tag:theconversation.com,2011:/us/topics/statistics-probability-and-risk-37151/articlesStatistics probability and risk – The Conversation2023-11-07T13:36:33Ztag:theconversation.com,2011:article/2171472023-11-07T13:36:33Z2023-11-07T13:36:33ZAcapulco was built to withstand earthquakes, but not Hurricane Otis’ destructive winds – how building codes failed this resort city<figure><img src="https://images.theconversation.com/files/557873/original/file-20231106-267225-w11vn6.jpg?ixlib=rb-1.1.0&rect=0%2C16%2C3593%2C2246&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Acapulco's beachfront condo towers were devastated by Hurricane Otis.</span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/news-photo/aerial-view-of-damages-caused-by-the-passage-of-hurricane-news-photo/1750791993">Rodrigo Oropeza/AFP via Getty Images</a></span></figcaption></figure><p>Acapulco wasn’t prepared when Hurricane Otis struck as a powerful Category 5 storm on Oct. 25, 2023. The short notice as the <a href="https://www.nesdis.noaa.gov/news/hurricane-otis-causes-catastrophic-damage-acapulco-mexico">storm rapidly intensified</a> over the Pacific Ocean wasn’t the only problem – the Mexican resort city’s buildings weren’t designed to handle anything close to Otis’ 165 mph winds.</p>
<p>While Acapulco’s oceanfront high-rises were built to withstand <a href="https://www.reuters.com/world/americas/strong-quake-rocks-mexicos-acapulco-damaging-airport-killing-one-2021-09-08/">the region’s powerful earthquakes</a>, they had a weakness. </p>
<p>Since powerful hurricanes are <a href="https://coast.noaa.gov/hurricanes">rare in Acapulco</a>, Mexico’s <a href="https://www.gob.mx/cms/uploads/attachment/file/247555/300617_EvaluacionEstructuras_02-Viento.pdf">building codes didn’t require</a> that their exterior materials be able to hold up to extreme winds. In fact, those materials were often kept light to help meet earthquake building standards.</p>
<p>Otis’ powerful winds ripped off exterior cladding and shattered windows, exposing bedrooms and offices to the wind and rain. The storm <a href="https://www.pbs.org/newshour/world/death-toll-from-hurricane-otis-hits-48-with-36-missing-as-search-and-recovery-continues">took dozens of lives</a> and caused <a href="https://www.reinsurancene.ws/corelogic-pegs-hurricane-otis-insurable-loss-at-10bn-to-15bn/">billions of dollars in damage</a>.</p>
<figure class="align-center ">
<img alt="A large glass tower with sloping sides, like a sliced egg, reflects the sunrise with the Pacific Ocean looking placid in the background." src="https://images.theconversation.com/files/557814/original/file-20231106-17-xzhpml.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/557814/original/file-20231106-17-xzhpml.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=397&fit=crop&dpr=1 600w, https://images.theconversation.com/files/557814/original/file-20231106-17-xzhpml.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=397&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/557814/original/file-20231106-17-xzhpml.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=397&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/557814/original/file-20231106-17-xzhpml.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=498&fit=crop&dpr=1 754w, https://images.theconversation.com/files/557814/original/file-20231106-17-xzhpml.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=498&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/557814/original/file-20231106-17-xzhpml.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=498&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">A US$130 million luxury condo building on the beach in Acapulco before Hurricane Otis struck on Oct. 25, 2023.</span>
<span class="attribution"><span class="source">Hamid Arabzadeh, PhD., P.Eng.</span></span>
</figcaption>
</figure>
<figure class="align-center ">
<img alt="A stormy sky shows through the floors that were once apartments." src="https://images.theconversation.com/files/557815/original/file-20231106-19-vbqly2.jpeg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/557815/original/file-20231106-19-vbqly2.jpeg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=450&fit=crop&dpr=1 600w, https://images.theconversation.com/files/557815/original/file-20231106-19-vbqly2.jpeg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=450&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/557815/original/file-20231106-19-vbqly2.jpeg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=450&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/557815/original/file-20231106-19-vbqly2.jpeg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=566&fit=crop&dpr=1 754w, https://images.theconversation.com/files/557815/original/file-20231106-19-vbqly2.jpeg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=566&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/557815/original/file-20231106-19-vbqly2.jpeg?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">
<figcaption>
<span class="caption">The same Acapulco condo tower after Hurricane Otis.</span>
<span class="attribution"><span class="source">Hamid Arabzadeh, PhD., P.Eng.</span></span>
</figcaption>
</figure>
<p>I have worked on engineering strategies to enhance disaster resilience for over three decades and recently wrote a book, “<a href="https://rowman.com/ISBN/9781633888234/The-Blessings-of-Disaster-The-Lessons-That-Catastrophes-Teach-Us-and-Why-Our-Future-Depends-on-It">The Blessings of Disaster</a>,” about the gambles humans take with disaster risk and how to increase resilience. Otis provided a powerful example of one such gamble that exists when building codes rely on probabilities that certain hazards will occur based on recorded history, rather than considering the severe consequences of storms that can devastate entire cities.</p>
<h2>The fatal flaw in building codes</h2>
<p>Building codes typically provide “<a href="https://asce7hazardtool.online/">probabilistic-based” maps</a> that specify wind speeds that engineers must consider when designing buildings. </p>
<p>The problem with that approach lies in the fact that “probabilities” are simply the odds that extreme events of a certain size will occur in the future, mostly calculated based on past occurrences. Some models may include additional considerations, but these are still typically anchored in known experience. </p>
<p>This is all good science. Nobody argues with that. It allows engineers to design structures in accordance with a consensus on what are deemed acceptable <a href="https://doi.org/10.5194/nhess-19-1347-2019">return periods</a> for various hazards, referring to the likelihood of those disasters occurring. Return periods are a somewhat arbitrary assessment of what is a reasonable balance between minimizing risk and keeping building costs reasonable.</p>
<p>However, <a href="https://www.structuremag.org/?p=13360">probabilistic maps</a> only capture the odds of the hazard occurring. A <a href="https://hazards.atcouncil.org/">probabilistic map</a> might specify a wind speed to consider for design, irrespective of whether that given location is a small town with a few hotels or a megapolis with high-rises and complex urban infrastructure. In other words, probabilistic maps do not consider the consequences when an extreme hazard exceeds the specified value and “all hell breaks loose.”</p>
