tag:theconversation.com,2011:/us/topics/percentages-75929/articlesPercentages – The Conversation2023-07-24T12:15:40Ztag:theconversation.com,2011:article/2046092023-07-24T12:15:40Z2023-07-24T12:15:40ZWill I ever need math? A mathematician explains how math is everywhere – from soap bubbles to Pixar movies<figure><img src="https://images.theconversation.com/files/533769/original/file-20230623-27-n6mym5.JPG?ixlib=rb-1.1.0&rect=0%2C3%2C2546%2C1810&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">In addition to explaining natural phenomena, math can help strengthen your brain.</span> <span class="attribution"><span class="source">Liz Arnold</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span></figcaption></figure><figure class="align-left ">
<img alt="" src="https://images.theconversation.com/files/281719/original/file-20190628-76743-26slbc.png?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/281719/original/file-20190628-76743-26slbc.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=293&fit=crop&dpr=1 600w, https://images.theconversation.com/files/281719/original/file-20190628-76743-26slbc.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=293&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/281719/original/file-20190628-76743-26slbc.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=293&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/281719/original/file-20190628-76743-26slbc.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=368&fit=crop&dpr=1 754w, https://images.theconversation.com/files/281719/original/file-20190628-76743-26slbc.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=368&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/281719/original/file-20190628-76743-26slbc.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=368&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
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<p><em><a href="https://theconversation.com/us/topics/curious-kids-us-74795">Curious Kids</a> is a series for children of all ages. If you have a question you’d like an expert to answer, send it to <a href="mailto:curiouskidsus@theconversation.com">curiouskidsus@theconversation.com</a>.</em></p>
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<p><strong>Will I ever need math besides for school or work? – Hadassah G., age 9, New Jersey</strong></p>
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<p>It can be easy to think that you need math only to do your algebra or geometry homework or if you have a job as an engineer. But, in fact, math pops up everywhere – even in the soap bubbles in your kitchen sink. </p>
<p>While washing dishes when I was 13, I noticed that the soap bubbles formed tiny 3D polygons, packed together like a honeycomb, but not all of these shapes were perfectly round. Why did some of the bubbles look like hexagons? Why were others shaped like squares full of air? Why didn’t I see any star-shaped bubbles, or bubbles with spikes?</p>
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<a href="https://images.theconversation.com/files/532515/original/file-20230618-19-uiu174.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="A tightly packed collection of hexagon-shaped, rainbow-colored bubbles against a dark background" src="https://images.theconversation.com/files/532515/original/file-20230618-19-uiu174.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/532515/original/file-20230618-19-uiu174.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=399&fit=crop&dpr=1 600w, https://images.theconversation.com/files/532515/original/file-20230618-19-uiu174.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=399&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/532515/original/file-20230618-19-uiu174.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=399&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/532515/original/file-20230618-19-uiu174.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=501&fit=crop&dpr=1 754w, https://images.theconversation.com/files/532515/original/file-20230618-19-uiu174.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=501&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/532515/original/file-20230618-19-uiu174.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>
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<span class="caption">Math helps explain the shapes of bubbles and the reason they naturally pack together without any gaps.</span>
<span class="attribution"><span class="source">Adrienne Bresnahan/Moment via Getty Images</span></span>
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<p>When I learned that math could help answer these questions, I thought that was so cool! Now, as a professor of mathematics who <a href="https://scholar.google.com/citations?user=AcLUMzkAAAAJ&hl=en">studies how people learn math through play</a>, I understand why <a href="https://americanhistory.si.edu/collections/object-groups/geometric-models-minimal-surfaces-as-soap-films#:%7E:text=Brill%20in%201885.-,A%20minimal%20surface%20is%20the%20surface%20of%20smallest%20area%20of,is%20one%20of%20a%20series">bubbles are naturally lazy</a>. I even <a href="https://pubs.nctm.org/view/journals/mt/97/3/article-p165.xml">studied the math behind</a> the reason I saw only some shapes in soapy dishwater.</p>
<p>Besides helping explain the behavior of bubbles and other curiosities of nature, math is likely part of many of your everyday activities, along with the technology you enjoy and even the inner workings of your brain. Doing math isn’t just about computing, memorizing, solving an equation or doing word problems by yourself. It’s really about creative problem-solving and logical thinking with other people. </p>
<h2>Math in everyday life</h2>
<p>Many topics you learn in elementary school – like fractions, percentages and measurements – are useful in everyday life. </p>
<p>For example, if you want to build a fence around your house, <a href="https://www.instructables.com/How-to-Paint-a-Mural-of-Your-Favorite-Photo-The-Gr/">paint your walls a new color or with a design</a>, or <a href="https://www.youtube.com/watch?v=3TexumwK274">sew yourself a new outfit or quilt</a>, all of those activities require knowledge about measurement and scaling. More complicated construction projects, such as <a href="https://noticing.nysci.org/lesson/treehouse-design/">building a treehouse</a>, require lots of mathematical problem-solving skills.</p>
<p>Once you’ve laid out the plans for one of these projects, you need to buy all the materials. Percentages – which are special kinds of fractions – are especially important to understand when managing money. Understanding percentages can help you <a href="https://www.youtube.com/watch?v=iQK-3hLRXJA">budget your money</a> and <a href="https://www.youtube.com/watch?v=rP6Cg3ObMgQ&t=15s">increase your net worth</a>.</p>
<p>Beyond budgeting, you might find yourself using percentages when cooking a double batch of brownies, determining how much medicine to take when you’re sick or <a href="https://www.weatherstationadvisor.com/what-does-the-percentage-of-rain-mean/">understanding the weather forecast</a>.</p>
<h2>Your favorite technology needs math</h2>
<p>Math is an essential tool that animators use to make movies.</p>
