drawn on to help us form an idea of how this “winter World Cup” will impact injury incidence in the Premier League and other leagues throughout Europe.</p>
<p>For example, players involved in the French and Argentinian teams that have successfully made it to the World Cup final may play a total of seven games in 28 days. Games played in quick succession with little recovery time have been shown to result in a <a href="https://bjsm.bmj.com/content/bjsports/50/12/764.full.pdf">greater overall risk of injury</a>.</p>
<p><a href="https://bjsm.bmj.com/content/bjsports/49/9/599.full.pdf">Other research</a> shows that injury incidence during World Cup competitions ranges from 50.8 to 72.8 injuries per 1,000 hours. This translates to between six and eight injuries for teams who make it to the final stages. And <a href="https://link.springer.com/content/pdf/10.1007/s40279-020-01411-8.pdf">a study</a> across all international top-flight football activity between 2012 and 2020 found a match and training injury incidence of, respectively, 31.8 and 3.8 injuries per 1,000 hours of play.</p>
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<p>The injury incidence in international football tournaments is consistently higher than what is observed in domestic football (<a href="https://bjsm.bmj.com/content/bjsports/55/19/1084.full.pdf">23.8 injuries per 1,000 hours</a>). But one reason for this could be cumulative fatigue, as international tournaments normally take place at the end of a long domestic season.</p>
<p>The greater injury incidence could also be attributed to factors such as new forms of training and match-play style that players are unaccustomed to, travel fatigue, and additional physiological and psychological strain experienced during World Cups.</p>
<h2>The benefits of a winter break</h2>
<p>Match-play injury incidence is commonly reported to be around <a href="https://bjsm.bmj.com/content/bjsports/54/12/711.full.pdf">ten-times higher than in training</a>. More specifically, international match injury incidence (<a href="https://link.springer.com/content/pdf/10.1007/s40279-020-01411-8.pdf">31.8 injuries per 1,000 hours of play</a>) is considerably higher than domestic training injury incidence (<a href="https://bjsm.bmj.com/content/bjsports/55/19/1084.full.pdf">3.4 injuries per 1,000 hours</a>). </p>
<p>So the risk of injury for players not appearing in this World Cup is clearly much lower. For them, this period has replicated a “winter break”, which many leagues around the world now incorporate into their domestic seasons. </p>
<p>On average, European teams have a winter break of ten days. Teams who don’t have a winter break suffer a higher incidence of severe injuries – <a href="https://bjsm.bmj.com/content/bjsports/53/19/1231.full.pdf">losing 303 more player-days</a> each season, on average – compared with teams who do get a winter break. This indicates some potential positives for club teams who did not have many players in this World Cup.</p>
<p>On the other hand, the World Cup has enforced a much longer break from match-play for individuals not playing than the usual winter break. A period of 42 days without playing a competitive fixture – as Premier League players have experienced – is unusual for a professional footballer. </p>
<p>So when their season resumes on Boxing Day, matchplay may represent a “spike” in workload intensity due to the demands of games being much higher than training. Sudden spikes in workload underpin an <a href="https://reader.elsevier.com/reader/sd/pii/S1440244016302304?token=B825BD454C8CA465C0E53C4074F22336C211C264D9B0BAC0664B382EA5F62A1B0EC3AF35AFA2B514D78DD386AECAE14B&originRegion=eu-west-1&originCreation=20221118164551*">increased risk of injury</a>. This may lead to some non-World Cup players being unaccustomed to the nature and demands of playing matches, which may exacerbate their injury risk.</p><img src="https://counter.theconversation.com/content/193982/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The authors do not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>From factors like the number of extra games to the time non-competing players go on break, having the World Cup in the middle of the domestic season could increase injuries.Ian Varley, Associate professor, Nottingham Trent UniversityBradley Sprouse, Research Assistant in Sport Science, Nottingham Trent UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1962812022-12-12T04:15:39Z2022-12-12T04:15:39ZThousands more Australians died in 2022 than expected. COVID was behind the majority of them<figure><img src="https://images.theconversation.com/files/500267/original/file-20221212-94530-9fo5k3.jpg?ixlib=rb-1.1.0&rect=43%2C34%2C5699%2C3794&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/melbourne-australia-july-29-2022-600w-2184218879.jpg">Shutterstock/David L Young</a></span></figcaption></figure><p>Last month, the Australian Bureau of Statistics (ABS) released a <a href="https://www.abs.gov.au/statistics/health/causes-death/provisional-mortality-statistics/jan-jul-2022">report</a> of mortality statistics. It showed that from January to July 2022, there were 17% more deaths (16,375) than the average expected for these months. </p>
<p>This historical average is based on an average of the deaths for 2017, 2018, 2019 and 2021. They did not include 2020 in the baseline for 2022 data because it included periods where numbers of deaths were significantly lower than expected. The difference between the expected number of deaths based on historical data, and the actual number, is called “excess deaths”. </p>
<p>However, as the ABS points out in its report, using previous years as the predictor for the expected number of deaths does not take into account changes in population age structure over time, or potential improvements in mortality rates. </p>
<p>As we will see, the excess deaths this year were likely lower than the ABS estimate – but still overwhelmingly related to COVID and its effects on health.</p>
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<em>
<strong>
Read more:
<a href="https://theconversation.com/there-are-still-good-reasons-to-avoid-catching-covid-again-for-one-your-risk-of-long-covid-goes-up-each-time-196041">There are still good reasons to avoid catching COVID again – for one, your risk of long COVID goes up each time</a>
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</p>
<hr>
<h2>A different approach</h2>
<p>Last week, the Australian Actuaries Institute released its <a href="https://www.actuaries.digital/2022/12/07/covid-19-mortality-working-group-excess-mortality-continues-in-august-2022/">report</a> looking at excess deaths. Actuaries are statisticians who specialise in assessing risk, and most often work for insurance companies, superannuation funds, banks or government departments. </p>
<p>Unlike the ABS, the actuaries’ report adjusts the expected deaths for differences in age distributions over time using a <a href="https://www.aihw.gov.au/getmedia/95237794-4b77-4683-9f00-77c4d33e0e7c/13406.pdf.aspx?inline=true#:%7E:text=Direct%20age%2Dstandardisation%20accounts%20for,distribution%20of%20a%20standard%20population.">method</a> called “direct age-standardisation”. </p>
<p>The report also uses a <a href="https://en.wikipedia.org/wiki/Counterfactual_thinking">counterfactual</a> approach which basically asks, what would the number of deaths have been in the absence of the pandemic? Their comparison between recorded and expected deaths is likely to be more accurate than the ABS comparison. </p>
<h2>What the actuaries saw</h2>
<p>Both the Actuaries Institute report and the ABS separate COVID deaths into two categories:</p>
<ul>
<li><p>deaths from COVID, where COVID is listed as the primary or underlying cause of death</p></li>
<li><p>deaths with COVID, where the underlying cause of death has been determined as something other than COVID, but the virus was a contributing factor.</p></li>
</ul>
<p>The Actuaries Institute report shows 13% excess mortality for the first eight months of 2022 (approximately 15,400 deaths), substantially lower than the ABS estimate for the first seven months. </p>
<p>Just over half of the excess mortality – 8,200 deaths, are deaths <em>from</em> COVID. Another 2,100 deaths are deaths <em>with</em> COVID. The remaining excess of 5,100 deaths makes no mention of COVID on the death certificate.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/500270/original/file-20221212-94717-p3m533.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="black hearse at cemetery" src="https://images.theconversation.com/files/500270/original/file-20221212-94717-p3m533.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/500270/original/file-20221212-94717-p3m533.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=338&fit=crop&dpr=1 600w, https://images.theconversation.com/files/500270/original/file-20221212-94717-p3m533.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=338&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/500270/original/file-20221212-94717-p3m533.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=338&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/500270/original/file-20221212-94717-p3m533.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=424&fit=crop&dpr=1 754w, https://images.theconversation.com/files/500270/original/file-20221212-94717-p3m533.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=424&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/500270/original/file-20221212-94717-p3m533.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=424&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">COVID was not listed on thousands of death certificates, but was still likely a factor in many.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/sydney-nsw-australia-february-25-600w-1936556404.jpg">Shutterstock/Rose Makin</a></span>
</figcaption>
</figure>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/even-mild-covid-raises-the-chance-of-heart-attack-and-stroke-what-to-know-about-the-risks-ahead-190552">Even mild COVID raises the chance of heart attack and stroke. What to know about the risks ahead</a>
</strong>
</em>
</p>
<hr>
<h2>So what is the likely cause of those non-COVID excess deaths?</h2>
<p>The actuaries’ report gives the following possible explanations for excess deaths not listed as from or with COVID:</p>
<p><strong>Long COVID and interactions with other serious health conditions</strong></p>
<p>A previous COVID infection can cause later illness or death. We know COVID is associated with higher <a href="https://www.thelancet.com/journals/lanepe/article/PIIS2666-7762(22)00087-4/fulltext">risk</a> of death from heart disease, cancer and other causes. </p>
<p>But a doctor tasked with completing a death certificate may not identify a link between the death and a COVID infection months earlier. Therefore, it seems likely some deaths were due to late COVID effects.</p>
<p><strong>Delayed deaths from other causes</strong></p>
<p>Deaths from respiratory disease in 2020 and 2021 were <a href="https://medicalrepublic.com.au/respiratory-deaths-fell-during-second-covid-19-wave/38109">lower</a> than expected. This is presumably due to public health measures like mask wearing. While those measures were in place, people caught fewer respiratory diseases. Some people may have died earlier had their systems been stressed by respiratory disease during this time. So, some of the reported non-COVID excess deaths may be due to the catch-up effect of those people succumbing to underlying illnesses. </p>
<p><strong>Delays in emergency care</strong></p>
<p>Around Australia, our health systems are under pressure, with staff absences due to COVID, ambulance ramping, and bed blocks in our acute hospitals. </p>
<p>Unfortunately, there have been <a href="https://www.abc.net.au/news/2022-09-13/report-released-into-south-australia-ambulance-delays/101434904">cases</a> of people dying while waiting for an ambulance. It could be that people with conditions such as heart disease, cancer or diabetes may not be getting lifesaving emergency care due to these factors. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/covid-death-data-can-be-shared-to-make-it-look-like-vaccines-dont-work-or-worse-but-thats-not-the-whole-picture-172411">COVID death data can be shared to make it look like vaccines don't work, or worse – but that's not the whole picture</a>
</strong>
</em>
</p>
<hr>
<p><strong>Delays in routine care</strong></p>
<p>Over the pandemic period we have seen <a href="https://ahpa.com.au/advocacy/australians-are-delaying-healthcare-appointments-and-tests-during-covid-19/#:%7E:text=Of%20those%20surveyed%2C%2059%25%20were,services%20would%20be%20too%20busy.">delays</a> in people <a href="https://www.pwc.com.au/media/2021/pwc-global-health-industry-issues-survey.html">seeking</a> routine health care or attending <a href="https://www.aihw.gov.au/reports/australias-health/cancer-screening-and-treatment#How%20has%20the%20COVID-19%20pandemic%20impacted%20the%20cancer%20screening%20programs?">screening tests</a> for breast and cervical cancer. </p>
<p>There have also been <a href="https://9now.nine.com.au/a-current-affair/coronavirus-elective-surgery-covid19-holds-become-ticking-time-bombs-for-aussie-patients/630d03bc-87e9-4ba9-b6b4-791d2690bda2">delays</a> in elective surgery. And people may have been <a href="https://janesthanalgcritcare.biomedcentral.com/articles/10.1186/s44158-021-00032-5">avoiding</a> health-care settings due to fear of catching COVID. These delays in routine care may have led to deaths that would have been prevented in previous years. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/500274/original/file-20221212-96198-4pofku.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="person getting blood pressure checked" src="https://images.theconversation.com/files/500274/original/file-20221212-96198-4pofku.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/500274/original/file-20221212-96198-4pofku.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/500274/original/file-20221212-96198-4pofku.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/500274/original/file-20221212-96198-4pofku.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/500274/original/file-20221212-96198-4pofku.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/500274/original/file-20221212-96198-4pofku.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/500274/original/file-20221212-96198-4pofku.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Many people have delayed routine health checks since the start of the pandemic.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/african-american-patient-undergoing-routine-600w-2099534764.jpg">Shutterstock</a></span>
</figcaption>
</figure>
<p><strong>Pandemic lifestyle changes</strong></p>