<h2>How probability left Acapulco exposed</h2>
<p>According to the Mexican building code, hotels, condos and other commercial and office buildings in Acapulco must be <a href="https://www.gob.mx/cms/uploads/attachment/file/247555/300617_EvaluacionEstructuras_02-Viento.pdf">designed to resist 88 mph winds</a>, corresponding to the strongest wind likely to occur on average once every 50 years there. That’s a Category 1 storm.</p>
<p>A 200-year return period for wind is used for essential facilities, such as hospital and school buildings, <a href="https://www.gob.mx/cms/uploads/attachment/file/247555/300617_EvaluacionEstructuras_02-Viento.pdf">corresponding to 118 mph winds</a>. But over a building’s life span of, say, 50 years, that still leaves a 22% chance that winds exceeding 118 mph will occur (yes, the world of statistics is that sneaky). </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/557871/original/file-20231106-15-ffcd7l.PNG?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="A map of the Mexico area with lots of storm tracks offshore and a few crossing land in the southern part of the country." src="https://images.theconversation.com/files/557871/original/file-20231106-15-ffcd7l.PNG?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/557871/original/file-20231106-15-ffcd7l.PNG?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=457&fit=crop&dpr=1 600w, https://images.theconversation.com/files/557871/original/file-20231106-15-ffcd7l.PNG?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=457&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/557871/original/file-20231106-15-ffcd7l.PNG?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=457&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/557871/original/file-20231106-15-ffcd7l.PNG?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=575&fit=crop&dpr=1 754w, https://images.theconversation.com/files/557871/original/file-20231106-15-ffcd7l.PNG?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=575&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/557871/original/file-20231106-15-ffcd7l.PNG?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=575&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Mexico’s hurricane history in storm tracks.</span>
<span class="attribution"><a class="source" href="https://coast.noaa.gov/hurricanes/#map">NOAA</a></span>
</figcaption>
</figure>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/557869/original/file-20231106-19-jxgqql.PNG?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="A map of the Acapulco area with lots of storm tracks offshore and a few crossing land." src="https://images.theconversation.com/files/557869/original/file-20231106-19-jxgqql.PNG?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/557869/original/file-20231106-19-jxgqql.PNG?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=427&fit=crop&dpr=1 600w, https://images.theconversation.com/files/557869/original/file-20231106-19-jxgqql.PNG?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=427&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/557869/original/file-20231106-19-jxgqql.PNG?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=427&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/557869/original/file-20231106-19-jxgqql.PNG?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=537&fit=crop&dpr=1 754w, https://images.theconversation.com/files/557869/original/file-20231106-19-jxgqql.PNG?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=537&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/557869/original/file-20231106-19-jxgqql.PNG?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=537&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 century of hurricane storm tracks near Acapulco show several offshore storms that brought strong winds and rain to the city, but few direct landfalls. Acapulco Bay is in the center of the map on the coast. Red, pink and purple lines are categories 3, 4 and 5, respectively.</span>
<span class="attribution"><a class="source" href="https://coast.noaa.gov/hurricanes/#map">NOAA</a></span>
</figcaption>
</figure>
<p>The probability wind maps for both return periods show Acapulco experiences lower average wind speeds than much of the 400 miles of Mexican coast north of the city. Yet, Acapulco is a major city, with a metropolitan population of over 1 million. It also has <a href="https://skyscraperpage.com/cities/?cityID=586&offset=100&statusID=1">more than 50 buildings</a> taller than 20 stories, according to the SkyscraperPage, a database of skyscrapers, and it is the only city with buildings that tall along that stretch of the Pacific coast.</p>
<p>Designing for a 50-year return period in this case is questionable, as it implies a near 100% chance of encountering wind exceeding this design value for a building with a 50-year life span or greater. </p>
<h2>Florida faces similiar challenges</h2>
<p>The shortcomings of probabilistic-based maps that specify wind speeds have also been observed in the United States. For example, new buildings along most of Florida’s coast must be able to <a href="https://www.flrules.org/gateway/readRefFile.asp?refId=13160&filename=Florida_Building_Code_7thEdition_1609_3_Tables.pdf">resist 140 mph winds</a> or greater, but there are a few exceptions. One is the Big Bend area where <a href="https://www.tampabay.com/hurricane/2023/09/02/map-idalia-flooding-big-bend-surge/">Hurricane Idalia made landfall</a> in 2023. Its design wind speed is about 120 mph instead.</p>
<p>A <a href="https://codes.iccsafe.org/content/FLBC2023P1/chapter-16-structural-design#FLBC2023P1_Ch16_Sec1609">2023 update to the Florida Building Code</a> raised the minimum wind speed to approximately 140 mph in Mexico Beach, the Panhandle town that was <a href="https://mexicobeachfl.gov/uploads/2022/06/Wind-load-Ordinance-21919.pdf">devastated by Hurricane Michael</a> in 2018. The Big Bend exception may be the next one to be eliminated.</p>
<h2>Acapulco’s earthquake design weakness</h2>
<p>A saving grace for Acapulco is that it is located in one of <a href="https://mexicodailypost.com/2021/04/19/earthquake-map-30-of-mexico-under-high-seismic-risk/">Mexico’s most active seismic risk zones</a> – for example, a <a href="https://www.nytimes.com/live/2021/09/07/world/mexico-earthquake">magnitude 7 earthquake struck nearby in 2021</a>. As a result, the lateral-load-resisting structural systems in tall buildings there are designed to resist seismic forces that are generally larger than hurricane forces.</p>
<p>However, a drawback is that the larger the mass of a building, <a href="https://www.wbdg.org/resources/seismic-design-principles">the larger the seismic forces</a> the building must be designed to resist. Consequently, light materials were typically used for the cladding – the exterior surface of the building that protects it against the weather – because that translates into lower seismic forces. This light cladding was not able to withstand hurricane-force winds.</p>