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<iframe width="440" height="260" src="https://www.youtube.com/embed/Ei4wseRRJhc?wmode=transparent&start=0" frameborder="0" allowfullscreen=""></iframe>
<figcaption><span class="caption">Pixar artists use math to make movies like ‘Elemental.’</span></figcaption>
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<p><a href="https://www.theverge.com/2013/3/7/4074956/pixar-senior-scientist-derose-explains-how-math-makes-movies-games">Studios like Pixar</a> rely on <a href="https://www.slashfilm.com/531138/math-of-pixar/">ideas from geometry</a> to bring characters like Ember from “Elemental” to life. With an understanding of geometric transformations like reflections, rotations and translations, you can <a href="https://www.khanacademy.org/computing/pixar">use your computer</a> to make your own animations.</p>
<p>Coordinate systems, which are fundamental to geometry, show up in video games like Minecraft. The 2D Minecraft world uses a <a href="https://www.khanacademy.org/math/basic-geo/basic-geo-coord-plane">2D coordinate system</a> – with an x-axis and a y-axis – where you can move north, south, east or west. In the 3D Minecraft world, there’s also a z-axis, allowing you to move up and down. Middle and high school teachers can even <a href="https://education.minecraft.net/en-us/resources/math-subject-kit">use Minecraft</a> to help students learn math concepts.</p>
<p>Many high-paying jobs <a href="https://www.collegeconsensus.com/majors/highest-paying-careers-math-majors/">use math</a>, especially <a href="https://www.statology.org/probability-real-life-examples/">probability</a> – again, fractions. Understanding probability helps doctors identify how effective medical treatments are, informs coaches about <a href="https://www.youtube.com/watch?v=11fCMcEQkLo">ways their teams can improve</a> and aids <a href="https://www.youtube.com/watch?v=UiJiXNEm-Go">cryptographers</a> in keeping private information – like your email password or ATM PIN – secret. Cryptography combines probability with number theory to create <a href="https://www.giftofcuriosity.com/secret-codes-for-kids/">secret codes</a> that are difficult to crack.</p>
<h2>Math helps your brain</h2>
<p>Math can have a big impact on your internal life, too. You can use math activities to train your brain the same way you would train your body for a sport. Doing math helps your <a href="https://www.byjusfutureschool.com/blog/how-learning-math-can-benefit-your-childs-brain-in-incredible-ways/">brain become flexible</a> so you can better handle new tasks and ideas of all kinds. </p>
<p>Even doing things that don’t look like your math homework, such as crossword puzzles, word searches and board games like <a href="https://www.setgame.com/set/puzzle">Set</a> and <a href="https://shop.mattel.com/products/blokus-game-bjv44">Blokus</a>, are deeply mathematical activities that <a href="https://www.verywellmind.com/cognitive-training-long-term-improvement-2795014">help your brain get stronger</a>. This kind of mental training helps the brain pay attention and solve problems and improves memory. A strong working memory supports brain functions that lower the risk of <a href="https://doi.org/10.1016/j.trci.2017.09.002">Alzheimer’s disease and dementia</a>.</p>
<p>Having a stronger, more flexible brain also aids <a href="https://www.mathvalues.org/masterblog/what-is-quantitative-reasoning">quantitative literacy</a>, which can help you make sense of graphs that appear in the media, reflect critically about news and understand health and financial information. </p>
<p>Math can even help you <a href="https://www.wsj.com/articles/chatgpt-ai-math-po-shen-loh-1e9f80dc">outsmart artificial intelligence</a>. With the rise of AI, <a href="https://fortune.com/2023/05/06/what-jobs-will-rise-disappear-in-future-wef-artificial-intelligence/">it’s important</a> to be able to think creatively, reason logically and make connections between concepts – whether mathematical or not. Puzzling through a difficult math problem nurtures these skills, even if you don’t get the right answer right away. </p>
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<span class="caption">Hortensia Soto demonstrates the hidden math of soap bubbles as part of Cafecito con Matemáticas, organized by Liz Arnold and Jocelyn Rios at Colorado State University.</span>
<span class="attribution"><span class="source">Liz Arnold</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
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<p>It’s important to remember that doing math doesn’t require you to be fast or to get the correct answer right away. In fact, you can learn a lot by <a href="https://www.waltonfamilyfoundation.org/stories/foundation/whats-a-great-way-to-learn-math-wrong-answers-only">getting the wrong answer</a>. Working with other people can also help you to make sure you really understand the problem and builds communication and <a href="https://mathsnoproblem.com/blog/teaching-practice/collaboration-for-meaningful-learning">teamwork skills</a>. </p>
<p>Math is so much more than memorizing times tables and filling out homework problem sets. So next time you kick back to watch your favorite animated movie, or start saving up for a fancy new tech gadget, hopefully you’ll appreciate how math is woven into so many parts of life.</p>
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<p><em>Hello, curious kids! Do you have a question you’d like an expert to answer? Ask an adult to send your question to <a href="mailto:curiouskidsus@theconversation.com">CuriousKidsUS@theconversation.com</a>. Please tell us your name, age and the city where you live.</em></p>
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<p class="fine-print"><em><span>Hortensia Soto 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>Math is more than memorizing times tables and doing homework problems. It is woven into more aspects of your life than you might think.Hortensia Soto, Professor of Mathematics, Colorado State UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1722722021-12-20T13:13:22Z2021-12-20T13:13:22ZPeople who are bad with numbers often find it harder to make ends meet – even if they are not poor<figure><img src="https://images.theconversation.com/files/436175/original/file-20211207-19-hif25s.jpg?ixlib=rb-1.1.0&rect=38%2C0%2C6458%2C4334&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Even college-educated adults can still struggle with numbers. </span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/photo/confusded-lady-in-hijab-and-her-upset-husband-with-royalty-free-image/1313791943?adppopup=true">Prostock-Studio/iStock via Getty Images</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>People who are bad with numbers are more likely to experience financial difficulties than people who are good with numbers. That’s according to <a href="https://doi.org/10.1371/journal.pone.0260378">our analyses</a> of the <a href="https://wrp.lrfoundation.org.uk/explore-the-poll">Lloyd’s Register Foundation World Risk Poll</a>. </p>