<p>There is evidence in <a href="https://bmcpublichealth.biomedcentral.com/articles/10.1186/s12889-021-11971-7">Australia</a> and the <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7540284/">United Kingdom</a> a higher proportion of people made less healthy lifestyle choices during lockdowns, such as drinking more alcohol and exercising less. Higher risks for childhood obesity were also <a href="https://www.bmj.com/content/374/bmj.n1716">noted</a>. We could be starting to see the impact of these changes.</p>
<p><strong>Undiagnosed COVID</strong></p>
<p>It is almost certain some of the excess deaths are from unidentified COVID. Unfortunately in Australia, we have no firm data on the percentage of undiagnosed COVID cases, and even less on how that percentage might have changed over time. </p>
<p>So, the good news is the ABS excess death estimate of 17% more deaths in the first eight months of this year is likely an over-estimate, with the true rate closer to 13%. Of this 13%, some 7% are deaths from COVID, 2% are deaths with COVID, and much of the remaining 4% is likely to still be COVID-related in some way. </p>
<p>Last week, there were <a href="https://www.covid19data.com.au/deaths">219</a> COVID-related deaths reported. If the actuaries’ analysis is accurate, then the true number of COVID-related deaths last week was closer to 250 – a sobering thought as we approach the festive season. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/we-were-on-a-global-panel-looking-at-the-staggering-costs-of-covid-17-7m-deaths-and-counting-here-are-11-ways-to-stop-history-repeating-itself-190658">We were on a global panel looking at the staggering costs of COVID – 17.7m deaths and counting. Here are 11 ways to stop history repeating itself</a>
</strong>
</em>
</p>
<hr>
<p><em>Editor’s note: After publication, the ABS contacted The Conversation to clarify its Provisional Mortality Statistics should not be used or reported as official excess mortality estimates.</em></p><img src="https://counter.theconversation.com/content/196281/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Adrian Esterman receives funding from the MRFF, the NHMRC and the ARC.</span></em></p>There were deaths from COVID and deaths with COVID – but other deaths are also likely linked to the virus’s impact on our health and our medical care.Adrian Esterman, Professor of Biostatistics and Epidemiology, University of South AustraliaLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1892872022-12-06T21:35:54Z2022-12-06T21:35:54ZHeads or tails: What statistical models tell us about the probability of living beyond 110<figure><img src="https://images.theconversation.com/files/483348/original/file-20220907-4832-q9y5k0.jpeg?ixlib=rb-1.1.0&rect=8%2C2%2C988%2C663&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Is there a limit to human life expectancy?</span> <span class="attribution"><span class="source">(Shutterstock)</span></span></figcaption></figure><p>The world’s presumed oldest person, Kane Tanaka of Japan, died in April in her native country <a href="https://www.nytimes.com/2022/04/27/world/asia/kane-tanaka-japan-worlds-oldest-person.html">at the age of 119</a>. Despite her spectacular longevity, she could not surpass the record set by France’s <a href="https://academic.oup.com/biomedgerontology/article/74/Supplement_1/S13/5569844">Jeanne Calment</a> 25 years ago.</p>
<p>Calment died on August 4, 1997 at the age of 122 years and five months (or precisely <a href="https://www.nytimes.com/1997/08/05/world/jeanne-calment-world-s-elder-dies-at-122.html">44,724 days</a>).</p>
<p>What are the chances of this record being beaten?</p>
<p>My area of expertise, a branch of statistics that deals with the modelling of rare events, can provide some answers to such questions.</p>
<h2>The question is, how many candidates for a new world record?</h2>
<p>It is worth noting that the phenomenon under study is exceedingly rare: according to the last census, only 0.3 per cent of the Canadian population is centenarian, or just over <a href="https://www12.statcan.gc.ca/census-recensement/2021/as-sa/98-200-X/2021004/98-200-x2021004-eng.cfm">9,500 people</a>. That’s less than in Japan, which boasted nearly <a href="https://www.stat.go.jp/english/data/jinsui/tsuki/index.html">87,000 people over 100 years old</a> in 2021.</p>
<p>Only a handful of these centenarians, less than one in a thousand, will reach 110. People who live beyond this age, the “<a href="https://www.genome.gov/27559848/researchers-examine-supercentenarians-genomes-for-longevity-key">supercentenarians</a>”, are rare exceptions.</p>
<h2>Statistical models to the rescue</h2>
<p>To determine whether or not the longevity record could be shattered, it is essential to build statistical models that describe mortality beyond 110 years.</p>
<p>For this, we need <a href="https://link.springer.com/book/10.1007/978-3-030-49970-9">quality data</a>. For example, the age at death of supercentenarians must be validated by analyzing registers and birth certificates, among other things, particularly to <a href="https://link.springer.com/book/10.1007/978-3-642-11520-2">identify inconsistencies</a>. This involves archival work: errors are frequent (bad transcription, identity theft, <a href="https://www.yourdictionary.com/necronym">necronyms</a>) and several applications are rejected because of insufficient evidence to establish identity or date of birth with certainty. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/466651/original/file-20220601-20-exsvqb.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Handwriting on old paper" src="https://images.theconversation.com/files/466651/original/file-20220601-20-exsvqb.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/466651/original/file-20220601-20-exsvqb.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/466651/original/file-20220601-20-exsvqb.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/466651/original/file-20220601-20-exsvqb.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/466651/original/file-20220601-20-exsvqb.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/466651/original/file-20220601-20-exsvqb.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/466651/original/file-20220601-20-exsvqb.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Obtaining quality data on the actual age of supercentenarians is sometimes difficult.</span>
<span class="attribution"><span class="source">(Shutterstock)</span></span>
</figcaption>
</figure>
<p>The main source of information for my research is the <a href="https://www.supercentenarians.org/en/">International Longevity Database</a> (IDL), a joint effort of gerontologists and demographers who have recorded the age at death of more than 1,041 supercentenarians from several central European countries, Japan, Canada and the United States. </p>
<p>There are significantly <a href="https://www.supercentenarians.org/en/publications/">more female than male supercentenarians</a> on record, but this imbalance is shrinking over time in several countries, including the <a href="https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/ageing/bulletins/estimatesoftheveryoldincludingcentenarians/2002to2020">United Kingdom</a>. </p>
<p>Data validation requires going back 150 years, a period when administration and census taking were of mixed quality. Countries that provide data have teams of demographers actively working on longevity, as well as archives that facilitate validation. Without a robust system, the data cannot be used.</p>
<p>Once we have acquired the necessary data on people living beyond 110 years, we can then tackle the modelling of their lifetimes. The simplest statistical model that is compatible with the data is roughly equivalent to a coin toss. If the coin comes up heads, the person will survive until their next birthday; if not, they will die within a year.</p>
<p>This model also implies that the risk of dying is stable and does not depend on the person’s past history. <a href="https://royalsocietypublishing.org/doi/10.1098/rsos.202097">According to our calculations</a>, the life expectancy of a supercentenarian person would be about a year and five months, a very short period.</p>
<p>Surviving from 110 to 122 years, like Calment, would therefore be like tossing 12 heads in a row, an event that occurs less than once in a million. In light of the number of living supercentenarians, it is not surprising that Calment’s record still stands after a quarter of a century.</p>
<h2>Jeanne Calment, unbeatable?</h2>
<p>This makes our initial question all the more intriguing: will <a href="https://academic.oup.com/biomedgerontology/article/74/Supplement_1/S13/5569844">Calment’s record</a> ever be broken? If so, what will be the new record? To answer these questions, we need demographic projections of supercentenarians that take into account the world population increase.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/466652/original/file-20220601-48776-4z2nb3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="vieil homme sur fond noir" src="https://images.theconversation.com/files/466652/original/file-20220601-48776-4z2nb3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/466652/original/file-20220601-48776-4z2nb3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=399&fit=crop&dpr=1 600w, https://images.theconversation.com/files/466652/original/file-20220601-48776-4z2nb3.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=399&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/466652/original/file-20220601-48776-4z2nb3.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=399&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/466652/original/file-20220601-48776-4z2nb3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=501&fit=crop&dpr=1 754w, https://images.theconversation.com/files/466652/original/file-20220601-48776-4z2nb3.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=501&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/466652/original/file-20220601-48776-4z2nb3.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=501&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Will Jeanne Calment’s record age at death ever be surpassed?</span>
<span class="attribution"><span class="source">(Shutterstock)</span></span>
</figcaption>
</figure>
<p>Based on these demographic projections and the coin toss model, researchers at the University of Washington have concluded that there is a good chance that Calment’s record will be broken by 2100, but that it is unlikely that the winner will live <a href="https://www.demographic-research.org/volumes/vol44/52/">past 130 years</a>.</p>
<h2>Is there a limit to human life expectancy?</h2>
<p>Several scientific studies have argued recently that human longevity is limited. <a href="https://www.annualreviews.org/doi/10.1146/annurev-statistics-040120-025426">These studies often have one feature in common</a>: they ignore how the data are collected, which skews their conclusions. </p>
<p>While life expectancy varies from country to country, longevity is an intrinsic characteristic of humankind. It is therefore illogical that a Dutch person cannot survive beyond 114 years while a Japanese person has survived to 119 years.</p>
<p>If we compare life to a long-distance race, a limit to longevity would be the equivalent of an insurmountable obstacle at the end of the run. A more logical explanation from a biological standpoint is that the person stops once his or her resources are exhausted.</p>
<p>Extrapolating the maximum age is fraught with uncertainty because of the small number of supercentenarians whose age at death has been validated. The increase in the number of countries offering reliable and validated historical data on centenarians is nevertheless promising for future research. </p>
<p><a href="https://www.annualreviews.org/doi/10.1146/annurev-statistics-040120-025426">Our analysis</a> of several reliable databases suggests that a limit to life expectancy would be well beyond Calment’s age, and that it would be surprising if it were less than 130 years.</p>
<p>Having no limit does not mean that a person could live forever: while it is possible to get tails on any coin toss, a long sequence where each throw falls on the same side is unlikely. </p>
<p>Even with the increase in the world’s population, the high mortality rate of supercentenarians limits the possibility of breaking Calment’s record. Only time will tell if the record will be beaten.</p><img src="https://counter.theconversation.com/content/189287/count.gif" alt="La Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Léo R. Belzile's research is funded by the Natural Sciences and Engineering Research Council of Canada (NSERC) and IVADO.</span></em></p>The oldest person in the world, Kane Tanaka of Japan, died in April 2022 at 119 years. The record of Jeanne Calment of France, who died at 122, has stood for almost 25 years. Will it be beaten?Léo R. Belzile, Professeur adjoint de sciences de la décision, HEC MontréalLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1947932022-11-21T13:15:49Z2022-11-21T13:15:49ZPeople don’t mate randomly – but the flawed assumption that they do is an essential part of many studies linking genes to diseases and traits<figure><img src="https://images.theconversation.com/files/496010/original/file-20221117-25-slwoe3.jpg?ixlib=rb-1.1.0&rect=110%2C96%2C4690%2C2134&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Statistical pitfalls in GWAS can result in misleading conclusions about whether some traits (like long horns or spotted skin, in the case of dinosaurs) are genetically linked.</span> <span class="attribution"><span class="source">@meanymoo</span>, <a class="license" href="http://creativecommons.org/licenses/by-nc-nd/4.0/">CC BY-NC-ND</a></span></figcaption></figure><p>The idea that <a href="https://doi.org/10.1002/0471667196.ess0209.pub2">correlation does not imply causation</a> is a fundamental caveat in epidemiological research. A classic example involves a hypothetical link between ice cream sales and drownings – instead of increased ice cream consumption causing more people to drown, it’s plausible that a third variable, summer weather, is driving up an appetite for ice cream and swimming, and hence opportunities to drown.</p>
<p>But what about correlations involving genes? How can researchers be sure that a particular trait or disease is truly genetically linked, and not caused by something else?</p>
<p>We are <a href="https://www.richardborder.com">statistical</a> <a href="https://scholar.google.com/citations?user=SPXgieEAAAAJ&hl=en">geneticists</a> who study the genetic and nongenetic factors that influence human variation. In our <a href="https://www.science.org/doi/10.1126/science.abo2059">recently published research</a>, we found that the genetic links between traits found in many studies might not be connected by genes at all. Instead, many are a result of how humans mate.</p>
<h2>Genome-wide association studies try to link genes to traits</h2>
<p>Because the genes you inherit from your parents remain unchanged throughout your life, with rare exception, it makes sense to assume that there is a causal relationship between certain traits you have and your genetics.</p>