<p>Had the cladding not failed, the full wind forces would have been transferred to the structural system, and the buildings would have survived with little or no damage.</p>
<h2>A ‘good engineering approach’ to hazards</h2>
<p>A better building code could go one step beyond “good science” probabilistic maps and adopt a “<a href="https://michelbruneau.com/TheBlessingsOfDisaster.htm">good engineering approach</a>” by taking stock of the consequences of extreme events occurring, not just the odds that they will.</p>
<p>In Florida, the incremental cost of designing for wind speeds of 140 mph rather than 120 mph is marginal compared to total building cost, given that cladding able to resist more than 140 mph is already used in nearly all of the state. In Acapulco, with the spine of buildings already able to resist earthquake forces much larger than hurricane forces, designing cladding that can withstand stronger hurricane-level forces is likely to be an even smaller percentage of total project cost.</p>
<p>Someday, the way that design codes deal with extreme events such as hurricanes, not only in Mexico, will hopefully evolve to more broadly account for what is at risk at the urban scale. Unfortunately, as I explain in “<a href="https://michelbruneau.com/TheBlessingsOfDisaster.htm">The Blessings of Disaster</a>,” we will see more extreme disasters before society truly becomes disaster resilient.</p><img src="https://counter.theconversation.com/content/217147/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Michel Bruneau 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>The best science is not always the best engineering when it comes to building codes. It’s also a problem across the US, as an engineer who works on disaster resilience explains.Michel Bruneau, Professor of Engineering, University at BuffaloLicensed 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/1822872022-05-17T12:26:39Z2022-05-17T12:26:39ZIt’s impossible to determine your personal COVID-19 risks and frustrating to try – but you can still take action<figure><img src="https://images.theconversation.com/files/463465/original/file-20220516-23-r0etgg.jpg?ixlib=rb-1.1.0&rect=151%2C92%2C4901%2C3581&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Before the pandemic, an intergenerational tea party wouldn't have seemed a risky proposition.</span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/photo/mature-woman-with-her-favorite-grandchild-royalty-free-image/947724704?adppopup=true">fotostorm/E+ via Getty Images</a></span></figcaption></figure><p>“How risky is being indoors with our 10-year-old granddaughter without masks? We have plans to have birthday tea together. Are we safe?”</p>
<p>That question, from a woman named Debby in California, is just one of hundreds I’ve received from concerned people who are worried about COVID-19. <a href="https://scholar.google.com/citations?user=xDbfMhwAAAAJ&hl=en">I’m an epidemiologist</a> and one of the women behind <a href="https://dearpandemic.org/">Dear Pandemic</a>, a science communication project that has delivered practical pandemic advice on social media since the beginning of the pandemic. </p>
<p>How risky is swim team? How risky is it to go to my orthodontist appointment? How risky is going to the grocery store with a mask on if no one else is wearing one and my father is an organ transplant recipient? How risky is it to have a wedding with 200 people, indoors, and the reception hall has a vaulted ceiling? And on and on.</p>
<p>These questions are <a href="https://dearpandemic.org/how-safe-is-my-specific-situation-event-activity/">hard to answer</a>, and even when we try, the answers are unsatisfying.</p>
<p>So in early April 2022, when Anthony Fauci, the president’s chief medical advisor, told Americans that from here on out, each of us is going to have to <a href="https://www.webmd.com/lung/news/20220411/fauci-weigh-personal-risk-amid-covid-uptick">do our own personal risk assessment</a>, I put my head down on my desk.</p>
<p>Individualized risk assessment is not a reasonable ask, even for someone who does risk assessment for a living, let alone for the rest of us. It’s impossible to evaluate our own risk for any given situation, and the impossibility of the task can make us feel like giving up entirely. So instead of doing that, I suggest focusing on risk reduction. Reframing in this way brings us back to the realm of what we can control and to the tried and true evidence-based strategies: wearing masks, getting vaccinated and boosted, avoiding indoor crowds and improving ventilation. </p>
<h2>A cascade of unknowable variables</h2>
<p>In my experience, nonscientists and epidemiologists use the word “risk” to mean different things. To most people, risk means a quality – something like danger or vulnerability.</p>
<p>When epidemiologists and other scientists use the word risk, though, we’re talking about a math problem. <a href="https://doi.org/10.1093/aje/kwv001">Risk is the probability of a particular outcome</a>, in a particular population at a particular time. To give a simple example, the chances that a coin flip will be heads is 1 in 2.</p>
<p>As public health researchers, we often offer risk information in this format: The probability that an unvaccinated person will die of COVID-19 if they catch it is about <a href="https://doi.org/10.1016/j.ijid.2020.09.1464">1 in 200</a>. As many as <a href="https://www.ons.gov.uk/peoplepopulationandcommunity/healthandsocialcare/conditionsanddiseases/bulletins/prevalenceofongoingsymptomsfollowingcoronaviruscovid19infectionintheuk/6may2022">1 in 8 people with COVID-19</a> will have symptoms persisting for weeks or months after recovering.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/463466/original/file-20220516-26-zikrhg.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="white-haired man in jacket and tie seated at mic with 'Dr. Fauci' on name plate" src="https://images.theconversation.com/files/463466/original/file-20220516-26-zikrhg.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/463466/original/file-20220516-26-zikrhg.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/463466/original/file-20220516-26-zikrhg.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/463466/original/file-20220516-26-zikrhg.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/463466/original/file-20220516-26-zikrhg.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/463466/original/file-20220516-26-zikrhg.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/463466/original/file-20220516-26-zikrhg.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">Anthony Fauci wore a mask in advance of Senate testimony.</span>
<span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/news-photo/director-of-the-national-institute-of-allergy-and-news-photo/1237661251">Shawn Thew/AFP via Getty Images</a></span>
</figcaption>
</figure>
<p>To embark on your personal risk assessment, as Fauci casually suggested, you first have to decide what outcome you’re talking about. People often aren’t very specific when they consider risk in a qualitative sense; they tend to lump a lot of different risks together. But risk is not a general concept. It’s always the risk of a specific outcome.</p>