<p>In this World Risk Poll, people from 141 countries were asked if 10% was bigger than, smaller than or the same as 1 out of 10. Participants were said to be bad with numbers if they did not provide the correct answer – which is that 10% is the same as 1 out of 10. <a href="https://doi.org/10.1371/journal.pone.0260378">Our analyses</a> found that people who answered incorrectly are often among the poorest in their country. Prior studies in the <a href="https://doi.org/10.1111/j.1468-0297.2010.02394.x">United States</a>, <a href="https://doi.org/10.1111/j.1475-5890.2007.00052.x">United Kingdom</a>, <a href="https://doi.org/10.1016/j.joep.2016.02.011">the Netherlands</a> and <a href="https://doi.org/10.1111/joca.12294">Peru</a> had also found that people who are bad with numbers are financially worse off. But <a href="https://doi.org/10.1371/journal.pone.0260378">our analyses of the World Risk Poll</a> further showed that people who are bad with numbers find it harder to make ends meet, even if they are not poor. </p>
<p>When we say that they found it harder to make ends meet, we mean that they reported on the poll that they found it difficult or very difficult to live on their current income, as opposed to living comfortably or getting by on their current income.</p>
<p><a href="https://doi.org/10.1371/journal.pone.0260378">Our analyses</a> also indicate that staying in school longer is related to better number ability. People with a high school degree tend to be better with numbers than people without a high school degree. And college graduates do even better. But even among college graduates there are people who are bad with numbers – and they struggle more financially. </p>
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<p>Of course, being good with numbers is not going to help you stretch your budget if you are very poor. <a href="https://doi.org/10.1371/journal.pone.0260378">We found</a> that the relationship between number ability and struggling to make ends meet holds across the world, except in low-income countries like Ethiopia, Somalia and Rwanda. </p>
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<h2>Why it matters</h2>
<p>The ability to understand and use numbers is also called <a href="http://doi.org/10.1093/oso/9780190861094.001.0001">numeracy</a>. Numeracy is <a href="https://doi.org/10.1787/1f029d8f-en">central to modern adult life</a> because numbers are everywhere. </p>
<p>A lot of well-paying jobs involve working with numbers. People who are bad with numbers often perform worse in these jobs, including <a href="https://doi.org/10.1111/ecin.12873">banking</a>. It can therefore be hard for people who are bad with numbers to <a href="http://www.doi.org/10.1108/00400919710164125">find employment and progress in their jobs</a>. </p>
<p>People who are bad with numbers are less likely <a href="https://www.pnas.org/content/116/39/19386.short">to make good financial decisions</a>. Individuals who can’t compute how interest compounds over time <a href="https://doi.org/10.1111/j.1540-6261.2009.01518.x">save the least and borrow the most</a>. People with poor numerical skills are also more likely <a href="https://doi.org/10.1037/0022-3514.41.3.586">to take on high-cost debt</a>. If you’re bad with numbers, it is hard to <a href="https://doi.org/10.1017/S1474747215000232">recognize</a> that paying the US$30 minimum payment on a credit card with a $3,000 balance and an annual percentage rate of 12% means it will never be paid off.</p>
<h2>What still isn’t known</h2>
<p>It is clear that people who are bad with numbers also tend to struggle financially. But we still need to explore whether teaching people math will help them to avoid financial problems. </p>
<h2>What’s next</h2>
<p>In her book “<a href="http://doi.org/10.1093/oso/9780190861094.001.0001">Innumeracy in the Wild</a>,” Ellen Peters, director of the Center for Science Communication Research at the University of Oregon, suggests that it is important for students to take math classes. American high school students who had to <a href="https://doi.org/10.3368/jhr.51.3.0113-5410R1">take more math courses</a> than were previously required had better financial outcomes later in life, such as avoiding bankruptcy and foreclosures. </p>
<p>Successfully teaching numeracy also means helping students gain confidence in using numbers. People with <a href="https://doi.org/10.1073/pnas.1903126116">low numerical confidence</a> experience bad financial outcomes, such as a foreclosure notice, independent of their numeric ability. This is because they may not even try to take on complex financial decisions.</p>
<p>Numerical confidence can be boosted in different ways. Among American <a href="https://doi.org/10.1037/0022-3514.41.3.586">elementary school children</a> who were bad with numbers, setting achievable goals led to better numerical confidence and performance. Among American <a href="https://doi.org/10.1371/journal.pone.0180674">undergraduate students</a>, a writing exercise that affirmed their positive values improved their numerical confidence and performance.</p>
<p>[<em>Over 140,000 readers rely on The Conversation’s newsletters to understand the world.</em> <a href="https://memberservices.theconversation.com/newsletters/?source=inline-140ksignup">Sign up today</a>.]</p>
<p>Other important next steps are to find out whether training in numeracy can also be provided to adults, and whether training in numeracy improves the financial outcomes of people who do not live in high-income countries.</p><img src="https://counter.theconversation.com/content/172272/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Wändi Bruine de Bruin receives funding from the Lloyd's Register Foundation and support from USC Dornsife's Public Exchange for a research project entitled "Understanding and informing public perceptions of risk around the world: A behavioral science approach" </span></em></p><p class="fine-print"><em><span>Paul Slovic 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>People who struggle with numbers are also likely to struggle in life, new research shows.Wändi Bruine de Bruin, Professor of Public Policy, Psychology and Behavioral Science, USC Sol Price School of Public Policy, USC Dornsife College of Letters, Arts and SciencesPaul Slovic, Professor of Psychology, University of OregonLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1584952021-04-27T12:13:47Z2021-04-27T12:13:47ZNumbers can trip you up during the pandemic – here are 4 tips to help you figure out tricky stats<figure><img src="https://images.theconversation.com/files/397201/original/file-20210426-21-1ueg8l2.jpg?ixlib=rb-1.1.0&rect=8%2C545%2C5421%2C3069&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Understanding vaccine effectiveness stats can help you weigh the risks of travel.</span> <span class="attribution"><a class="source" href="https://newsroom.ap.org/detail/AirTravelTSA/70f978c9355240efaf56bf6ca3947434/photo?boardId=d7f2514f50804466b15dfb81ed00d9cd&st=boards&mediaType=audio,photo,video,graphic&sortBy=&dateRange=Anytime&totalCount=39&currentItemNo=1">AP Photo/Rick Bowmer</a></span></figcaption></figure><p>The COVID-19 pandemic thrust many news consumers into a world of statistics and deep uncertainty. An endless swirl of numbers – case counts, infection rates, vaccine efficacy – can <a href="https://www.nytimes.com/2020/03/12/opinion/sunday/coronavirus-statistics.html">leave you feeling stressed, anxious</a> and powerless if you’re not confident you know what they really mean.</p>