<p>This logic is the basis for <a href="https://www.genome.gov/about-genomics/fact-sheets/Genome-Wide-Association-Studies-Fact-Sheet">genome-wide association studies, or GWAS</a>. These studies collect DNA from many people to identify positions in the genome that might be correlated with a trait of interest. For example, if you have certain forms of the <a href="https://www.cancer.gov/about-cancer/causes-prevention/genetics/brca-fact-sheet"><em>BRCA1</em> and <em>BRCA2</em> genes</a>, you may have an increased risk for certain types of cancer.</p>
<p>Similarly, there may be gene variants that play a role in whether or not someone has schizophrenia. The hope is to learn something about the complex mechanisms that link variation at the molecular level to individual differences. With a clearer understanding of the genetic basis of different traits, scientists would be better able to determine risk factors for related diseases. </p>
<figure>
<iframe width="440" height="260" src="https://www.youtube.com/embed/sOP8WacfBM8?wmode=transparent&start=0" frameborder="0" allowfullscreen=""></iframe>
<figcaption><span class="caption">GWAS studies seek to find genetic associations between individual traits.</span></figcaption>
</figure>
<p>Researchers have run <a href="https://doi.org/10.1093/nar/gky1120">thousands of GWAS to date</a>, identifying genetic variants associated with myriad diseases and disease-related traits. In many instances, researchers have identified genetic variants that affect more than one trait. This form of biological overlap, in which the same genes are thought to influence several apparently unrelated traits, is known as <a href="https://doi.org/10.1186/s13073-016-0332-x">pleiotropy</a>. For example, certain variants of the <a href="https://medlineplus.gov/genetics/gene/pah"><em>PAH</em> gene</a> can have <a href="https://medlineplus.gov/genetics/condition/phenylketonuria/">several distinct effects</a>, including altering skin pigmentation and causing seizures.</p>
<p>One way scientists assess pleiotropy is through <a href="https://doi.org/10.1038/ng.3604">genetic correlation analysis</a>. Here, geneticists investigate whether the genes associated with a given trait are associated with other traits or diseases by statistically analyzing large samples of genetic data. Over the past decade, genetic correlation analysis has become the primary method for assessing potential pleiotropy across fields as diverse as <a href="https://doi.org/10.1038/ng.3406">internal medicine</a>, <a href="https://www.thessgac.org">social science</a> and <a href="https://doi.org/10.1017/s0033291717002318">psychiatry</a>. </p>
<p>Scientists use the findings from genetic correlation analyses to figure out the potential shared causes of these traits. For instance, if <a href="https://doi.org/10.1126/science.aap8757">genes associated with bipolar disorders</a> also predict anxiety disorders, perhaps the two conditions may partially involve some of the same neural circuits or respond to similar treatments.</p>
<h2>Assortative mating and genetic correlation</h2>
<p>However, just because a gene is correlated with two or more traits doesn’t necessarily mean it causes them.</p>
<p>Virtually all the statistical methods researchers commonly use to assess genetic correlations <a href="https://doi.org/10.1046/j.1439-0388.2002.00356.x">assume that mating is random</a>. That is, they assume that potential mating partners decide who they will have children with based on a roll of the dice. In reality, many factors likely influence who mates with whom. The simplest example of this is geography – people living in different parts of the world are less likely to end up together than people living nearby.</p>
<p>We wanted to find out how much the assumption of random mating affects the accuracy of genetic correlation analyses. In particular, we focused on the potential confounding effects of <a href="https://doi.org/10.1038/s41562-018-0476-3">assortative mating</a>, or how people tend to mate with those who share similar characteristics with them. Assortative mating is a widely documented phenomenon seen across a broad array of traits, interests, measures and social factors, including <a href="https://doi.org/10.1002/ajhb.22917">height</a>, <a href="https://doi.org/10.2307/2095670">education</a> and <a href="https://doi.org/10.1016/j.biopsych.2019.06.025">psychiatric conditions</a>.</p>
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<iframe width="440" height="260" src="https://www.youtube.com/embed/bK85aZPR3UY?wmode=transparent&start=0" frameborder="0" allowfullscreen=""></iframe>
<figcaption><span class="caption">Humans do not mate randomly – rather, people tend to gravitate toward certain traits.</span></figcaption>
</figure>
<p>In <a href="https://doi.org/10.1126/science.abo2059">our study</a> we examined cross-trait assortative mating, whereby people with one trait (for example, being tall) tend to mate with people with a completely different trait (for example, being wealthy). From our database of 413,980 mate pairs in the U.K. and Denmark, we found evidence of cross-trait assortative mating for many traits – for instance, an individual’s time spent in formal schooling was correlated not only with their mate’s educational attainment, but also with many other characteristics, including height, smoking behaviors and risk for different diseases.</p>
<p>We found that taking into consideration the similarities across mates could strongly predict which traits would be considered genetically linked. In other words, just based on how many characteristics a pair of mates shared, we could identify around 75% of the presumed genetic links between these traits – all without sampling any DNA.</p>
<h2>Genetic correlation does not imply causation</h2>
<p>Cross-trait assortative mating shapes the genome. If people with one heritable trait tend to mate with people with another heritable trait, then these two distinct characteristics will become genetically correlated to each other in subsequent generations. This will happen regardless of whether or not these traits are truly genetically linked to each other.</p>
<p>Cross-trait assortative mating means that the genes you inherit from one parent will be correlated with those you inherit from the other. How people mate is not random, violating the key assumption behind genetic correlation analyses. This inflates the genetic association between traits that aren’t truly linked together by genes.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/495756/original/file-20221116-21-hyom6p.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Illustration of dinosaurs with and without long horns or spiked backs." src="https://images.theconversation.com/files/495756/original/file-20221116-21-hyom6p.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/495756/original/file-20221116-21-hyom6p.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=424&fit=crop&dpr=1 600w, https://images.theconversation.com/files/495756/original/file-20221116-21-hyom6p.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=424&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/495756/original/file-20221116-21-hyom6p.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=424&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/495756/original/file-20221116-21-hyom6p.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=533&fit=crop&dpr=1 754w, https://images.theconversation.com/files/495756/original/file-20221116-21-hyom6p.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=533&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/495756/original/file-20221116-21-hyom6p.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=533&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">If dinosaurs with long horns preferentially mate with dinosaurs with spiked backs, genes for both of these traits can become associated with each other in subsequent generations even though the same gene doesn’t code for them.</span>
<span class="attribution"><span class="source">Aaqilah M</span>, <a class="license" href="http://creativecommons.org/licenses/by-nc-nd/4.0/">CC BY-NC-ND</a></span>
</figcaption>
</figure>
<p>Recent studies corroborate our findings. Earlier this year, researchers computed genetic correlations using a method that examines the association between the <a href="https://doi.org/10.1038/s41588-022-01062-7">traits and genes of siblings</a>. The genetic links between traits influenced by cross-trait assortative mating were substantially weakened.</p>
<p>But without accounting for cross-trait assortative mating, using genetic correlation estimates to study the biological pathways causing disease can be misleading. Genes that affect only one trait will appear to influence multiple different conditions. For example, a genetic test designed to assess the risk for one disease may incorrectly detect vulnerability for a broad number of unrelated conditions.</p>
<p>The ability to measure variation across individuals at the genetic and molecular level is truly a feat of modern science. However, genetic epidemiology is still an observational enterprise, subject to the same caveats and challenges facing other forms of nonexperimental research. Though our findings don’t discount all genetic epidemiology research, understanding what genetic studies are truly measuring will be essential to translate research findings into new ways to treat and assess disease.</p><img src="https://counter.theconversation.com/content/194793/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Richard Border receives funding from the National Institutes of Health.</span></em></p><p class="fine-print"><em><span>Noah Zaitlen receives funding from the NIH, NSF, DoD, and CZI. </span></em></p>People don’t randomly select who they have children with. And that means an underlying assumption in research that tries to link particular genes to certain diseases or traits is wrong.Richard Border, Postdoctoral Researcher in Statistical Genetics, University of California, Los AngelesNoah Zaitlen, Professor of Neurology and Human Genetics, University of California, Los AngelesLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1908822022-09-29T12:32:25Z2022-09-29T12:32:25ZUN slavery estimate raises question: Are 50 million people really enslaved today?<figure><img src="https://images.theconversation.com/files/486639/original/file-20220926-26-nievn5.jpg?ixlib=rb-1.1.0&rect=529%2C41%2C1467%2C1287&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Forced laborers lived in prison cells at one palm oil plantation in Indonesia. </span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/news-photo/private-prison-cell-is-seen-at-house-former-head-of-news-photo/1238075980?adppopup=true"> Kiki Cahyadi/Anadolu Agency via Getty Images</a></span></figcaption></figure><p>According to the United Nations, <a href="https://news.un.org/en/story/2022/09/1126421">about 50 million people</a> are enslaved worldwide.</p>
<p>The report, released Sept. 12, 2022, by the U.N.’s <a href="http://www.ilo.org">International Labor Organization</a>, <a href="https://www.iom.int">the International Organization for Migration</a> and the human rights group <a href="https://www.walkfree.org">the Walk Free Foundation</a>, revealed that 28 million people are in forced labor and another 22 million in forced marriage. </p>
<p>Forced labor includes exploitation in domestic work, agriculture and manufacturing. It also includes state-imposed forced labor and commercial sexual exploitation. Poverty is a powerful driver for forced labor around the globe, particularly in India, East Asia and West Africa. </p>
<p>Forced marriage, mainly affecting women and girls, often has gendered, patriarchal roots. </p>
<p>The U.N.’s latest estimate of 50 million has grown substantially <a href="https://www.cnn.com/2017/09/19/world/global-slavery-estimates-ilo">since its last estimate in 2017</a>, when it reported 40 million persons were enslaved. </p>
<p><a href="https://scholar.google.com/citations?user=WuHCE3sAAAAJ&hl=en">As someone who studies modern slavery</a>, I am intrigued by global estimates. </p>
<p>Are there really 50 million persons living in slavery today as the U.N. claims? </p>
<p>What explains how the global estimate increased by 10 million over five years? Does that mean we will see an annual increase of 2 million slaves each year moving forward? </p>
<h2>Getting better at global estimates</h2>
<p>Global estimates of modern slavery have improved over time. </p>
<p>In 2013, Walk Free’s <a href="https://scholarship.richmond.edu/cgi/viewcontent.cgi?article=1031&context=polisci-faculty-publications">first Global Slavery Index</a> reported 29.8 million persons enslaved. </p>
<p>But that estimate was based almost entirely on expert input instead of nationally representative random sample surveys – the gold standard of research design. </p>
<p>For its <a href="https://legacy.globalslaveryindex.org/download/">2016 Global Slavery Index</a>, <a href="https://www.walkfree.org/">Walk Free</a> partnered with <a href="https://www.gallup.com/home.aspx">Gallup</a> and commissioned random sample surveys for 25 countries. </p>
<p>By partnering with the world’s premier polling organization and using advanced survey techniques, Walk Free was able to embark on groundbreaking work.</p>
<p>However, Walk Free ended up generating a global estimate for 168 nations, not just the 25 nations it had surveyed. That meant for the other countries in its 2016 estimate, Walk Free relied on both expert input and statistical techniques – and didn’t solely use nationally representative survey data. </p>
<h2>The devil in the details</h2>
<p>That same technique of mixing survey data with statistical techniques applies to the U.N.’s 2017 and 2022 global estimates. </p>
<p>For its <a href="https://www.alliance87.org/global_estimates_of_modern_slavery-forced_labour_and_forced_marriage.pdf">2017 estimate</a>, the U.N., working with Walk Free and other organizations, commissioned surveys in 48 countries from 2014 to 2016. And for its <a href="https://www.ilo.org/wcmsp5/groups/public/---ed_norm/---ipec/documents/publication/wcms_854733.pdf">2022 report</a>, the U.N. gathered data from 68 countries to estimate forced marriage and from 75 countries to estimate forced labor. </p>
<p>Though the report revealed a clear increase in the number of nationally representative surveys to generate these global estimates, it still fell short in measuring a majority of the countries in the world. </p>