<p>Let’s think about Debby. First, there’s the risk that she will be exposed to COVID-19 during tea; this depends on her granddaughter. Where does she live? How many kids at her school have COVID-19 this week? Will she take a rapid test before she comes over? These factors all influence the granddaughter’s risk of exposing Debby to COVID-19, but I don’t know any of them and likely neither does Debby. Given the lack of systematic testing, I have no idea how many people in my own community have COVID-19 right now. At this point, our best guess at community rates is <a href="https://www.cdc.gov/healthywater/surveillance/wastewater-surveillance/wastewater-surveillance.html">literally in the toilet</a> – <a href="https://theconversation.com/wastewater-monitoring-took-off-during-the-covid-19-pandemic-and-heres-how-it-could-help-head-off-future-outbreaks-180775">monitoring sewage for the coronavirus</a>.</p>
<p>If I assume that Debby’s granddaughter does have COVID-19 on the appointed day, I can start thinking about Debby’s downstream risks: whether she’ll get COVID-19 from her granddaughter; the chances that she’ll be hospitalized and that she’ll die; and the probability that she’ll have <a href="https://www.cdc.gov/coronavirus/2019-ncov/long-term-effects/index.html">long COVID</a>. I can also consider the risk that Debby will catch COVID-19 and then give it to others, perpetuating an outbreak. If she gets sick, the whole hierarchy of risks comes into play for everyone Debby sees after she is infected. </p>
<p>Finally, there are competing risks. If Debby decides to skip the party, there may be risks to her own or her granddaughter’s mental health or their relationship. Many skipped celebrations in many families <a href="https://theconversation.com/why-nobody-will-ever-agree-on-whether-covid-lockdowns-were-worth-it-161154">could negatively affect the economy</a>. People could lose business; they could lose their jobs.</p>
<p>Each of these probabilities is influenced by a cascade of fickle conditions. Some of the factors that shape risks are in your control. For example, I decided to get vaccinated and boosted. Therefore, <a href="https://www.cdc.gov/mmwr/volumes/71/wr/mm7112e1.htm">I’m less likely to end up in the hospital and to die if I get COVID-19</a>. But some risks are not in your control – age, other health conditions, gender, race and the behavior of the people all around you. And many, many of the risk factors are simply unknowns. We’ll never be able to accurately evaluate the whole volatile landscape of risk for a particular situation and come up with a number. </p>
<h2>Taking charge of what you can</h2>
<p>There will never be a situation where I can say to Debby: The risk is 1 in 20. And even if I could, I’m not sure it would be helpful. Most people have a very hard time understanding probabilities they encounter every day, such as <a href="https://doi.org/10.1080/20445911.2018.1553884">the chance that it will rain</a>.</p>
<p>The statistical risk of a particular outcome doesn’t address Debby’s underlying question: Are we safe?</p>
<p>Nothing is entirely safe. If you want my professional opinion on whether it’s safe to walk down the sidewalk, I will have to say no. Bad things happen. I know someone who tore a tendon in her hand while putting a fitted sheet on a bed last week.</p>
<p>It’s much more practical to ask: What can I do to reduce the risk? </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/463468/original/file-20220516-19-1vlpcp.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="young girl shows off her 'I got my COVID-19 vaccine' sticker" src="https://images.theconversation.com/files/463468/original/file-20220516-19-1vlpcp.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/463468/original/file-20220516-19-1vlpcp.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=382&fit=crop&dpr=1 600w, https://images.theconversation.com/files/463468/original/file-20220516-19-1vlpcp.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=382&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/463468/original/file-20220516-19-1vlpcp.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=382&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/463468/original/file-20220516-19-1vlpcp.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=480&fit=crop&dpr=1 754w, https://images.theconversation.com/files/463468/original/file-20220516-19-1vlpcp.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=480&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/463468/original/file-20220516-19-1vlpcp.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=480&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Getting vaccinated is one important way to cut your risk of serious illness or death from COVID-19.</span>
<span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/news-photo/girl-shows-her-sticker-after-being-vaccinated-at-a-covid-19-news-photo/1240240694">Zou Zheng/Xinhua News Agency via Getty Images</a></span>
</figcaption>
</figure>
<p>Focusing on actions that reduce risk frees us from obsessing over unanswerable questions with useless answers so we can focus on what is within our control. I will never know precisely how risky Debby’s tea is, but I <a href="https://dearpandemic.org/protecting-against-new-covid-virus-variants/">do know how to make the risks smaller</a>. </p>
<p>I suspect the question folks are really asking is: How can I manage the risks? I like this question better because it has an answer: You should do what you can. If it’s reasonable to wear a mask, wear one. <a href="https://theconversation.com/should-you-wear-a-mask-on-a-plane-bus-or-train-when-theres-no-mandate-4-essential-reads-to-help-you-decide-181582">Yes, even if it isn’t required</a>. If it’s reasonable to do an <a href="https://theconversation.com/just-how-accurate-are-rapid-antigen-tests-two-testing-experts-explain-the-latest-data-180405">at-home antigen test</a> before you see your vulnerable grandparents, do that. <a href="https://www.cdc.gov/coronavirus/2019-ncov/vaccines/index.html">Get vaccinated and boosted</a>. <a href="https://doi.org/10.1016/j.vaccine.2021.10.039">Tell your friends and family</a> that you did, and why. Choose outdoor gatherings. <a href="https://theconversation.com/keeping-indoor-air-clean-can-reduce-the-chance-of-spreading-coronavirus-149512">Open a window</a>. </p>