<p>But when used effectively, statistics can help you know more, <a href="https://doi.org/10.1111/j.1539-6924.1995.tb00341.x">trust more</a> and avoid surprise and regret when the unexpected occurs. People also tend to <a href="https://doi.org/10.3758/BF03334162">want them</a> and <a href="https://doi.org/10.1080/10410236.2017.1407276">find them useful</a> when weighing uncertain risks and making decisions. </p>
<p>I’m a <a href="https://scholar.google.com/citations?user=Y5HYFV8AAAAJ&hl=en&oi=ao">decision psychologist</a>. I study how people understand and use numbers as they’re figuring out risks and making choices. I then try to <a href="https://scr.uoregon.edu/">improve how numbers are communicated</a> to help people make better decisions. Here are four ways that stats in the news can confuse you – and my advice on how to understand them.</p>
<h2>1. Look for consistent categories</h2>
<p>Uncertainty and risk are often presented numerically. Rain is 35% likely today; 10% of patients will suffer this side effect. But sometimes how those numbers are presented is confusing.</p>
<p><div data-react-class="Tweet" data-react-props="{"tweetId":"1254802547719757830"}"></div></p>
<p>For example, early in the pandemic, The New York Times <a href="https://twitter.com/nytimes/status/1254802547719757830?s=20">tweeted</a> that “nearly half of New York City voters know someone who died of Covid-19. 74% of white voters said they did not know someone who died from coronavirus, but 48% of black voters, and 52% of Latino voters, said they did.”</p>
<p>Notice that some statistics referred to knowing someone, and others to not knowing someone.</p>
<p>This difference shouldn’t matter because once you know the proportion of people who knew someone who died, you also know the proportion who didn’t – people either know someone or they don’t. If 74% of white voters didn’t know someone, then 26% did know someone (74% plus 26% = 100%).</p>
<p>But how options are described can be misleading. In a <a href="https://doi.org/10.1056/NEJM198205273062103">classic example</a>, researchers described cancer treatment options either in terms of survival (that is, 90% of patients survive) or mortality (10% died). The numbers are logically the same in both descriptions. But people, including experts, tend to feel worse when a likelihood is described in the negative mortality frame, and they’re less likely to choose a treatment described in those terms. People who are <a href="https://doi.org/10.1111/j.1467-9280.2006.01720.x">not great with numbers</a> are even more likely to be swayed by the positive or negative frame.</p>
<p>When you’re reading a tweet like the one above, pay attention to the words as well as the numbers. Are they describing things in a consistent way? If not, consider the flip side. The tweet should have read “26% of white voters said they knew someone who died from the coronavirus, and so did 48% of black voters, and 52% of Latino voters.” With consistency between numbers and words, you can more easily compare across groups.</p>
<h2>2. Convert numbers for easier comparison</h2>
<p>Numbers can be communicated in other ways, too, that make them hard to decipher. One example comes from a list of the proportion of people in the U.S. who died of COVID-19 within several racial categories.</p>
<p><iframe id="E155R" class="tc-infographic-datawrapper" src="https://datawrapper.dwcdn.net/E155R/4/" height="400px" width="100%" style="border: none" frameborder="0"></iframe></p>
<p>It’s challenging to make out which groups have fared worse during the pandemic when you’re looking at a “one in something” format.</p>
<p>That “something” is the denominator of the fraction. It’s far easier to understand the data if you pick a single number you want them all to be out of. This becomes the new denominator. I chose 10,000 because it was bigger than the other denominators.</p>
<p>Then, divide 10,000 by what the original number was “out of” (the original denominator). For example, with the category Indigenous Americans, I divided 10,000 by 390. That equals 25.6, or approximately 26. Therefore, I wrote 26 in 10,000 Indigenous Americans.</p>
<p>So instead of 1 in 390 versus 1 in 665, you can compare 26 in 10,000 versus 15 in 10,000. It’s a lot easier to see that Indigenous Americans died at almost twice the rate of white Americans.</p>
<h2>3. Think about absolute vs. relative percentages</h2>
<p>CNN recently wrote about flying safely, claiming that <a href="https://www.cdc.gov/mmwr/volumes/70/wr/mm7013e3.htm?s_cid=mm7013e3_w">90% vaccine effectiveness</a> meant that “for every million fully vaccinated people who fly, <a href="https://twitter.com/zeynep/status/1381223370436530176">some 100,000 could still become infected</a>.”</p>
<p>This is grossly incorrect.</p>
<p>Vaccine effectiveness concerns the relative risk of getting infected if you get the vaccine compared with not getting it. To calculate it, you need two groups of people, one vaccinated, one not. You wait and see what infections emerge in both groups. Then you calculate the proportion of people in the vaccinated group who got infected and the proportion of people in the unvaccinated group who did.</p>
<p>Divide the vaccinated proportion by the unvaccinated proportion, and the resulting number is the risk ratio. One minus the risk ratio is vaccine effectiveness, the 90% number from a <a href="http://dx.doi.org/10.15585/mmwr.mm7013e3">recent study published by the Centers for Disease Control and Prevention</a>. </p>
<p>What this number means is that, all else being equal, with vaccination, you are 10 times less likely to get a COVID-19 infection. This is true whether you live in Michigan or Oregon, <a href="https://doi.org/10.1001/jama.2020.19108">fly on planes or don’t</a>, even wear a mask or don’t. Whatever the average infection rate you face – based on where you live and how you act – you are 10 times less likely to get infected if you get vaccinated. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/397153/original/file-20210426-15-1lkeo5l.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Masked passengers moving through airline terminal" src="https://images.theconversation.com/files/397153/original/file-20210426-15-1lkeo5l.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/397153/original/file-20210426-15-1lkeo5l.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/397153/original/file-20210426-15-1lkeo5l.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/397153/original/file-20210426-15-1lkeo5l.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/397153/original/file-20210426-15-1lkeo5l.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/397153/original/file-20210426-15-1lkeo5l.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/397153/original/file-20210426-15-1lkeo5l.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">A vaccine with 90% effectiveness does not mean 10% of vaccinated travelers will get COVID-19.</span>
<span class="attribution"><a class="source" href="https://newsroom.ap.org/detail/ArizonaDailyLIfe/bdbcda82cbc444deb6929c33061cf643/photo?Query=air%20AND%20passengers&mediaType=photo&sortBy=creationdatetime:desc&dateRange=Anytime&totalCount=3653&currentItemNo=4">AP Photo/Sue Ogrocki</a></span>
</figcaption>
</figure>