<p>There are currently <a href="https://www.un.org/en/about-us">193 member states</a> in the United Nations. The U.N.’s 2022 global estimate that surveyed 75 countries to estimate forced labor did not survey the remaining 118 countries, instead basing its numbers on expert input and statistical techniques. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/417728/original/file-20210825-23-1jren5z.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="A view from above shows buildings in a grid, with identifying labels such as police station, hospital and visitation center." src="https://images.theconversation.com/files/417728/original/file-20210825-23-1jren5z.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/417728/original/file-20210825-23-1jren5z.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=540&fit=crop&dpr=1 600w, https://images.theconversation.com/files/417728/original/file-20210825-23-1jren5z.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=540&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/417728/original/file-20210825-23-1jren5z.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=540&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/417728/original/file-20210825-23-1jren5z.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=679&fit=crop&dpr=1 754w, https://images.theconversation.com/files/417728/original/file-20210825-23-1jren5z.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=679&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/417728/original/file-20210825-23-1jren5z.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=679&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">A 2018 satellite image shows detention camps built near the Kunshan Industrial Park in China’s Xinjiang region.</span>
<span class="attribution"><span class="source">Planet Labs/AP,</span></span>
</figcaption>
</figure>
<p>Nor did the U.N. publish a full list of the countries for which it conducted nationally representative surveys in 2017. It’s difficult, then, to know how many of those 48 countries sampled for the 2017 report were repeated for the 2022 report. </p>
<p>We also don’t have publicly available data for those 48 countries, let alone the countries surveyed for the 2022 global estimate. </p>
<p>And without access to any of the statistical calculations made by the U.N. for either estimates, scholars cannot independently replicate the findings of the U.N. for either of its 2017 or 2022 reports. </p>
<h2>Comparing apples and oranges</h2>
<p>This lack of transparency makes it difficult to claim that there really was an increase of 10 million in the number of enslaved persons from 2017 to 2022. </p>
<p>Two things are happening here. The U.N. seems to be getting much better at estimating global slavery. But because the survey techniques are improving over time, it is impossible to make comparisons. </p>
<p>Consider the analogy of a bathroom scale. In weighing yourself, you might purchase an inexpensive scale at first just to get a rough idea of how much you weigh. But then, becoming more concerned about your health, you then purchase a much better scale that gives you a far more precise measurement. </p>
<p>This doesn’t mean that your weight changed radically. It just means you now have a much better sense of your weight. </p>
<p>This analogy applies to measuring contemporary slavery. </p>
<p>The scale used by Walk Free was novel in 2013, and improved by 2016. The scale the U.N. used in 2017 was more precise, and the figures for 2022 got even better. </p>
<p>But to go back and say there are 10 million more persons enslaved today than there were in 2017 is not warranted. </p>
<h2>Finding clarity</h2>
<p>Global estimates of modern slavery are eye-catching and important.</p>
<p>The 50 million figure today is one of the best estimates of modern slavery available and can prompt policymakers to take action. Without awareness of this crime, the problem cannot be solved. </p>
<p>Yet, moving forward, the public still needs more reliable, more valid and more transparent data. Science advances on the promise that data is freely available to enable others to replicate or improve the analysis.</p><img src="https://counter.theconversation.com/content/190882/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Monti Datta was a consultant with the Walk Free Foundation from 2013 to 2016.</span></em></p>Global estimates of modern-day slavery by the United Nations reveal improving methods for calculating the data.Monti Datta, Associate Professor of Political Science, University of RichmondLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1864882022-08-18T15:10:12Z2022-08-18T15:10:12ZBeyond GDP: changing how we measure progress is key to tackling a world in crisis – three leading experts<p>It’s an odd quirk of history that, on the first day of his ill-fated presidential campaign in March 1968, Robert F Kennedy chose to talk to his audience about the <a href="https://cusp.ac.uk/themes/aetw/rfk-gdp50/">limitations of gross domestic product</a>* (GDP) – the world’s headline indicator of economic progress.</p>
<p>It seems stranger still that, despite the power of that iconic speech, growth in <a href="https://www.imf.org/external/pubs/ft/fandd/basics/gdp.htm">GDP</a> remains to this day the predominant measure of progress across the world. Economic success is measured by it. Government policy is assessed by it. Political survival hangs on it.</p>
<p>Kennedy’s speech inspired a host of critiques. It has been quoted by presidents, prime ministers and Nobel laureates. <a href="https://press.princeton.edu/books/paperback/9780691169859/gdp">Yet GDP itself has survived until now</a>, more-or-less unscathed. But amid ever-louder concerns about the failure of national economies to tackle the multiple threats posed by climate change, spiralling energy costs, insecure employment and widening levels of inequality, the need to define and measure progress in a different way now looks as unarguable as it is urgent.</p>
<h2>The goods, the bads, and the missing</h2>
<p>In simple terms, GDP is a measure of the size of a country’s economy: how much is produced, how much is earned, and how much is spent on goods and services across the nation. The monetary total, whether in dollars or euros, yuan or yen, is then adjusted for any general increase in prices to give a measure of “real” economic growth over time. When governments adopt policies to pursue economic growth, this is how those policies are evaluated.</p>
<p>Since 1953, GDP has been the headline measure in a complex <a href="https://unstats.un.org/unsd/nationalaccount/sna.asp#:%7E:text=The%20System%20of%20National%20Accounts%20(SNA)&text=The%20SNA%20describes%20a%20coherent,definitions%2C%20classifications%20and%20accounting%20rules.">system of national accounts</a> overseen by the United Nations. Developed during the second world war, these accounts were motivated in part by the need to determine how much governments could afford to spend on the war effort.</p>
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<p><strong><em>This story is part of Conversation Insights</em></strong>
<br><em>The Insights team generates <a href="https://theconversation.com/uk/topics/insights-series-71218">long-form journalism</a> and is working with academics from different backgrounds who have been engaged in projects to tackle societal and scientific challenges.</em></p>
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<p>But in measuring the monetary value of economic activity, GDP can incorporate many of the “bads” that detract from our quality of life. War, pollution, crime, <a href="https://theconversation.com/is-prostitution-really-worth-5-7-billion-a-year-33497">prostitution</a>, traffic congestion, disasters like wildfires and the destruction of nature – all can have a positive impact on GDP. Yet they cannot really be construed as components of economic success.</p>
<p>At the same time, there are numerous aspects of our lives that simply go missing from this conventional account. The inequality in our societies. The contributions from unpaid work. The labour of those who care for the young and the elderly at home or in the community. The depletion of natural resources or biodiversity. And the value of data and many digital services.</p>
<p>What lies outside the market, including public services funded out of taxation, remains unmeasured in a metric of monetary exchange. Kennedy was blunt: “[GDP] measures everything, in short, except that which makes life worthwhile.”</p>
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<p>It’s a sentiment that has resonance half a century later. In a striking encounter during the Brexit debate, a UK academic was trying to convey to a public meeting the dangers of leaving the EU. The impact on GDP would dwarf any savings from the UK’s contributions to the EU budget, he told the audience. “That’s your bloody GDP!” <a href="https://www.theguardian.com/commentisfree/2017/jan/10/blunt-heckler-economists-failing-us-booming-britain-gdp-london">shouted</a> a woman in the crowd. “It’s not ours.”</p>
<p>This sense of an indicator out of touch with reality may be one of the reasons there is momentum for reform. When GDP conceals crucial differences between the richest and the poorest in society, it inevitably says little about the prospects for ordinary people.</p>
<p>But there are other reasons too for an emerging change of heart. The pursuit of GDP growth as a policy goal, and the impact that has on government, business and personal decision-making, has accompanied increasing devastation of the natural world, a loss of forests and habitats, the destabilisation of the climate, and near-meltdowns of the world’s financial markets. At the same time, GDP has become a poor measure of the technological transformation of society.</p>
<p>Its tenacity as a measure of progress, despite these well-known limitations, arises from factors which are on the one hand technocratic, and on the other sociological. As the headline measure in a sophisticated system of national accounts, GDP has a technocratic convenience and analytical elegance that remains unsurpassed by many alternative measures. Its authority arises from its ability to be simultaneously a measure of production output, consumption expenditure and income in the economy.</p>
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Read more:
<a href="https://theconversation.com/gdp-numbers-are-not-what-they-seem-how-they-boost-us-and-uk-at-expense-of-developing-countries-162468">GDP numbers are not what they seem: how they boost US and UK at expense of developing countries</a>
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<p>Despite this complex framework, it also offers the deceptive simplicity of a single headline figure which appears to be directly comparable from year to year and across nations, based on the simple (if inadequate) idea that more economic activity necessarily leads to a better life.</p>
<p>However, the combined technical authority and political usefulness of this idea has led to “path dependence” and forms of social lock-in that are difficult to address without significant effort. Think of switching to an alternative as being like switching from driving on the left to the right-hand side of the road.</p>
<p>Yet what we measure matters. And while we’re busy looking in the wrong direction, as Kennedy pointed out, bad things can happen. Kennedy’s campaign – and his critique of GDP – was cut cruelly short on June 5 1968, when he was fatally wounded by an assassin’s bullet. More than half a century later, his call for reform of how we assess progress (or its absence) has never been stronger.</p>
<h2>The trouble with GDP: historical flaws</h2>
<p>The way societies have understood and measured progress has changed considerably over the centuries. Measurement of “the economy” as a whole is a relatively modern, 20th-century concept, beginning with efforts by statisticians and economists such as Colin Clark and Simon Kuznets in the 1920s and 1930s to understand the impact of financial crisis and depression.</p>
<p>Kuznets, now best known for his <a href="https://www.sciencedirect.com/topics/earth-and-planetary-sciences/environmental-kuznets-curve">curve</a> describing the relationship between GDP and income inequality, was particularly concerned to develop a measure of economic welfare rather than just activity. For example, he argued for omitting expenditures that were unwelcome necessities rather than services or goods consumers actively wanted – such as defence spending.</p>
<p>However, the second world war overtook and absorbed these earlier notions of a single measure of economic welfare, resulting in what first became modern gross national product <a href="https://apps.bea.gov/scb/2021/03-march/pdf/0321-reprint-gnp.pdf">(GNP</a>), and then GDP. The imperative – set out on the Allied side by John Maynard Keynes in his 1940 pamphlet <a href="https://fraser.stlouisfed.org/title/pay-war-6021">How to Pay for the War</a> – was measuring productive capacity, and the reduction in consumption required to have enough resources to support the military effort. Economic welfare was a peacetime concern.</p>
<p>Post-war, unsurprisingly, American and British economists such as Milton Gilbert, James Meade and Richard Stone took the lead in codifying these statistical definitions through the UN – and its process for agreeing and formalising definitions in the system of national accounts (SNA) is still in place today. However, since at least the 1940s, some important inadequacies of both the SNA and GDP have been widely known and debated.</p>
<p>Indeed, as long ago as 1934, Margaret Reid published her book <a href="https://www.journals.uchicago.edu/doi/10.1086/255033">Economics of Household Production</a>, which pointed out the need to include unpaid work in the home when thinking about economically useful activity.</p>
<p>The question of whether and how to measure the household and informal sectors was debated during the 1950s – particularly as this makes up a larger share of activity in low-income countries – but was omitted until some countries, including the UK, started to create <a href="https://www.ons.gov.uk/economy/nationalaccounts/satelliteaccounts/compendium/householdsatelliteaccounts/previousReleases">household satellite accounts</a> around 2000. Omitting unpaid work meant, for instance, that the UK’s increased productivity growth between the 1960s and 1980s was then overstated, because it in part reflected the <a href="https://voxeu.org/article/changing-business-cycles-role-women-s-employment">inclusion of many more women in paid work</a> whose contributions had previously been invisible to the national GDP metric.</p>
<p>Another longstanding and widely understood failure of GDP is not including environmental externalities and the depletion of natural capital. The metric takes incomplete account of many activities that do not have market prices, and ignores the additional social costs of pollution, greenhouse gas emissions and similar outputs associated with economic activities.</p>
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Read more:
<a href="https://theconversation.com/an-obsession-with-economic-growth-will-not-make-the-best-use-of-natural-assets-30283">An obsession with economic growth will not make the best use of natural assets</a>