<p>Constantly assessing and reassessing risks has <a href="https://theconversation.com/pandemic-decision-making-is-difficult-and-exhausting-heres-the-psychology-that-explains-why-176968">given many people decision fatigue</a>. I feel that too. But you don’t need to recalibrate risks of everything, every day, for every variant, because the strategies to reduce risk remain the same. Reducing risk – even if it’s just a little bit – is better than doing nothing.</p><img src="https://counter.theconversation.com/content/182287/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Malia Jones 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 want a simple answer. Is this action safe? But despite Anthony Fauci bouncing responsibility for COVID-19 risk assessment to individuals, your risk can’t be boiled down to one probability.Malia Jones, Scientist in Health Geography, University of Wisconsin-MadisonLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1366752020-04-30T16:09:41Z2020-04-30T16:09:41ZCoronavirus is significant, but is it a true black swan event?<figure><img src="https://images.theconversation.com/files/329227/original/file-20200420-152597-42q13c.jpg?ixlib=rb-1.1.0&rect=360%2C54%2C2684%2C1999&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">A black swan event must meet three criteria: it must be an outlier, must have a major impact and must be declared predictable in hindsight.</span> <span class="attribution"><a class="source" href="https://commons.wikimedia.org/w/index.php?curid=85763152">(Buiobuione/Wikimedia)</a>, <a class="license" href="http://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA</a></span></figcaption></figure><p>Since the “black swan” metaphor was coined in the <a href="https://www.penguinrandomhouse.com/books/176226/the-black-swan-second-edition-by-nassim-nicholas-taleb/">2007 book of the same name</a> it has become fashionable to label virtually all low probability/high impact events black swans.</p>
<p>But the danger of making an occurrence like the COVID-19 outbreak appear to be astronomically rare is that we will treat it as such and fail to prepare for the next pandemic. What’s more, those accountable for this preparation will dismiss their blatant failures because of the perceived exceptional nature of the event.</p>
<p>As managing director of the oldest university-based disaster risk reduction research institute in Canada, and with almost 30 years of researching and writing about disaster risk management, I know this all too well. When you make an event seem exceptional when it really isn’t, it will be used as a crutch by those who failed to prepare in the face of the known risk.</p>
<h2>What is a black swan?</h2>
<p>In <em>The Black Swan</em>, written by professor, statistician and former options trader Nassim Taleb, the author explains how an event can come to be named a black swan:</p>
<blockquote>
<p>“First, it is an outlier, as it lies outside the realm of regular expectations, because nothing in the past can convincingly point to its possibility. Second, it carries an extreme ‘impact.’ Third, in spite of its outlier status, human nature makes us concoct explanations for its occurrence after the fact, making it explainable and predictable.”</p>
</blockquote>
<p>So, by their very nature, black swan events are quite exclusive. They must be, because if next to everything is a black swan, then nothing is.</p>
<p>But this still leaves the question: Can COVID-19 be considered a black swan?</p>
<p>Let’s look at some of the facts and place them against the three attributes set out by Taleb.</p>
<h2>Attribute one: Is the COVID pandemic an outlier?</h2>
<p><a href="https://www.bbc.com/future/article/20200325-covid-19-the-history-of-pandemics">History shows</a> that infectious diseases, epidemics and pandemics, have been the number 1 mass killers of people, outperforming even natural disasters and wars (indeed, more people died from the 1918 flu outbreak than died in the First World War).</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/316651/original/file-20200221-92558-afqz51.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/316651/original/file-20200221-92558-afqz51.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=498&fit=crop&dpr=1 600w, https://images.theconversation.com/files/316651/original/file-20200221-92558-afqz51.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=498&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/316651/original/file-20200221-92558-afqz51.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=498&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/316651/original/file-20200221-92558-afqz51.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=626&fit=crop&dpr=1 754w, https://images.theconversation.com/files/316651/original/file-20200221-92558-afqz51.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=626&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/316651/original/file-20200221-92558-afqz51.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=626&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Walter Reed Hospital flu ward during the flu epidemic of 1918-19, in Washington D.C.</span>
<span class="attribution"><a class="source" href="https://theconversation.com/coronavirus-fears-should-we-take-a-deep-breath-130859">(Shutterstock)</a></span>
</figcaption>
</figure>
<p>That pandemics break out from time to time is well known and well documented.</p>
<p>So, too, are warnings about the “next” outbreak. Says journalist <a href="https://www.theatlantic.com/health/archive/2020/03/how-will-coronavirus-end/608719/">Ed Yong in <em>The Atlantic</em></a>: </p>
<blockquote>
<p>“In recent years, hundreds of health experts have written books, white papers and op-eds warning of the possibility. Bill Gates has been telling anyone who would listen, including the 18 million viewers of his <a href="https://www.youtube.com/watch?v=6Af6b_wyiwI">TED Talk</a>. In 2018, I wrote a story for <em>The Atlantic</em> arguing that <a href="https://www.theatlantic.com/magazine/archive/2018/07/when-the-next-plague-hits/561734/">America was not ready for the pandemic that would eventually come</a>.”</p>
</blockquote>
<p>Both <a href="https://www.youtube.com/watch?v=spcj6KUr4aA">George W. Bush</a> (in November 2005) and <a href="https://www.youtube.com/watch?v=w50tZonOgoU">Barack Obama</a> (in December 2014) warned of the next pandemic in speeches at the National Institutes of Health.</p>
<p>Along with the historical record and the many articles, papers and other sources that warn of the next pandemic, governments themselves often conduct exercises, <a href="https://www.centerforhealthsecurity.org/event201/about">including table-top simulations</a> and other planning, in an attempt to determine how to get ahead of the next pandemic.</p>
<p>Seven days before Donald Trump took office on January 20, 2017, his aides and out-going Obama administration officials <a href="https://www.politico.com/news/2020/03/16/trump-inauguration-warning-scenario-pandemic-132797">were briefed on a table-top exercise</a> that played through a fictitious outbreak of H9N2 — an influenza virus — with effects not unlike what we have seen with SARS-CoV-2. </p>
<p>Similarly, in 2019, the Trump administration’s own Department of Health and Human Services carried out a pandemic simulation tagged as “<a href="https://www.npr.org/2020/03/20/819186528/what-last-years-government-simulation-predicted-about-todays-pandemic">Crimson Contagion</a>,” which played out a viral outbreak originating in China that could kill close to 600,000 people in the United States alone.</p>
<p>So, can we say in all fairness and honesty that no one saw the possibility of COVID-19 coming?</p>
<h2>Attribute two: Does COVID-19 carry an extreme impact?</h2>
<p>Taleb’s second requirement is that the event must have a major impact.</p>