<p>Next time you see a percentage number, stop and think about whether it’s an absolute number, like the percentage who know or don’t know someone who has died from COVID-19. Or is it a relative percentage, like vaccine effectiveness – a comparison of people who get vaccinated to those who do not.</p>
<p>A 90% effective vaccine means that, if in a group of 1 million unvaccinated <a href="https://doi.org/10.1016/j.tmaid.2020.101915">people who flew</a>, 100 of them got infected, then among 1 million vaccinated people who flew, only 10 of them would get COVID-19.</p>
<p>These vaccines are imperfect, but they are phenomenally effective in that relative sense.</p>
<h2>4. Don’t let an anecdote displace the data</h2>
<p>News articles often tell a story about an individual that draws readers in. You can be tricked by these compelling stories, though, especially if any accompanying numbers are hard to understand.</p>
<p><a href="https://www.cnn.com/2020/04/08/us/coronavirus-leilani-jordan-grocery-worker/index.html">Leilani Jordan</a> continued to work as a clerk at a Maryland grocery store so she could help seniors, even though she had cerebral palsy and came in frequent contact with the public. She ultimately died from COVID-19, but her story may have persuaded some people to behave more carefully.</p>
<p>[<em>Understand key political developments, each week.</em> <a href="https://theconversation.com/us/newsletters/politics-weekly-74/?utm_source=TCUS&utm_medium=inline-link&utm_campaign=newsletter-text&utm_content=politics-understand">Subscribe to The Conversation’s election newsletter</a>.]</p>
<p>Some celebrity stories may have had the opposite effect. <a href="https://www.vulture.com/article/famous-people-celebrities-with-coronavirus.html">Tom Hanks and Rita Wilson</a> had particularly mild cases of COVID-19. Reading about them may have reduced worry and caused some people to ease off hand-washing and physical distancing.</p>
<p>When you read a story, think carefully about what’s useful. Stories can help you understand experiences – what it feels like to have COVID-19 or become unemployed because of the pandemic. But they leave out other experiences and don’t tell you how common different experiences are.</p>
<p>After being drawn into a good story, think about how relevant it is to you and what is its likelihood. You can even look up statistics to better inform yourself about a situation rather than rely on anecdotes that might leave you with a false impression. </p>
<p>Knowing statistics can help you, but sometimes you need to empower yourself to understand what the numbers are telling you.</p><img src="https://counter.theconversation.com/content/158495/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Ellen Peters receives funding from the National Science Foundation and USAFacts. </span></em></p>Understanding numbers in the news or social media can empower you to figure out risks and make good choices. Here’s what to look out for to make sure you aren’t misled by COVID-19 coverage.Ellen Peters, Director, Center for Science Communication Research, University of OregonLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1356982020-04-16T23:05:12Z2020-04-16T23:05:12ZMore testing will give us a better picture of the coronavirus spread and its slowdown<p><a href="https://7news.com.au/lifestyle/health-wellbeing/coronavirus-australia-infection-rate-continues-to-decline-as-australia-ponders-exit-strategy-c-979164">Many states</a> are <a href="https://www.abc.net.au/news/2020-04-15/sa-broadens-coronavirus-testing-with-two-week-covid-blitz/12150524">now</a> <a href="https://www.abc.net.au/news/2020-04-14/victoria-expands-coronavirus-testing-criteria/12146166">ramping up the number of tests</a> by relaxing the criteria for who can get tested for COVID-19. This should give us a better idea of whether the spread is easing or getting worse.</p>
<p>We get regular updates about COVID-19 with lots of data, figures and graphs with some interpretations to see if we are flattening the curve on the number of new cases.</p>
<p>But most of these are based on using only the total or the daily number of confirmed new cases. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/how-much-has-australia-really-flattened-the-curve-of-coronavirus-until-we-keep-better-records-we-dont-know-136252">How much has Australia really flattened the curve of coronavirus? Until we keep better records, we don't know</a>
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</p>
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<p>This does not provide enough information about whether the situation is improving, stabilising or getting worse. That is why we also need to consider the number of people tested daily for COVID-19.</p>
<p>For example, in percentage terms there is no actual difference between getting 20 positive cases out of 1,000 tests one day and 100 positive cases out of 5,000 tests the next. Both lead to the conclusion we have 2% reported infected people of those tested.</p>
<p>If we are only given the number of new cases, getting 100 in a day sounds a lot worse than getting 20. The 2% percentage figure here tells us things are pretty much the same over the two days.</p>
<h2>Curves and trends</h2>
<p>Take Victoria, if we look at the total number of confirmed cases we see it followed an exponential trend for a while – one that was increasingly rising – and then started to divert on April 3.</p>
<hr>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/328279/original/file-20200416-140745-urr91b.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/328279/original/file-20200416-140745-urr91b.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/328279/original/file-20200416-140745-urr91b.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=558&fit=crop&dpr=1 600w, https://images.theconversation.com/files/328279/original/file-20200416-140745-urr91b.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=558&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/328279/original/file-20200416-140745-urr91b.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=558&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/328279/original/file-20200416-140745-urr91b.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=701&fit=crop&dpr=1 754w, https://images.theconversation.com/files/328279/original/file-20200416-140745-urr91b.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=701&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/328279/original/file-20200416-140745-urr91b.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=701&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption"></span>
<span class="attribution"><span class="source">The Conversation</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<hr>
<p>In the daily number of confirmed cases we see high jumps and large fluctuations going back and forth.</p>