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<p>What’s more, the depletion or loss of assets such as natural resources (or indeed buildings and infrastructure lost in disasters) boosts GDP in the short term because these resources are used in economic activities, or because there is a surge in construction after a disaster. Yet the long-term opportunity costs are never counted. This massive shortcoming was widely discussed at the time of landmark publications such as the <a href="https://www.clubofrome.org/publication/the-limits-to-growth/">1972 Limits to Growth report</a> from the Club of Rome, and the 1987 <a href="https://www.are.admin.ch/are/en/home/media/publications/sustainable-development/brundtland-report.html">Brundtland Report</a> from the World Commission on Environment and Development.</p>
<p>As with household and informal activity, there has been recent progress in accounting for nature, with the development of the <a href="https://seea.un.org/content/about-seea">System of Environmental Economic Accounting</a> (SEEA) and publication of regular (but separate) statistics on natural capital in a number of countries. The <a href="https://www.ons.gov.uk/economy/environmentalaccounts/methodologies/naturalcapital">UK</a> has again been a pioneer in this area, while the <a href="https://www.whitehouse.gov/ostp/news-updates/2022/04/24/accounting-for-nature-on-earth-day-2022/">US recently announced</a> it would start following this approach too.</p>
<h2>New challenges to the value of GDP</h2>
<p>Other, perhaps less obvious failings of GDP have become more prominent recently. Digitisation of the economy has transformed the way many people spend their days in work and leisure, and the way many businesses operate, yet these transformations are not apparent in official statistics.</p>
<p>Measuring innovation has always been tricky, because new goods or improved quality need to be incorporated into observable prices and quantities – and what is the metric for a unit of software or management consultancy? But it is harder now because many digital services are “free” at point of use, or have the features of public goods in that many people can use them at the same time, or are intangible. For example, data is without doubt improving the productivity of companies that know how to use it to improve their services and produce goods more effectively – but how should a dataset’s value, or potential value, to society (as opposed to a big tech company) be estimated?</p>
<p><a href="https://www.insee.fr/en/statistiques/4770156?sommaire=4770271">Recent work</a> looking at the price of telecommunications services in the UK has estimated that output growth in this sector since 2010 has ranged anywhere from <a href="https://www.ons.gov.uk/economy/nationalaccounts/uksectoraccounts/methodologies/doubledeflationmethodsanddeflatorimprovementstouknationalaccountsbluebook2021">about 0% to 90%</a>, depending on how the price index used to convert market prices to real (inflation-adjusted) prices takes account of the economic value of our rapidly growing use of data. Similarly, it is not obvious how to incorporate advertising-funded “free” search, crypto currencies and <a href="https://theconversation.com/nfts-explained-what-they-are-why-rock-stars-are-using-them-and-why-theyre-selling-for-millions-of-dollars-156389#:%7E:text=NFTs%20are%20digital%20certificates%20that,alternative%20to%20a%20central%20database.">NFTs</a> in the measurement framework.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/479625/original/file-20220817-8075-ynmg73.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Crowd looking into art showroom" src="https://images.theconversation.com/files/479625/original/file-20220817-8075-ynmg73.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/479625/original/file-20220817-8075-ynmg73.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/479625/original/file-20220817-8075-ynmg73.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/479625/original/file-20220817-8075-ynmg73.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/479625/original/file-20220817-8075-ynmg73.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/479625/original/file-20220817-8075-ynmg73.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/479625/original/file-20220817-8075-ynmg73.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=503&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
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<span class="caption">Street artist Banksy’s temporary showroom critiquing global society in south London, October 2019.</span>
<span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/london-uk-october-2-2019-crowds-1523572547">Shutterstock</a></span>
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<p>A key limitation of GDP, particularly in terms of its use as an indicator of social progress, is that it offers no systematic account of the distribution of incomes. It is entirely possible for average or aggregate GDP to be rising, even as a significant proportion of the population find themselves worse off.</p>
<p>Ordinary incomes have stagnated or fallen in recent decades even as the richest in society have become wealthier. In the US, for example, <a href="https://www.nytimes.com/interactive/2017/08/07/opinion/leonhardt-income-inequality.html">Thomas Piketty and his colleagues</a> have shown that in the period between 1980 and 2016, the top 0.001% of society saw their incomes grow by an average of 6% per year. Income for the poorest 5% of society fell in real terms.</p>
<p>Given these many issues, it might seem surprising that the debate about “<a href="https://www.bennettinstitute.cam.ac.uk/blog/beyond-gdp-impact/">Beyond GDP</a>” is only now – possibly – turning into actions to change the official statistical framework. But paradoxically, one hurdle has been the proliferation of alternative progress metrics.</p>
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Read more:
<a href="https://theconversation.com/how-poorer-citizens-pay-the-price-of-economic-change-in-the-uk-172356">How poorer citizens pay the price of economic change in the UK</a>
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<p>Whether these are single indices that combine a number of different indicators or dashboards showcasing a wide range of metrics, they have been ad hoc and too varied to build consensus around a new global way of measuring progress. Few of them provide an economic framework for consideration of trade-offs between the separate indicators, or guidance as to how to interpret indicators moving in different directions. There is a breadth of information but as a call to action, this cannot compete against the clarity of a single GDP statistic.</p>
<p>Statistical measurement is like a technical standard such as voltage in electricity networks or the Highway Code’s rules of the road: a shared standard or definition is essential. While an overwhelming majority might agree on the need to go beyond GDP, there also needs to be enough agreement about what “beyond” actually involves before meaningful progress on how we measure progress can be made.</p>
<h2>Change behaviour, not just what we measure</h2>
<p>There are many <a href="https://theconversation.com/uk/search?adapter=pg3&date=all&language=en&page=2&q=beyond+GDP&sort=relevancy">visions to supplant GDP growth</a> as the dominant definition of progress and better lives. In the wake of the COVID pandemic, it has been reported that most people want a <a href="https://theconversation.com/life-after-covid-most-people-dont-want-a-return-to-normal-they-want-a-fairer-more-sustainable-future-173290">fairer, more sustainable future</a>.</p>
<p>Politicians can make it sound straightforward. Writing in 2009, the then-French president Nicolas Sarkozy explained he had convened a commission – led by internationally acclaimed economists Amartya Sen, Joseph Stiglitz and Jean-Paul Fitoussi – on the measurement of economic performance and social progress on the basis of a firm belief: that we will not change our behaviour “unless we change the ways we measure our economic performance”.</p>
<p>Sarkozy also committed to encouraging other countries and international organisations to follow the example of France in implementing <a href="https://ec.europa.eu/eurostat/documents/8131721/8131772/Stiglitz-Sen-Fitoussi-Commission-report.pdf">his commission’s recommendations</a> for a suite of measures beyond GDP. The ambition was no less than the construction of a new global economic, social and environmental order.</p>
<p>In 2010, the recently-elected UK prime minister, David Cameron, launched a programme to implement the Sarkozy commission’s recommendations in the UK. He described this as starting to measure progress as a country “not just by how our economy is growing, but by how our lives are improving – not just by our standard of living, but by our quality of life”.</p>
<p>Once again, the emphasis was on measurement (how far have we got?) rather than behaviour change (what should people do differently?). The implication is that changing what we measure necessarily leads to different behaviours – but the relationship is not that simple. Measures and measurers exist in political and social spheres, not as absolute facts and neutral agents to be accepted by all.</p>
<p>This should not dissuade statisticians from developing new measures, but it should prompt them to engage with all who might be affected – not just those in public policy, commerce or industry. The point after all is to change behaviour, not just to change the measures.</p>
<p>Economists are increasingly adopting complex systems thinking, including both social and psychological understandings of human behaviour. For example, <a href="https://www.economist.com/letters/2017/09/14/letters-to-the-editor">Jonathan Michie</a> has pointed to ethical and cultural values, as well as public policy and the market economy, as the big influences on behaviour. <a href="https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3548365">Katharina Lima di Miranda and Dennis Snower</a> have highlighted social solidarity, individual agency and concern for the environment alongside the “traditional” economic incentives captured by GDP.</p>
<h2>GDP alternatives in practice</h2>
<p>Since Kennedy’s 1968 critique, there have been numerous initiatives to replace, augment or complement GDP over the years. Many dozens of indicators have been devised and implemented at local, national and international scales.</p>
<p>Some aim to account more directly for subjective wellbeing, for example by measuring self-reported life satisfaction or “happiness”. Some hope to reflect more accurately the state of our natural or social assets by developing adjusted monetary and non-monetary measures of “<a href="https://www.worldbank.org/en/news/press-release/2021/10/27/global-wealth-has-grown-but-at-the-expense-of-future-prosperity-world-bank">inclusive wealth</a>” (including a team at the University of Cambridge led by this article’s co-author Diane Coyle). The UK government has accepted this as a meaningful approach to measurement in several recent policy documents, including its <a href="https://www.gov.uk/government/publications/levelling-up-the-united-kingdom">Levelling Up white paper</a>.</p>
<p>There are two fundamental arguments for a wealth-based approach:</p>
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<li><p>It embeds consideration for sustainability in the valuing of all assets: their value today depends on the entire future flow of services they make available. This is exactly why stockmarket prices can fall or rise suddenly, when expectations about the future change. Similarly, the prices at which assets such as natural resources or the climate are valued are not just market prices; the true “accounting prices” include social costs and externalities.</p></li>
<li><p>It also introduces several dimensions of progress, and flags up the correlations between them. Inclusive wealth includes produced, natural and human capital, and also intangible and social or organisational capital. Using a comprehensive wealth balance sheet to inform decisions could contribute to making better use of resources – for example, by considering the close links between sustaining natural assets and the social and human capital context of people living in areas where those assets are under threat.</p></li>
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<p>Other initiatives aim to capture the multi-dimensional nature of social progress by compiling a dashboard of indicators – often measured in non-monetary terms – each of which attempts to track some aspect of what matters to society.</p>
<p>New Zealand’s <a href="https://www.treasury.govt.nz/information-and-services/nz-economy/higher-living-standards/our-living-standards-framework">Living Standards Framework</a> is the best-known example of this dashboard approach. Dating back to a 1988 Royal Commission on Social Policy and developed over more than a decade within the New Zealand Treasury, this framework was precipitated by the need to do something about the discrepancy between what GDP can reflect and the ultimate aim of the Treasury: to make life better for people in New Zealand.</p>
<p>The NZ Treasury now uses it to allocate fiscal budgets in a manner consistent with the identified needs of the country in relation to social and environmental progress. The relevance to combating climate change is particularly clear: if government spending and investment are focused on narrow measures of economic output, there is every possibility that the deep decarbonisation needed to achieve a just transition to a <a href="https://theconversation.com/uk/topics/net-zero-carbon-economy-102230">net zero carbon economy</a> will be impossible. Equally, by identifying areas of society with declining wellbeing, such as children’s mental health, it becomes possible to allocate Treasury resources directly to alleviate the problem.</p>
<p>The <a href="https://www.ons.gov.uk/peoplepopulationandcommunity/wellbeing/articles/measuringnationalwellbeing/apr2017">UK’s Measuring National Wellbeing</a> (MNW) programme, directed by Paul Allin (a co-author of this article), was launched in November 2010 as part of a government-led drive to place greater emphasis on wellbeing in national life and business. Much of the emphasis was on the subjective <a href="https://www.ons.gov.uk/peoplepopulationandcommunity/wellbeing/bulletins/measuringnationalwellbeing/april2020tomarch2021">personal wellbeing measures</a> that the UK’s Office for National Statistics (ONS) continues to collect and publish, and which appear to be increasingly taken up as policy goals (driven in part by the <a href="https://whatworkswellbeing.org/">What Works Centre for Wellbeing</a>).</p>