<p>At writing, attempting to provide an accurate quantitative impact of COVID-19 would be akin to snapping a picture of an odometer as the car is racing down the Autobahn.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/330471/original/file-20200425-163088-18to55.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/330471/original/file-20200425-163088-18to55.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=400&fit=crop&dpr=1 600w, https://images.theconversation.com/files/330471/original/file-20200425-163088-18to55.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=400&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/330471/original/file-20200425-163088-18to55.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=400&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/330471/original/file-20200425-163088-18to55.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=503&fit=crop&dpr=1 754w, https://images.theconversation.com/files/330471/original/file-20200425-163088-18to55.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=503&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/330471/original/file-20200425-163088-18to55.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">
<figcaption>
<span class="caption">The need for social distancing to prevent the spread of COVID-19 has required the temporary closing of non-essential businesses, like these boarded-up clothing stores on Robson Street in Vancouver.</span>
<span class="attribution"><span class="source">THE CANADIAN PRESS/Darryl Dyck</span></span>
</figcaption>
</figure>
<p>However, while COVID-19 is not anticipated to have an impact even remotely close to that of the 1918 flu outbreak (<a href="https://www.cdc.gov/flu/pandemic-resources/1918-pandemic-h1n1.html">at least 50 million deaths</a>), there can be no question that the current pandemic has had — and will continue to have — an extreme impact, both on people and on national economies.</p>
<h2>Attribute three: Is it, or will it be, normalized after the fact?</h2>
<p>The concept of “normalizing” a large event — by rendering it explainable or predictable in hindsight — completes the three criteria and makes it a black swan. However, this element seems quite arbitrary, raising several questions:</p>
<p>Who is qualified to normalize an event in this manner, whereby the initial shock of the event is then casually dismissed?</p>
<p>How can we know if an event is normalized unjustly or if the normalization is legitimate?</p>
<p>Can important comments by journalists like <a href="https://www.bbc.com/future/article/20200325-covid-19-the-history-of-pandemics">Bryan Walsh</a> (“COVID-19, could not have been more predictable” and “COVID-19 marks the return of a very old — and familiar — enemy”) and <a href="https://www.theatlantic.com/health/archive/2020/03/how-will-coronavirus-end/608719/">Yong</a> (“A global pandemic of this scale was inevitable”) be effectively neutralized by dismissing them as mere attempts to normalize or brush off the current crisis? The danger in doing so is that rejecting the inevitability of a pandemic like COVID-19 also enables us to reject the likelihood of future pandemics, and the need to be better prepared.</p>
<p>And, since the propensity to normalize can be attributed to a blind spot in human cognition (that is, <a href="https://dictionary.apa.org/hindsight-bias">people are hardwired to normalize</a>), should it even be an attribute of a black swan in the first place?</p>
<p>Since we are still in the midst of the current pandemic crisis, we do not yet know whether the COVID-19 pandemic will be normalized. </p>
<h2>So COVID-19, a black swan or no?</h2>
<p>In the study of natural hazards, the chances of a flood or an earthquake or a hurricane happening in any given period in a given place is expressed in terms of time and probability. For example, the probability of one in 100 years for a flood means that there is a one per cent chance of a flood affecting a given area in any one year. This means that there is a 99 per cent chance that a given place will not be flooded — pretty good odds.</p>
<figure class="align-right ">
<img alt="" src="https://images.theconversation.com/files/331251/original/file-20200429-110775-oaar8g.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/331251/original/file-20200429-110775-oaar8g.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=925&fit=crop&dpr=1 600w, https://images.theconversation.com/files/331251/original/file-20200429-110775-oaar8g.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=925&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/331251/original/file-20200429-110775-oaar8g.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=925&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/331251/original/file-20200429-110775-oaar8g.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1163&fit=crop&dpr=1 754w, https://images.theconversation.com/files/331251/original/file-20200429-110775-oaar8g.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1163&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/331251/original/file-20200429-110775-oaar8g.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1163&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Is COVID-19 a black swan, or not?</span>
<span class="attribution"><span class="source">(Penguin Random House)</span></span>
</figcaption>
</figure>
<p>However, if you carry that same probability over a longer time frame — say over the life of a mortgage or the time residents plan to stay in a home (let’s say it’s 30 years) — the probability of a one in 100 flood hitting that house goes from one per cent per year to 26 per cent over the course of the mortgage — greater than one in four odds.</p>
<p>In <a href="https://dx.doi.org/10.2471%2FBLT.17.199588">a 2018 research study</a>, investigators made the assumption that the probability of a pandemic of a certain level occurring is one in 100, or one per cent in any given year. So, just as with a flood, when calculated for a 30-year period, there is greater than a one in four chance of a pandemic occurring. Carrying the odds over 50 years means there is almost a 40 per cent chance of a global outbreak.</p>
<p>The subtitle of Taleb’s book is “The impact of the highly improbable.” But an event like COVID-19 is not all that rare. Indeed, history is replete with such events, there have been numerous warnings from many sources, and the mathematical odds of an occurrence are not all that remote. With pandemics, it is not really a question of if, but usually when.</p>
<p>Indeed, <a href="https://www.newyorker.com/news/daily-comment/the-pandemic-isnt-a-black-swan-but-a-portent-of-a-more-fragile-global-system">Taleb recently weighed in</a> on the question of whether COVID-19 is or isn’t a black swan. </p>
<p>Spoiler alert: it isn’t.</p><img src="https://counter.theconversation.com/content/136675/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Glenn McGillivray works for the Institute for Catastrophic Loss Reduction, an independent, not for profit research institute with a focus on disaster risk reduction. The Institute is funded by the Canadian property and casualty insurance industry and receives occasional funding from various levels of government to conduct research.