<hr>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/328281/original/file-20200416-140719-npy0fk.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/328281/original/file-20200416-140719-npy0fk.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/328281/original/file-20200416-140719-npy0fk.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=527&fit=crop&dpr=1 600w, https://images.theconversation.com/files/328281/original/file-20200416-140719-npy0fk.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=527&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/328281/original/file-20200416-140719-npy0fk.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=527&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/328281/original/file-20200416-140719-npy0fk.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=662&fit=crop&dpr=1 754w, https://images.theconversation.com/files/328281/original/file-20200416-140719-npy0fk.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=662&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/328281/original/file-20200416-140719-npy0fk.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=662&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption"></span>
<span class="attribution"><span class="source">The Conversation</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<hr>
<p>When the daily number of applied tests is considered, we can calculate the actual percentage of new cases each day. Now we have a way flatter curve (below) with different fluctuations.</p>
<hr>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/328284/original/file-20200416-140729-sfncn1.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/328284/original/file-20200416-140729-sfncn1.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/328284/original/file-20200416-140729-sfncn1.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=838&fit=crop&dpr=1 600w, https://images.theconversation.com/files/328284/original/file-20200416-140729-sfncn1.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=838&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/328284/original/file-20200416-140729-sfncn1.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=838&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/328284/original/file-20200416-140729-sfncn1.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1054&fit=crop&dpr=1 754w, https://images.theconversation.com/files/328284/original/file-20200416-140729-sfncn1.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1054&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/328284/original/file-20200416-140729-sfncn1.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1054&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption"></span>
<span class="attribution"><span class="source">The Conversation</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<hr>
<p>The peak is now on March 24 when the number of tests is included. If we just look at the daily count, the highest number of confirmed cases was on March 27. When we look at the percentage, it shows a decrease rather than an increase with more than 2,300 tests.</p>
<p>From the daily new cases data it looks like there is a strongly decreasing trend in the number of confirmed cases between April 2 and 6. </p>
<p>But we do not see the same strong downward movement in the percentage data on the number of tests. Although both figures go down, then up slightly, the percentage trend downward is not as strong as the daily trend.</p>
<p>This is a good example of the discrepancy between the inferences from the raw and percentage data. When we consider the number of tested people, we get a different view on the progress of the pandemic.</p>
<h2>More tests needed</h2>
<p>In using the number of tests to get a more reliable picture of the situation, there is an important point to consider. That’s were the purple error bars in the graph (above) come in.</p>
<p>They show the margin of error where each percentage estimate swings for the daily number of applied tests, so the actual number could be higher or lower but within those purple bars.</p>
<p>When we have a larger number of applied tests, we get a reduced margin of error, and that gives us a clearer picture of what is happening. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/even-in-a-pandemic-continue-with-routine-health-care-and-dont-ignore-a-medical-emergency-136246">Even in a pandemic, continue with routine health care and don't ignore a medical emergency</a>
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<p>Since the peak on March 24 is backed up by only 500 tests, it has the largest margin of error. The figure on March 28 is based on 8,900 tests with a very small amount of error. </p>
<p>To get a more reliable picture of the situation, the number of applied tests has to be expanded, which it is what is happening in some states. This should reduce the margin of error.</p>
<h2>Out in the community</h2>
<p>After getting some signals of flattening the curve in <a href="https://www.theage.com.au/national/victoria/wonderful-success-optimism-that-victoria-has-started-to-flatten-the-curve-20200405-p54h9v.html">Victoria</a> and <a href="https://www.theguardian.com/world/2020/apr/05/health-officials-hopeful-australia-is-flattening-coronavirus-curve-but-warn-against-complacency">Australia</a> as well, do we see an exponential increase in just the community transmission? </p>
<p>Community transmission is where someone has caught the virus locally, not an infected traveller who’s returned from a cruise or overseas. At the moment they are <a href="https://www.health.gov.au/news/health-alerts/novel-coronavirus-2019-ncov-health-alert/coronavirus-covid-19-current-situation-and-case-numbers">the minority of cases</a> and authorities would like it to stay that way to <a href="https://www.abc.net.au/news/2020-04-11/what-is-community-transmission-of-coronavirus-covid-19/12142638">contain the spread of the virus</a>.</p>
<p>Again, we need to consider the number of tests to answer this question clearly. The raw numbers of community transmission in Victoria looked like they were increasing exponentially.</p>
<hr>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/328296/original/file-20200416-140741-12r4ldn.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/328296/original/file-20200416-140741-12r4ldn.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/328296/original/file-20200416-140741-12r4ldn.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=453&fit=crop&dpr=1 600w, https://images.theconversation.com/files/328296/original/file-20200416-140741-12r4ldn.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=453&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/328296/original/file-20200416-140741-12r4ldn.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=453&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/328296/original/file-20200416-140741-12r4ldn.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=569&fit=crop&dpr=1 754w, https://images.theconversation.com/files/328296/original/file-20200416-140741-12r4ldn.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=569&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/328296/original/file-20200416-140741-12r4ldn.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=569&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption"></span>
<span class="attribution"><span class="source">The Conversation</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<hr>
<p>But the numbers as a percentage of the number tested tell a different story. Although there is some increase in the rate of community transmissions recently, it still shows a way flatter behaviour far from the exponential curve.</p>