<p>The MNW team was also charged with addressing the full “beyond GDP” agenda, and undertook a large consultation and engagement exercise to find out what matters to people in the UK. This provided the basis for a <a href="https://www.ons.gov.uk/peoplepopulationandcommunity/wellbeing/articles/measuringnationalwellbeing/internationalcomparisons2019">set of indicators</a> covering ten broad areas which are updated by the ONS from time to time. While these indicators <a href="https://www.ons.gov.uk/releases/qualityoflifeintheukaugust2022">continue to be published</a>, there is no evidence that they are being used to supplement GDP as the UK’s measure of progress.</p>
<p>Accounting for inequality within a single aggregate index is obviously tricky. But several solutions to this problem exist. One of them, advocated by the Sen-Stiglitz-Fitoussi commission, is to report median rather than mean (or average) values when calculating GDP per head.</p>
<p>Another fascinating possibility is to adjust the aggregate measure using a welfare-based index of inequality, such as the one devised by the late Tony Atkinson. An exercise using the <a href="https://www.census.gov/topics/income-poverty/income-inequality/about/metrics/atkinson-index.html">Atkinson index</a> carried out by Tim Jackson, also a co-author of this article, calculated that the <a href="https://limits2growth.org.uk/publication/aetw_no2/">welfare loss associated with inequality</a> in the UK in 2016 amounted to almost £240 billion – around twice the annual budget of the NHS at that time.</p>
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Read more:
<a href="https://theconversation.com/the-search-for-an-alternative-to-gdp-to-measure-a-nations-progress-the-new-zealand-experience-118169">The search for an alternative to GDP to measure a nation's progress – the New Zealand experience</a>
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<p>Among the most ambitious attempts to create a single alternative to GDP is a measure which has become known as the <a href="https://oxfordre.com/environmentalscience/view/10.1093/acrefore/9780199389414.001.0001/acrefore-9780199389414-e-776">Genuine Progress Indicator</a> (GPI). Proposed initially by economist Herman Daly and theologian John Cobb, GPI attempts to adjust GDP for a range of factors – environmental, social and financial – which are not sufficiently well reflected in GDP itself.</p>
<p>GPI has been used as a progress indicator in the US state of Maryland since 2015. Indeed, a <a href="https://www.congress.gov/bill/117th-congress/house-bill/4894?r=5&s=1">bill introduced to US Congress in July 2021</a> would, if enacted, require the Department of Commerce to publish a US GPI, and to “use both the indicator and GDP for budgetary reporting and economic forecasting”. GPI is also used in <a href="http://www.gpiatlantic.org/">Atlantic Canada</a>, where the process of building and publishing the index forms part of this community’s approach to its development.</p>
<h2>A potential gamechanger?</h2>
<p>In 2021, the UN secretary-general António Guterres concluded his Our Common Agenda <a href="https://www.un.org/en/content/common-agenda-report/assets/pdf/Common_Agenda_Report_English.pdf">report</a> with a call for action. “We must urgently find measures of progress that complement GDP, as we were tasked to do by 2030 in target 17.19 of the <a href="https://sdgs.un.org/2030agenda">Sustainable Development Goals</a>.” He repeated this demand in his <a href="https://www.un.org/sg/en/content/sg/speeches/2022-01-21/remarks-general-assembly-his-priorities-for-2022">priorities for 2022</a> speech to the UN General Assembly.</p>
<p>Guterres called for a process “to bring together member states, international financial institutions and statistical, science and policy experts to identify a complement or complements to GDP that will measure inclusive and sustainable growth and prosperity, building on the work of the Statistical Commission”.</p>
<p>The first manual explaining the UN’s system of national accounts was published in 1953. It has since been through five revisions (the last in 2008) designed to catch up with developments in the economy and financial markets, as well as to meet user needs across the world for a wider spread of information.</p>
<p><a href="https://unstats.un.org/unsd/nationalaccount/Towards2025.asp">The next SNA revision</a> is currently in development, led by the UN Statistics Division and mainly involving national statistical offices, <a href="https://www.escoe.ac.uk/programmes/national-accounts-and-beyond-gdp/">other statistical experts</a> and institutional stakeholders such as the IMF, World Bank and Eurostat.</p>
<p>But unlike the UN’s COP processes relating to climate change and, to a lesser extent, biodiversity, there has, to date, been little wider engagement with interested parties – from business leaders and political parties to civil society, non-governmental organisations and the general public.</p>
<p>As the British science writer <a href="https://www.bbc.co.uk/sounds/play/m000ynb8">Ehsan Masood</a> has observed, this revision process is happening below the radar of most people who are not currently users of national accounts. And this means many very useful ideas that could be being fed in are going unheard by those who will ultimately make decisions about how nations measure their progress in the future.</p>
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Read more:
<a href="https://theconversation.com/why-uks-treasured-free-market-economy-will-not-achieve-net-zero-180922">Why UK's 'treasured free-market economy' will not achieve net zero</a>
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<p>The essence of sustainable development was captured in the 1987 <a href="https://www.un.org/esa/sustdev/csd/csd15/media/backgrounder_brundtland.pdf">Brundtland Report</a>: “To contribute to the welfare and wellbeing of the current generation, without compromising the potential of future generations for a better quality of life.” Yet it remains unclear how the next SNA revision will provide such an intergenerational lens, despite a new focus on “missing” capitals including natural capital.</p>
<p>Similarly, while the revision programme is addressing globalisation issues, these are only about global production and trade – not, for example, the impacts of national economies on the environment and wellbeing of other countries and populations.</p>
<p>Ambitious deadlines have been set further into the future: achieving the UN’s Sustainable Development Goals by 2030, and reducing global net emissions of greenhouse gases to zero before 2050. The SNA revision process – which will see a new system of national accounts agreed in 2023 and enacted from 2025 – is a key step in achieving these longer-term goals. That is why opening up this revision process to wider debate and scrutiny is so important.</p>
<h2>It’s time to abandon this ‘GDP fetish’</h2>
<p>One lesson to learn from the history of indicators, such as those about poverty and social exclusion, is that their impact and effectiveness depends not only on their technical robustness and their fitness for purpose, but also on the political and social context – what are the needs of the time, and the prevailing climate of ideas?</p>
<p>The current SNA revision should be a process as much about the use and usefulness of new measures as about their methodological rigour. Indeed, we might go as far as <a href="https://www.ft.com/content/e3b356b4-dbcc-42ef-811d-74d649139916">Gus O’Donnell</a>, the former UK cabinet secretary, who said in 2020: “Of course measurement is hard. But roughly measuring the right concepts is a better way to make policy choices than using more precise measures of the wrong concepts.”</p>
<p>In short, there is an inherent tension involved in constructing an alternative to GDP – namely achieving a balance between technical robustness and social resonance. The complexity of a dashboard of indicators such as New Zealand’s Living Standards Framework is both an advantage in terms of meaningfulness, and a disadvantage in terms of communicability. In contrast, the simplicity of a single measure of progress such as the Genuine Progress Indicator – or, indeed, GDP – is both an advantage in terms of communication, and a disadvantage in terms of its inability to provide a more nuanced picture of progress.</p>
<p>Ultimately, a plurality of indicators is probably essential in navigating a pathway towards a sustainable prosperity that takes full account of individual and societal wellbeing. Having a wider range of measures should allow for more diverse narratives of progress.</p>
<p>Some momentum in the current SNA revisions process and ongoing statistical research is directed toward measurement of inclusive wealth – building on the economics of sustainability brought together in <a href="https://www.gov.uk/government/publications/final-report-the-economics-of-biodiversity-the-dasgupta-review">Partha Dasgupta’s recent review of the economics of biodiversity</a>. This framework can probably gain a broad consensus among economists and statisticians, and is already being implemented by the UN, starting with natural capital and environmental accounting.</p>
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Read more:
<a href="https://theconversation.com/nature-how-do-you-put-a-price-on-something-that-has-infinite-worth-154704">Nature: how do you put a price on something that has infinite worth?</a>
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<p>Including wellbeing measures in the mix would signal that wellbeing matters, at least to some of us, while also recognising that many different things can affect wellbeing. The evidence to date is that planting wellbeing measures in a different part of the data ecosystem means they will be overlooked or ignored. Wellbeing measures are not a panacea, but without them we will continue to do things that restrict rather than enhance wellbeing and fail to recognise the potential economic, social and environmental benefits that a wellbeing focus should bring.</p>
<p>The task of updating the statistical framework to measure economic progress better is non-trivial. The development of the SNA and its spread to many countries took years or even decades. New data collection methodologies should be able to speed things up now – but the first step in getting political buy-in to a better framework for the measurement of progress is an agreement about what to move to.</p>
<p>National accounting needs what the name suggests: an internally-consistent, exhaustive and mutually exclusive set of definitions and classifications. A new framework will require collecting different source data, and therefore changing the processes embedded in national statistical offices. It will need to incorporate recent changes in the economy due to digitalisation, as well as the long-standing issues such as inadequate measurement of environmental change.</p>
<figure class="align-center ">
<img alt="Politician surrounded by children in a street" src="https://images.theconversation.com/files/479656/original/file-20220817-1692-564oum.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/479656/original/file-20220817-1692-564oum.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=480&fit=crop&dpr=1 600w, https://images.theconversation.com/files/479656/original/file-20220817-1692-564oum.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=480&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/479656/original/file-20220817-1692-564oum.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=480&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/479656/original/file-20220817-1692-564oum.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=603&fit=crop&dpr=1 754w, https://images.theconversation.com/files/479656/original/file-20220817-1692-564oum.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=603&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/479656/original/file-20220817-1692-564oum.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=603&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">‘That which makes life worthwhile’: Robert Kennedy visits a summer reading programme in Harlem, 1963.</span>
<span class="attribution"><a class="source" href="https://www.alamy.com/stock-photo-attorney-general-robert-kennedy-surrounded-by-african-american-children-50061032.html?imageid=DDD82FF2-5A5A-4E7C-82DC-5E56884212EA&p=167342&pn=1&searchId=0c74a3c5497b7d923e9264b334f535ea&searchtype=0">Alamy</a></span>
</figcaption>
</figure>
<p>Ultimately, this “beyond GDP” process needs to grapple not only with measurement problems but also with the various uses and abuses to which GDP has been put. Kennedy’s neat summary that it measures “everything except that which makes life worthwhile” points as much to the misuse of GDP as to its statistical limitations. Its elegance in being simultaneously a measure of income, spending and output means that in some form, it is likely to remain a valid tool for macroeconomic analysis. But its use as an unequivocal arbiter of social progress was never appropriate, and probably never will be.</p>
<p>Clearly, the desire to know if society is moving in the right direction remains a legitimate and important goal – perhaps more so now than ever. But in their search for a reliable guide towards social wellbeing, governments, businesses, statisticians, climate scientists and all other interested parties must abandon once and for all what the Nobel Laureate Stiglitz called a “GDP fetish”, and work with civil society, the media and the public to establish a more effective framework for measuring progress.</p>
<p><em>*Strictly speaking, Robert Kennedy referred to gross national product (GNP) in his 1968 speech. You can read more about the UN’s Towards the 2025 SNA process <a href="https://unstats.un.org/unsd/nationalaccount/towards2025.asp">here</a>.</em></p>
<hr>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/313478/original/file-20200204-41481-1n8vco4.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/313478/original/file-20200204-41481-1n8vco4.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=112&fit=crop&dpr=1 600w, https://images.theconversation.com/files/313478/original/file-20200204-41481-1n8vco4.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=112&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/313478/original/file-20200204-41481-1n8vco4.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=112&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/313478/original/file-20200204-41481-1n8vco4.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=140&fit=crop&dpr=1 754w, https://images.theconversation.com/files/313478/original/file-20200204-41481-1n8vco4.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=140&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/313478/original/file-20200204-41481-1n8vco4.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=140&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<span class="caption"></span>
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<p><em>For you: more from our <a href="https://theconversation.com/uk/topics/insights-series-71218?utm_source=TCUK&utm_medium=linkback&utm_campaign=TCUKengagement&utm_content=InsightsUK">Insights series</a>:</em></p>
<ul>