</span></em></p>The danger of treating COVID-19 as an astronomically rare and improbable event is that we will treat it as such and fail to prepare for the next pandemic. And there will be another pandemic.Glenn McGillivray, Managing Director, Institute for Catastrophic Loss Reduction, Western UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/744402017-04-04T19:25:00Z2017-04-04T19:25:00ZParadoxes of probability and other statistical strangeness<figure><img src="https://images.theconversation.com/files/163220/original/image-20170329-14155-f440dl.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Statistics and probability can sometimes yield mind bending results.</span> <span class="attribution"><span class="source">Shutterstock</span></span></figcaption></figure><p><em>Statistics is a useful tool for understanding the patterns in the world around us. But our intuition often lets us down when it comes to interpreting those patterns. In this series we look at some of the common mistakes we make and how to avoid them when thinking about <a href="https://theconversation.com/au/topics/statistics-probability-and-risk-37151">statistics, probability and risk</a>.</em></p>
<hr>
<p>You don’t have to wait long to see a headline proclaiming that some food or behaviour is associated with either an increased or a decreased health risk, or <a href="http://fivethirtyeight.com/features/you-cant-trust-what-you-read-about-nutrition/">often both</a>. How can it be that seemingly rigorous scientific studies can produce opposite conclusions?</p>
<p>Nowadays, researchers can access a wealth of software packages that can readily analyse data and output the results of complex statistical tests. While these are powerful resources, they also open the door to people without a full statistical understanding to misunderstand some of the subtleties within a dataset and to draw wildly incorrect conclusions.</p>
<p>Here are a few common statistical fallacies and paradoxes and how they can lead to results that are counterintuitive and, in many cases, simply wrong. </p>
<hr>
<h2>Simpson’s paradox</h2>
<h3>What is it?</h3>
<p>This is where trends that appear within different groups disappear when data for those groups are combined. When this happens, the overall trend might even appear to be the opposite of the trends in each group. </p>
<p>One example of this paradox is where a treatment can be detrimental in all groups of patients, yet can appear beneficial overall once the groups are combined.</p>
<h3>How does it happen?</h3>
<p>This can happen when the sizes of the groups are uneven. A trial with careless (or unscrupulous) selection of the numbers of patients could conclude that a harmful treatment appears beneficial.</p>
<h3>Example</h3>
<p>Consider the following <a href="https://en.wikipedia.org/wiki/Blinded_experiment#Double-blind_trials">double blind trial</a> of a proposed medical treatment. A group of 120 patients (split into subgroups of sizes 10, 20, 30 and 60) receive the treatment, and 120 patients (split into subgroups of corresponding sizes 60, 30, 20 and 10) receive no treatment.</p>
<p>The overall results make it look like the treatment was beneficial to patients, with a higher recovery rate for patients with the treatment than for those without it.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/163229/original/image-20170330-8593-t93w83.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/163229/original/image-20170330-8593-t93w83.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=249&fit=crop&dpr=1 600w, https://images.theconversation.com/files/163229/original/image-20170330-8593-t93w83.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=249&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/163229/original/image-20170330-8593-t93w83.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=249&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/163229/original/image-20170330-8593-t93w83.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=313&fit=crop&dpr=1 754w, https://images.theconversation.com/files/163229/original/image-20170330-8593-t93w83.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=313&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/163229/original/image-20170330-8593-t93w83.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=313&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<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>
<p>However, when you drill down into the various groups that made up the cohort in the study, you see in all groups of patients, the recovery rate was 50% higher for patients who had <em>no</em> treatment. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/163232/original/image-20170330-30365-f2956l.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/163232/original/image-20170330-30365-f2956l.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=311&fit=crop&dpr=1 600w, https://images.theconversation.com/files/163232/original/image-20170330-30365-f2956l.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=311&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/163232/original/image-20170330-30365-f2956l.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=311&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/163232/original/image-20170330-30365-f2956l.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=391&fit=crop&dpr=1 754w, https://images.theconversation.com/files/163232/original/image-20170330-30365-f2956l.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=391&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/163232/original/image-20170330-30365-f2956l.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=391&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<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>
<p>But note that the size and age distribution of each group is different between those who took the treatment and those who didn’t. This is what distorts the numbers. In this case, the treatment group is disproportionately stacked with children, whose recovery rates are typically higher, with or without treatment.</p>
<hr>
<h2>Base rate fallacy</h2>
<h3>What is it?</h3>
<p>This fallacy occurs when we disregard important information when making a judgement on how likely something is. </p>
<p>If, for example, we hear that someone loves music, we might think it’s more likely they’re a professional musician than an accountant. However, there are many more accountants than there are professional musicians. Here we have neglected that the <em>base rate</em> for the number of accountants is far higher than the number of musicians, so we were unduly swayed by the information that the person likes music.</p>
<h3>How does it happen?</h3>
<p>The base rate fallacy occurs when the base rate for one option is substantially higher than for another.</p>
<h3>Example</h3>
<p>Consider testing for a rare medical condition, such as one that affects only 4% (1 in 25) of a population.</p>
<p>Let’s say there is a test for the condition, but it’s not perfect. If someone has the condition, the test will correctly identify them as being ill around 92% of the time. If someone <em>doesn’t</em> have the condition, the test will correctly identify them as being healthy 75% of the time.</p>
<p>So if we test a group of people, and find that over a quarter of them are diagnosed as being ill, we might expect that most of these people really do have the condition. But we’d be wrong.</p>