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<p>That is why it is important to understand the impact of the number of tests on the figures displaying the progress of the pandemic. Understanding this relationship could reassure people about new numbers.</p><img src="https://counter.theconversation.com/content/135698/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Haydar Demirhan 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>Don’t just tell us how many new cases of COVID-19 have been confirmed, tell us how many people you tested as well. That helps us to know if things are getting better or worse.Haydar Demirhan, Senior Lecturer in Analytics, RMIT UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1231292019-09-09T19:01:01Z2019-09-09T19:01:01ZMath skills aren’t enough to get through hard decisions – you need confidence, too<figure><img src="https://images.theconversation.com/files/291551/original/file-20190909-109927-12opn56.jpg?ixlib=rb-1.1.0&rect=20%2C0%2C4021%2C2869&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Numeracy has real implications for your life.</span> <span class="attribution"><a class="source" href="https://unsplash.com/photos/3xwrg7Vv6Ts">Ray Reyes/Unsplash</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span></figcaption></figure><p>Almost a third of American adults <a href="https://doi.org/10.1787/9789264204256-en">don’t have the math skills</a> necessary to make effective decisions about their health and finances.</p>
<p>These 73 million people can count, sort and do simple arithmetic. But they likely cannot select the <a href="https://www.ncbi.nlm.nih.gov/books/NBK224823/">health plan with the lowest cost</a> based on annual premiums and deductibles, or figure out that they can’t <a href="https://doi.org/10.1017/S1474747215000232">pay off credit card debt</a> based on the amount they owe, minimum monthly payments and an annual percentage rate.</p>
<p>These people are innumerate, meaning they’re unskilled with numbers. Numerate people, in contrast, are mathematically proficient.</p>
<p><a href="https://scholar.google.com/citations?user=Y5HYFV8AAAAJ&hl=en&oi=ao">In our</a> <a href="https://scholar.google.com/citations?user=AQy9khYAAAAJ&hl=en&oi=ao">research</a> as psychologists, we measure numeracy with a math test. If you can answer the following question correctly, your response falls in the <a href="https://psycnet.apa.org/record/2012-03055-003">top half of well-educated Americans</a>, and you are highly numerate:</p>
<blockquote>
<p>“Out of 1,000 people in a small town, 500 are members of a choir. Out of these 500 members in the choir, 100 are men. Out of the 500 inhabitants that are not in the choir, 300 are men. What is the probability that a randomly drawn man is a member of the choir?” (The answer is at the end of this article.)</p>
</blockquote>
<p>People who are better at answering these kinds of math questions <a href="https://doi.org/10.1111/j.1467-9280.2006.01720.x">make decisions differently</a> than those who struggle with them. The highly numerate <a href="http://journal.sjdm.org/13/131002a/jdm131002a.html">search for</a> and <a href="https://doi.org/10.1002/bdm.1934">think hard about</a> numbers when they make decisions. Ultimately, they <a href="https://doi.org/10.1177/0272989X04265482">trust numbers more</a> and have a clearer understanding of what the <a href="https://doi.org/10.1111/j.1467-9280.2006.01720.x">numbers mean for their decisions</a>.</p>
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<a href="https://images.theconversation.com/files/291558/original/file-20190909-109939-80hz6v.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/291558/original/file-20190909-109939-80hz6v.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/291558/original/file-20190909-109939-80hz6v.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=366&fit=crop&dpr=1 600w, https://images.theconversation.com/files/291558/original/file-20190909-109939-80hz6v.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=366&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/291558/original/file-20190909-109939-80hz6v.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=366&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/291558/original/file-20190909-109939-80hz6v.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=460&fit=crop&dpr=1 754w, https://images.theconversation.com/files/291558/original/file-20190909-109939-80hz6v.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=460&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/291558/original/file-20190909-109939-80hz6v.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=460&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">About 29% of Americans are innumerate – and that comes with real-world repercussions.</span>
<span class="attribution"><a class="source" href="https://unsplash.com/photos/pzMP-RGJ7mY">Christopher Burns/Unsplash</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
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<p>The less numerate, however, <a href="https://doi.org/10.1177/0272989X17704858">rely more on</a> <a href="https://doi.org/10.1111/j.1539-6924.2009.01279.x">compelling stories</a> and <a href="https://doi.org/10.1177/0963721411429960">emotional reactions</a> in decisions rather than the hard facts. They tend to make worse decisions for themselves when numbers are involved.</p>
<p>Being numerate doesn’t guarantee you’ll use numbers well in decisions, though. Confidence matters too. We <a href="https://doi.org/10.1177/0272989X07304449">measure numeric confidence with questions</a> like “How good are you at working with fractions?” More numerically confident people <a href="https://psycnet.apa.org/record/1997-08589-000">stick longer</a> with even tedious or difficult mathematical tasks. For best outcomes, you need to use numbers correctly, and you need to persist when the going gets tough. That is, you need to be numerate and you need to be numerically confident.</p>
<p>But <a href="https://doi.org/10.1073/pnas.1903126116">our new research suggests</a> that more is not always better when it comes to number skills and number confidence. Instead, having a good understanding of your ability – a match between ability and confidence – is critical. </p>
<h2>Clear-eyed assessment of one’s own numeracy</h2>
<p>To investigate this connection between math ability and confidence, we carried out two separate studies.</p>
<p>In one, we measured 13 self-reported good financial outcomes among 4,572 Americans – things like not having high credit-card debt or a payday loan. Out of our 13 possible financial outcome scenarios, we then counted up how many good outcomes each person experienced.</p>
<p>In the second, we collected data on physician-reported disease activity among 91 lupus patients. Less disease activity – for example, better medical test results or fewer new rashes – means a healthier patient.</p>
<p>We saw the best financial and health outcomes in those with high numeracy and high numeric confidence. “Mismatched” individuals – with either high ability and low confidence, or low ability and high confidence – experienced the worst outcomes.</p>
<p>And the effects were not small.</p>
<p>Individuals in our financial survey who scored perfectly on our math test and also had high confidence in their ability – meaning their ability and confidence matched – reported 82% of the good financial outcomes that were possible, and therefore only 18% of the possible bad outcomes, like filing for bankruptcy. People who scored just as well on the test but had low confidence in their numeric skills – so were mismatched – reported fewer good outcomes, only 78%.</p>