<li><p><em><a href="https://theconversation.com/climate-scientists-concept-of-net-zero-is-a-dangerous-trap-157368?utm_source=TCUK&utm_medium=linkback&utm_campaign=TCUKengagement&utm_content=InsightsUK">Climate scientists: concept of net zero is a dangerous trap
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<li><p><em><a href="https://theconversation.com/sexual-exploitation-by-un-peacekeepers-in-drc-fatherless-children-speak-for-first-time-about-the-pain-of-being-abandoned-188248?utm_source=TCUK&utm_medium=linkback&utm_campaign=TCUKengagement&utm_content=InsightsUK">Sexual exploitation by UN peacekeepers in DRC: fatherless children speak for first time about the pain of being abandoned
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<p class="fine-print"><em><span>Paul Allin is a member of the UK National Statistician's Expert User Advisory Committee and he is the Royal Statistical Society's Honorary Officer for National Statistics. Views expressed in this article are personal do not necessarily represent those of the NSEUAC or the RSS.. </span></em></p><p class="fine-print"><em><span>Diane Coyle receives funding from the Economic Statistics Centre of Excellence and ESRC via the Productivity Institute. She is a member of the UK National Statistician's Expert User Advisory Committee and of the Royal Statistical Society. These are personal views. </span></em></p><p class="fine-print"><em><span>Tim Jackson is Director of the Centre for the Understanding of Sustainable Prosperity which receives funding from the Economic and Social Research Council and Laudes Foundation. CUSP provides the secretariat for the All-Party Parliamentary Group on Limits to Growth. The views expressed here are personal.</span></em></p>Amid the global threats posed by climate change, spiralling energy costs, insecure employment and widening inequality, the need to rethink our notion of progress is now an urgent priority.Paul Allin, Visiting Professor in Statistics, Imperial College LondonDiane Coyle, Professor of Public Policy, University of CambridgeTim Jackson, Professor of Sustainable Development and Director of the Centre for the Understanding of Sustainable Prosperity (CUSP), University of SurreyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1846252022-08-10T12:18:22Z2022-08-10T12:18:22ZOld age isn’t a modern phenomenon – many people lived long enough to grow old in the olden days, too<figure><img src="https://images.theconversation.com/files/478361/original/file-20220809-16-3s77rh.jpg?ixlib=rb-1.1.0&rect=668%2C129%2C5728%2C2901&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">If you made it past early childhood, your chances got better to see your golden years.</span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/illustration/midwife-bathing-newborn-after-birth-in-royalty-free-illustration/1039652044">Grafissimo/DigitalVision Vectors via Getty Images</a></span></figcaption></figure><p>Every year I ask the college students in the course I teach about the <a href="https://scholarworks.wmich.edu/cgi/viewcontent.cgi?article=1011&context=tmg">14th-century Black Death</a> to imagine they are farmers or nuns or nobles in the Middle Ages. What would their lives have been like in the face of this terrifying disease that killed millions of people in just a few years?</p>
<p>Setting aside how they envision what it would be like to confront the plague, these undergrads often figure that during the medieval period they would already be considered middle-aged or elderly at the age of 20. Rather than being in the prime of life, they think they’d soon be decrepit and dead.</p>
<p>They’re reflecting a common misperception that long life spans in humans are very recent, and that no one in the past lived much beyond their 30s.</p>
<p>But that’s just not true. <a href="https://scholar.google.com/citations?user=5mhMQ-8AAAAJ&hl=en&oi=ao">I am a bioarchaeologist</a>, which means that I <a href="https://doi.org/10.1002/ajpa.23322">study human skeletons excavated from archaeological sites</a> to understand what life was like in the past. I’m especially interested in <a href="https://doi.org/10.1002/ajpa.23317">demography</a> – mortality (deaths), fertility (births) and migration – and how it was linked with <a href="https://doi.org/10.1073/pnas.0705460105">health conditions and diseases</a> such as the <a href="https://doi.org/10.1371/journal.pone.0096513">Black Death</a> hundreds or thousands of years ago. There’s physical evidence that plenty of people in the past lived long lives – just as long as some people do today.</p>
<h2>Bones record the length of a life</h2>
<p>One of the first steps in research about demography in the past is to estimate how old people were when they died. Bioarchaeologists do this using information about how your bones and teeth change as you get older.</p>
<p>For example, I look for changes to <a href="https://doi.org/10.1016/j.forsciint.2011.11.031">joints in the pelvis</a> that are common at older ages. Observations of these joints in people today whose ages we know allow us to estimate ages for people from archaeological sites with joints that look similar.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/478359/original/file-20220809-16-1w3he4.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="jawbone with teeth, a tooth, and a microscopy view of layers within a tooth's cementum" src="https://images.theconversation.com/files/478359/original/file-20220809-16-1w3he4.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/478359/original/file-20220809-16-1w3he4.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=268&fit=crop&dpr=1 600w, https://images.theconversation.com/files/478359/original/file-20220809-16-1w3he4.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=268&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/478359/original/file-20220809-16-1w3he4.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=268&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/478359/original/file-20220809-16-1w3he4.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=337&fit=crop&dpr=1 754w, https://images.theconversation.com/files/478359/original/file-20220809-16-1w3he4.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=337&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/478359/original/file-20220809-16-1w3he4.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=337&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">A researcher can count the layers within a tooth that were added over time to determine how old a person lived to be.</span>
<span class="attribution"><a class="source" href="https://commons.wikimedia.org/wiki/File:Cementochronology.tif">Benoitbertrand1974/Wikimedia Commons</a>, <a class="license" href="http://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA</a></span>
</figcaption>
</figure>
<p>Another way to estimate age is to use a microscope to count the yearly additions of a mineralized tissue called cementum on teeth. It’s similar to counting a tree’s rings to see how many years it lived. Using approaches like these, <a href="https://doi.org/10.1371/journal.pone.0096513">many</a> <a href="https://doi.org/10.1016/j.ijpp.2015.05.001">studies</a> have documented the existence of people who lived long lives in the past.</p>
<p>For example, by examining skeletal remains, anthropologist <a href="https://www.semanticscholar.org/author/Meggan-Bullock/36970527">Meggan Bullock</a> and colleagues found that in the city of Cholula, Mexico, between 900 and 1531, most people who <a href="https://doi.org/10.1002/ajpa.22329">made it to adulthood lived past the age of 50</a>.</p>
<p>And of course there are many examples from historical records of people who lived very <a href="https://www.medievalists.net/2022/05/most-important-people-middle-ages/">long lives in the past</a>. For example, the sixth-century Roman Emperor Justinian I <a href="https://www.worldhistory.org/article/782/justinians-plague-541-542-ce/">reportedly died at the age of 83</a>.</p>
<p>Analysis of the tooth development of an ancient anatomically modern <em>Homo sapiens</em> individual from Morocco suggests that our species has experienced <a href="https://doi.org/10.1073/pnas.0700747104">long life spans for at least the past 160,000 years</a>.</p>
<h2>Clearing up a math misunderstanding</h2>
<p>Given physical and historical evidence that many people did live long lives in the past, why does the misperception that everyone was dead by the age of 30 or 40 persist? It stems from confusion about the difference between individual life spans and life expectancy.</p>
<p><a href="https://ourworldindata.org/life-expectancy-how-is-it-calculated-and-how-should-it-be-interpreted">Life expectancy</a> is the average number of years of life remaining for people of a particular age. For example, <a href="https://jech.bmj.com/content/55/1/38">life expectancy at birth (age 0)</a> is the average length of life for newborns. Life expectancy at age 25 is how much longer people live on average given they’ve survived to age 25.</p>
<p>In medieval England, life expectancy at birth for boys born to families that owned land was a mere <a href="https://doi.org/10.1093/ije/dyi211">31.3 years</a>. However, <a href="https://doi.org/10.1080/08898480902790387">life expectancy at age 25</a> for landowners in medieval England was 25.7. This means that people in that era who celebrated their 25th birthday could expect to live until they were 50.7, on average – 25.7 more years. While 50 might not seem old by today’s standards, remember that this is an average, so many people would have lived much longer, into their 70s, 80s and even older.</p>
<p>Life expectancy is a population-level statistic that reflects the conditions and experiences of a huge variety of people with very different health conditions and behaviors, some who die at very young ages, some who live to be over 100 years old, and lots whose life spans fall somewhere in between. Life expectancy is not a promise (or a threat!) about the life span of any single person.</p>
<p>What some people don’t realize is that low life expectancy at birth for any population usually reflects very high rates of <a href="https://www.cdc.gov/reproductivehealth/maternalinfanthealth/infantmortality.htm">infant mortality</a>. That’s a measure of deaths in the first year of life. Given that life expectancies reflect averages for a population, a high number of deaths at very young ages will skew calculations of life expectancy at birth toward younger ages. But typically, many people in those populations who make it past the vulnerable infant and early childhood years can expect to live relatively long lives.</p>
<p>Advances in <a href="https://doi.org/10.1371/journal.pone.0262802">modern sanitation</a> – which reduce the spread of diarrheal diseases that are a major killer of infants – <a href="https://doi.org/10.1073/pnas.1413559111">and vaccinations</a> can greatly increase life expectancies.</p>
<p>Consider the effect of infant mortality on overall age patterns in two contemporary populations with dramatically different life expectancies at birth.</p>
<p><iframe id="aP2wK" class="tc-infographic-datawrapper" src="https://datawrapper.dwcdn.net/aP2wK/3/" height="400px" width="100%" style="border: none" frameborder="0"></iframe></p>
<p>In <a href="https://www.cia.gov/the-world-factbook/countries/afghanistan/">Afghanistan, life expectancy at birth</a> is low, at just over 53 years, and infant mortality is high, at almost 105 deaths for every 1,000 children born.</p>
<p>In <a href="https://www.cia.gov/the-world-factbook/countries/singapore/#people-and-society">Singapore, life expectancy at birth</a> is much higher, at over 86 years, and infant mortality is very low – fewer than two infants die for every 1,000 who are born. In both countries, people do survive to very old ages. But in Afghanistan, because so many more people die at very young ages, proportionally fewer people survive to old age. </p>
<h2>Living a long life has long been possible</h2>
<p>It’s incorrect to view long lives as a remarkable and unique characteristic of the “modern” era.</p>
<p>Knowing that people often did have long lives in the past might help you feel more connected with the past. For example, you can imagine multigenerational households and gatherings, with grandparents in Neolithic China or Medieval England bouncing their grandchildren on their knees and telling them stories about their own childhoods decades before. You might have more in common with people who lived long ago than you had realized.</p><img src="https://counter.theconversation.com/content/184625/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Sharon DeWitte receives funding from the National Science Foundation.</span></em></p>Nasty, brutish – but not necessarily short. Here’s how archaeologists know plenty of people didn’t die young.Sharon DeWitte, Professor of Anthropology, University of South CarolinaLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1646762022-07-28T12:23:35Z2022-07-28T12:23:35ZWomen are better at statistics than they think<figure><img src="https://images.theconversation.com/files/413758/original/file-20210729-25-1fao6bt.jpeg?ixlib=rb-1.1.0&rect=60%2C0%2C6720%2C4466&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Undergraduate students at the University of Nebraska Omaha collaborate on a group assignment for a STEM course.</span> <span class="attribution"><span class="source">Derrick Nero, University of Nebraska Omaha</span>, <a class="license" href="http://creativecommons.org/licenses/by-nc-nd/4.0/">CC BY-NC-ND</a></span></figcaption></figure><p><em>The <a href="https://theconversation.com/us/topics/research-brief-83231">Research Brief</a> is a short take about interesting academic work.</em></p>
<h2>The big idea</h2>
<p>Women in statistics classes do better academically than men over a semester despite having more negative attitudes regarding their own abilities, according to our recent study in the <a href="https://doi.org/10.1080/26939169.2022.2093805">Journal of Statistics and Data Science Education</a>. </p>
<p>Using data from more than 100 male and female students from multiple statistics classes, <a href="https://scholar.google.com/citations?user=p35egd0AAAAJ&hl=en&oi=ao">my colleague</a> <a href="https://scholar.google.com/citations?user=2NQw3F0AAAAJ&hl=en">and I</a> assessed gender differences in grades over the course of a semester. As part of the study, students also answered surveys at the start and end of the semester that measured six different things: their fear of statistics teachers in general; their thoughts about the usefulness of statistics; their perceptions of their own mathematical ability; their anxiety in taking tests; their anxiety in interpreting statistics; and their fear of asking for help.</p>
<p>Overall, we found that students with more negative perceptions of their own mathematical ability had lower grades over the course of the semester. What’s even more interesting are the gender differences that emerged.</p>
<p>Even though men and women scored similarly on exams at the start of the semester, women finished the semester with almost 10% higher final exam grades. This was the case even though women had significantly worse attitudes about their mathematical abilities at the start of the semester than their male counterparts.</p>
<p>At the beginning of the semester specifically, women were more likely to rate their mathematical abilities as lower than men in the class and report more anxiety toward exams and toward interpreting statistical findings. However, each of these self-assessments improved over the course of the semester such that women’s attitudes didn’t differ from men’s by the end. </p>
<p>Meanwhile, the grades of male students who reported fear of statistics teachers or fear of asking for help decreased more sharply over the course of the semester. For men whose attitudes improved during the semester, grades also improved – though not as much as women’s grades improved.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/475718/original/file-20220723-16881-vx6abm.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="line graph showing association of fear of asking for help and grades among men and women over the course of a semester" src="https://images.theconversation.com/files/475718/original/file-20220723-16881-vx6abm.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/475718/original/file-20220723-16881-vx6abm.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=199&fit=crop&dpr=1 600w, https://images.theconversation.com/files/475718/original/file-20220723-16881-vx6abm.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=199&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/475718/original/file-20220723-16881-vx6abm.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=199&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/475718/original/file-20220723-16881-vx6abm.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=250&fit=crop&dpr=1 754w, https://images.theconversation.com/files/475718/original/file-20220723-16881-vx6abm.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=250&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/475718/original/file-20220723-16881-vx6abm.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=250&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Figure reflecting the effect of fear of asking for help and its change over time among women and men. Average grades decreased overall across the semester, likely because of coursework getting more challenging over time.</span>
<span class="attribution"><span class="source">Jonathan Santo</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<h2>Why it matters</h2>
<p>A number of studies have shown that from an early age, <a href="https://www.psychologytoday.com/us/blog/the-moment-youth/201912/learning-math-are-boys-better-girls">boys and girls learn math equally well</a>. </p>
<p>However, <a href="https://www.nber.org/papers/w20909">girls are less likely to be called on</a> in math classes than boys, even when they raise their hands as much as boys do. Moreover, some teachers unconsciously <a href="https://www.nber.org/papers/w20909">grade girls’ math tests more harshly than boys’</a>. By middle school, gender differences in math scores emerge. These factors may contribute to adult women’s being more likely to rate themselves <a href="https://knowledge.wharton.upenn.edu/article/gender-gap-mathematics-achievement/">as less mathematically skilled than men</a>. As a result, <a href="https://www.wgu.edu/blog/why-are-there-so-few-women-in-stem1907.html">women are also less likely to pursue STEM</a> – science, technology, engineering and math – occupations.</p>
<p>The results from our study, <a href="https://www.jstor.org/stable/pdf/1165255.pdf">in line with others</a>, bolster the notion that women have the potential to do as well as men, and even better, in STEM fields, such as statistics. We contend that <a href="https://thehill.com/changing-america/enrichment/education/557138-why-girls-are-better-at-math-but-dont-get-stem-jobs">women would benefit from additional mentoring</a> to encourage them as they begin pursuing STEM-related education.</p>
<h2>What still isn’t known</h2>
<p>The evidence above provides hints at some of the causes of the gender discrepancy in perceived ability. However, there is much we still don’t know.</p>
<p>For example, why did the attitudes of the women in our study improve over time? Was it based on their confidence in their abilities as their grades improved, or did their statistics teachers influence their perception of their own abilities over time? </p>
<p>More research is needed to understand exactly how women differed from men in their attitudes over the course of the school semester, among other questions. In particular, we’d like to disentangle exactly which classroom or instructor factors can lead to better attitudes among students, ultimately translating to better grades.</p><img src="https://counter.theconversation.com/content/164676/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Jonathan B. Santo received funding from the Social Sciences and Humanities Research Council (SSHRC) of Canada and Fonds Québécois de la Recherche Sur la Société et la Culture (FQRSC). He is a member of the Society for Research in Child Development and the International Society for the Study of Behavioral Development.</span></em></p><p class="fine-print"><em><span>Kelly Rhea MacArthur does not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Female statistics students had higher final exam grades than their male peers, even though they had less confidence in their statistics abilities at the start of the semester.Jonathan B. Santo, Professor of Psychology, University of Nebraska OmahaKelly Rhea MacArthur, Associate Professor of Sociology, University of Nebraska OmahaLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1790822022-03-22T12:16:35Z2022-03-22T12:16:35ZThe ‘hot hand’ is a real basketball phenomenon – but only some players have the ability to go on these basket-making streaks<figure><img src="https://images.theconversation.com/files/453118/original/file-20220318-19-gfjkk4.jpg?ixlib=rb-1.1.0&rect=233%2C0%2C5748%2C3161&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Kevin Durant is one of the NBA players who shows the ability to go on hot streaks.</span> <span class="attribution"><a class="source" href="https://newsroom.ap.org/detail/KnicksNetsBasketball/e57ce0bc5e624b1ea17f1892fd47d63b/photo?Query=kevin%20durant&mediaType=photo&sortBy=&dateRange=now-14d&totalCount=59&currentItemNo=2">AP Photo/Seth Wenig</a></span></figcaption></figure><p>March Madness is here, and basketball fans are making predictions: Who will be the <a href="https://www.ncaa.com/news/basketball-men/article/2021-03-01/11-greatest-march-madness-cinderella-stories">Cinderella story of the college tournament</a>? Which teams will make a run to the Final Four? And of course, which player is going to get “hot” and carry their team to a championship?</p>
<p>To say a player is “hot” or has “hot hands” means the player is on a streak of making many consecutive shots. A question that has dogged researchers, coaches and fans for years is whether players on these streaks can defy random chance, or if hot hands are just an illusion and fit within statistical norms.</p>
<p>We are two researchers who study <a href="https://scholar.google.com/citations?user=mVj8o7gAAAAJ&hl=en">information sciences</a> and <a href="https://kelley.iu.edu/faculty-research/faculty-directory/profile.html?id=WINSTON">operations and decision technologies</a>. In <a href="https://doi.org/10.1371/journal.pone.0261890">our recent study</a>, we examined whether players can indeed get hot in actual live-game situations. Our analysis showed that some players do get consistently “hot” during games and make more shots than expected following two shots made consecutively. However, when we looked at all players together, we found that usually when a player makes more shots than normal after making consecutive shots, they are likely to revert toward the shooting average by missing the next one. Hot hands do exist, but they are rare.</p>
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<figcaption><span class="caption">When players get hot, they are a force to be reckoned with on a basketball court.</span></figcaption>
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<h2>The science of going on a streak</h2>
<p>Fans have always believed in the ability of players to go on a hot streak – as reflected in video games like <a href="https://www.si.com/extra-mustard/2013/11/25/why-on-fire-lives-on-20-years-after-nba-jam">NBA Jam where the virtual ball would catch fire</a> if a player made multiple shots in a row. But academics have been skeptical of the idea ever since a 1985 study concluded that what people perceive as hot hands is nothing more than the <a href="https://doi.org/10.1016/0010-0285(85)90010-6">human brain’s tendency to misunderstand chance and averages.</a></p>
<p>This changed in 2017 when a seminal paper showed that the original study – and the later ones based on it – <a href="https://theconversation.com/momentum-isnt-magic-vindicating-the-hot-hand-with-the-mathematics-of-streaks-74786">suffered from small but significant selection bias</a> that threw off the statistical calculations. Basically, the way the team chose which shots to look at when searching for streaks or a hot hand threw the math itself off. When researchers accounted for this bias, the hot hand turned out to be real. </p>
<p>The vast majority of studies on hot streaks in basketball have focused on <a href="https://doi.org/10.1016/0010-0285(85)90010-6">either free throws</a>, <a href="https://doi.org/10.1016/j.euroecorev.2021.103771">three-point contests</a> or <a href="http://dx.doi.org/10.2139/ssrn.2450479">controlled field experiments</a>. We wanted to test the theory in actual competitive games and used data from the 2013-14 and 2014-15 NBA seasons. But in actual game situations, shots are not identical. To control for this, we <a href="https://doi.org/10.1371/journal.pone.0261890">developed a model that predicts how often a shot will go in</a> based on a number of different factors. These included who the shooter was, the distance from the basket, the type of shot, the distance from the closest defender, who the closest defender was, whether the shot was assisted and other considerations. It is only thanks to the modern, <a href="https://theconversation.com/the-nfl-joins-the-data-revolution-in-sports-64717">data-driven era of sports</a> that we could even do such an analysis.</p>
<p>Using this model, we were able to simulate any shot by flipping a figurative coin that represents the probability any particular shot will go in. We could then quantify the hot hand effect by comparing the real world field goal percentage of a player after they were on a streak with the expected percentage obtained through simulating the same shots in our model.</p>
<p>For example, imagine that in the real world a player made 55% of shots after making the two shots before. But our model only predicted he would hit 46% of shots after making the two shots before. If this difference between the model prediction and the real world is statistically significant over time, then it is <a href="https://doi.org/10.1371/journal.pone.0261890">good evidence that the player can get hot and go on streaks</a>.</p>
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<h2>Who has the hot hand?</h2>
<p>Our analysis looked at 153 players who took at least 1,000 shots during the 2013-14 and 2014-15 NBA seasons. We examined shots taken after two, three and four consecutively made shots.</p>
<p>When looking at the shots from all the qualified players, we found that if a person made the two shots prior, their chance of making the next shot was 1.9% percentage lower than the model predicted – their make rate would regress to the mean. </p>
<p>However, when we looked at players individually, the hot hand emerged for a sizable set of players. Specifically, there were 30 players who exhibited a statistically significant higher field goal percentage on a shot following two makes compared to their expected field goal percentage. Of the players who demonstrated the ability to go on hot streaks, the average hot hand effect led to a 2.71% increase in the chance of making a third shot in a row.</p>
<p>For streaks of three and four consecutively made shots, the hot hand effect was even higher – 4.42% on average and 5.81% on average, respectively.</p>
<h2>Why do some people get hot?</h2>
<p>It’s important to note that having a hot hand does not mean any player can suddenly make baskets from anywhere on the court. For example, Tim Duncan, Roy Hibbert and Marcin Gortat all showed the ability to go on hot streaks, but these are all centers who do not typically take shots far from the basket. Their hot hands increased their shooting percentages of close-range shots. This led us to the hypothesis that part of the hot hand effect may come from what is called the <a href="https://joshkaufman.net/explore-exploit/">explore and exploit approach</a>, which refers to a short period of exploring different approaches to solving a problem followed by a period of exploiting the best approach found. For basketball, this would look like a player finding a mismatch during a game – perhaps a shorter player defending them than normal – and exploiting it by taking more of a certain type of shot. Research has also suggested that the explore and exploit approach is connected to <a href="https://doi.org/10.1038/s41467-021-25477-8">streaks of success in artistic and scientific careers</a>. </p>
<p>While this hypothesis is plausible, it may not be the only factor accounting for hot streaks. Could short-term neuroplasticity – the ability of a player’s brain to quickly adapt to conditions in a game – be a cause? What about focus and mental preparation? Whatever the reason, our study provides strong evidence that supports the existence of hot hands. For coaches and players in the NBA or in this year’s NCAA March Madness, it might be a good strategy to follow the old cliche: “Go with the hot hand.”</p>
<p>[<em>The Conversation’s science, health and technology editors pick their favorite stories.</em> <a href="https://memberservices.theconversation.com/newsletters/?nl=science&source=inline-science-favorite">Weekly on Wednesdays</a>.]</p><img src="https://counter.theconversation.com/content/179082/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The authors do not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>A study shows that a select group of NBA players really do go on hot streaks by making more shots in a row than statistics suggest they should.Konstantinos Pelechrinis, Associate Professor of Computing and Information, University of PittsburghWayne Winston, Professor of Decision and Information Systems, Indiana UniversityLicensed as Creative Commons – attribution, no derivatives.