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<p>Just a few percentage points here actually have a big impact on how well someone is doing financially. For instance, imagine a group of people who are similar to one another, sharing characteristics like the same numeracy and education level. The 4% difference in good financial outcomes between those who are low and high in confidence is similar to the difference you’d see between people who make $50,000 and $144,000, a $94,000 salary difference.</p>
<p>Among lupus patients higher in numeric confidence, if they scored perfectly on our numeracy test, they had only a 7% chance of needing more aggressive treatment to control their disease at their doctor’s visit. However, those with high confidence and the lowest numeracy score had a much higher, 44%, chance of needing additional treatment to control their disease.</p>
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<p>What we think happens is that people who are more confident about their ability with numbers play a more active role in their health and financial decisions. If they also have good math skills, they can flourish. For example, with high numeric confidence, they would be more likely to engage in decisions about their health. With high numeric skills, they are then better able to choose high-quality doctors and take medications appropriately. But if they have poorer math skills that don’t support their confidence, they may make mistakes that go unnoticed and suffer the consequences.</p>
<p>For those who are lower in numeric confidence, having good math skills makes little difference to their health or finances, presumably because they fail to try.</p>
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<a href="https://images.theconversation.com/files/291556/original/file-20190909-109919-1t835s3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/291556/original/file-20190909-109919-1t835s3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/291556/original/file-20190909-109919-1t835s3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=380&fit=crop&dpr=1 600w, https://images.theconversation.com/files/291556/original/file-20190909-109919-1t835s3.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=380&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/291556/original/file-20190909-109919-1t835s3.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=380&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/291556/original/file-20190909-109919-1t835s3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=478&fit=crop&dpr=1 754w, https://images.theconversation.com/files/291556/original/file-20190909-109919-1t835s3.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=478&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/291556/original/file-20190909-109919-1t835s3.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=478&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">Did you stop consciously thinking your math skills when you handed in your last homework assignment?</span>
<span class="attribution"><a class="source" href="https://unsplash.com/photos/JexAuNCfefs">Annie Spratt/Unsplash</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
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<h2>Boosting your own math brain</h2>
<p>No matter your own situation, you are bound to encounter numbers in the course of living your life. Here are a few things you can do to help yourself become more numerate – and hopefully improve your financial and physical health.</p>
<p>First, understand your skills.</p>
<p>Believing you are not skilled can harm you, even if it’s not true. Be open to the possibility that you are good at math. Then again, believing you are skilled when you aren’t also can hurt. Ask for and accept help as needed. For example, you could ask a financial planner to assist with your retirement planning.</p>
<p>Secondly, ask people to communicate numbers in ways that make them easy to understand and use.</p>
<p>Research shows that <a href="https://www.ncbi.nlm.nih.gov/books/NBK224823/">how numbers are presented</a> can matter as much as what is presented. For example, you might see a news story that says 1 out of 100,000 people who ate some food got cancer. If that sounds scary, try calculating that proportion as a percentage, or ask your doctor to translate the number to that format. In this case, it’s only 0.001%. For many people, a number presented in that first <a href="https://doi.org/10.1177/0272989X10391672">frequency format seems highly risky</a>, even though the equivalent percentage is tiny.</p>
<p>And lastly, practice, practice, practice.</p>
<p>Begin by working on simple math like addition and subtraction. Most important, get feedback. Learning requires knowing what you’ve gotten right and wrong.</p>
<p>You can also help your numeric confidence and make later practice more effective by maintaining a positive overall view of yourself. One way to do this is to remind yourself about what is truly important to you, like family and friends, religion or politics. This way, you can feel good about yourself even while you attempt to get better at something that challenges you, like math. <a href="https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0180674">Our research</a> shows that taking these steps improves numeracy and outcomes.</p>
<p>These and other results cry out for better math instruction, and for everyone to take math learning and careful communication of numbers more seriously. Many older adults are facing health issues and retirement with insufficient finances. We believe that improving numeracy, numeric confidence and their match will help younger generations to plan better.</p>
<p>And that question about choir membership from above? If there are 100 men in the choir and 300 men not in the choir, that means there are 400 men in total. So 100 out of the total 400 men are in the choir. The chance of a man being in the choir = 100/400 = 0.25 = 25%.</p>
<p>[ <em>You’re smart and curious about the world. So are The Conversation’s authors and editors.</em> <a href="https://theconversation.com/us/newsletters?utm_source=TCUS&utm_medium=inline-link&utm_campaign=newsletter-text&utm_content=youresmart">You can read us daily by subscribing to our newsletter</a>. ]</p><img src="https://counter.theconversation.com/content/123129/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Ellen Peters receives funding from the National Science Foundation and National Institutes of Health. </span></em></p><p class="fine-print"><em><span>Brittany Shoots-Reinhard receives funding from the National Science Foundation and National Institutes of Health.</span></em></p>How mathematically proficient are you? And do you have the skills to back up your level of math confidence? The answers to those questions may have ramifications for your financial and physical health.Ellen Peters, Philip H. Knight Professor of Science Communication, University of OregonBrittany Shoots-Reinhard, Research Assistant Professor of Psychology, The Ohio State UniversityLicensed as Creative Commons – attribution, no derivatives.