<hr>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/163027/original/image-20170329-1664-htfx0x.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/163027/original/image-20170329-1664-htfx0x.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=383&fit=crop&dpr=1 600w, https://images.theconversation.com/files/163027/original/image-20170329-1664-htfx0x.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=383&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/163027/original/image-20170329-1664-htfx0x.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=383&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/163027/original/image-20170329-1664-htfx0x.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=482&fit=crop&dpr=1 754w, https://images.theconversation.com/files/163027/original/image-20170329-1664-htfx0x.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=482&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/163027/original/image-20170329-1664-htfx0x.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=482&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">In a typical sample of 300 patients, for every 11 people correctly identified as unwell, a further 72 are incorrectly identified as unwell.</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>According to our numbers above, of the 4% of patients who are ill, almost 92% will be correctly diagnosed as ill (that is, about 3.67% of the overall population). But of the 96% of patients who are not ill, 25% will be <em>incorrectly</em> diagnosed as ill (that’s 24% of the overall population).</p>
<p>What this means is that of the approximately 27.67% of the population who are diagnosed as ill, only around 3.67% actually are. So of the people who were diagnosed as ill, only around 13% (that is, 3.67%/27.67%) actually are unwell.</p>
<p>Worryingly, when <a href="http://www.archwoodside.com/wp-content/uploads/2015/09/Gigerenzer-Hoffrage-How-to-improve-Bayesian-reasoning-without-instruction.pdf">a famous study</a> asked general practitioners to perform a similar calculation to inform patients of the correct risks associated with mammogram results, just 15% of them did so correctly.</p>
<hr>
<h2>Will Rogers paradox</h2>
<h3>What is it?</h3>
<p>This occurs when moving something from one group to another raises the average of both groups, even though no values actually increase.</p>
<p>The name comes from the <a href="https://en.wikipedia.org/wiki/Will_Rogers">American comedian Will Rogers</a>, who joked that “when the Okies left Oklahoma and moved to California, they raised the average intelligence in both states”. </p>
<p>Former New Zealand Prime Minister Rob Muldoon provided a <a href="http://www.independent.co.uk/news/world/australasia/more-people-moving-from-australia-to-new-zealand-than-in-the-other-direction-for-first-time-in-24-10268060.html">local variant on the joke</a> in the 1980s, regarding migration from his nation into Australia.</p>
<h3>How does it happen?</h3>
<p>When a datapoint is reclassified from one group to another, if the point is below the average of the group it is leaving, but above the average of the one it is joining, both groups’ averages will increase.</p>
<h3>Example</h3>
<p>Consider the case of six patients whose life expectancies (in years) have been assessed as being 40, 50, 60, 70, 80 and 90. </p>
<p>The patients who have life expectancies of 40 and 50 have been diagnosed with a medical condition; the other four have not. This gives an average life expectancy within diagnosed patients of 45 years and within non-diagnosed patients of 75 years. </p>
<p>If an improved diagnostic tool is developed that detects the condition in the patient with the 60-year life expectancy, then the average within both groups rises by 5 years. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/162814/original/image-20170328-21243-1wcp3a8.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/162814/original/image-20170328-21243-1wcp3a8.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=459&fit=crop&dpr=1 600w, https://images.theconversation.com/files/162814/original/image-20170328-21243-1wcp3a8.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=459&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/162814/original/image-20170328-21243-1wcp3a8.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=459&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/162814/original/image-20170328-21243-1wcp3a8.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=577&fit=crop&dpr=1 754w, https://images.theconversation.com/files/162814/original/image-20170328-21243-1wcp3a8.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=577&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/162814/original/image-20170328-21243-1wcp3a8.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=577&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<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>
<h2>Berkson’s paradox</h2>
<h3>What is it?</h3>
<p>Berkson’s paradox can make it look like there’s an association between two independent variables when there isn’t one.</p>
<h3>How does it happen?</h3>
<p>This happens when we have a set with two independent variables, which means they should be entirely unrelated. But if we only look at a subset of the whole population, it can look like there is a negative trend between the two variables.</p>
<p>This can occur when the subset is not an unbiased sample of the whole population. It has been <a href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3237868/">frequently cited in medical statistics</a>. For example, if patients only present at a clinic with disease A, disease B or both, then even if the two diseases are independent, a negative association between them may be observed.</p>
<h3>Example</h3>
<p>Consider the case of a school that recruits students based on both academic and sporting ability. Assume that these two skills are totally independent of each other. That is, in the whole population, an excellent sportsperson is just as likely to be strong or weak academically as is someone who’s poor at sport.</p>
<p>If the school admits only students who are excellent academically, excellent at sport or excellent at both, then within this group it would appear that sporting ability is negatively correlated with academic ability.</p>
<p>To illustrate, assume that every potential student is ranked on both academic and sporting ability from 1 to 10. There are an equal proportion of people in each band for each skill. Knowing a person’s band in either skill does not tell you anything about their likely band in the other.</p>
<p>Assume now that the school only admits students who are at band 9 or 10 in at least one of the skills.</p>
<p>If we look at the whole population, the average academic rank of the weakest sportsperson and the best sportsperson are both equal (5.5). </p>
<p>However, within the set of admitted students, the average academic rank of the elite sportsperson is still that of the whole population (5.5), but the average academic rank of the weakest sportsperson is 9.5, wrongly implying a negative correlation between the two abilities.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/163073/original/image-20170329-1649-h3kvxl.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/163073/original/image-20170329-1649-h3kvxl.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=1032&fit=crop&dpr=1 600w, https://images.theconversation.com/files/163073/original/image-20170329-1649-h3kvxl.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=1032&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/163073/original/image-20170329-1649-h3kvxl.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=1032&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/163073/original/image-20170329-1649-h3kvxl.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1297&fit=crop&dpr=1 754w, https://images.theconversation.com/files/163073/original/image-20170329-1649-h3kvxl.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1297&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/163073/original/image-20170329-1649-h3kvxl.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1297&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<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>
<h2>Multiple comparisons fallacy</h2>
<h3>What is it?</h3>
<p>This is where unexpected trends can occur through random chance alone in a data set with a large number of variables.</p>
<h3>How does it happen?</h3>
<p>When looking at many variables and mining for trends, it is easy to overlook how many possible trends you are testing. For example, with 1,000 variables, there are almost half a million (1,000x999/2) potential pairs of variables that might appear correlated by pure chance alone. </p>
<p>While each pair is extremely unlikely to look dependent, the chances are that from the half million pairs, quite a few will look dependent.</p>
<h3>Example</h3>
<p>The Birthday paradox is a classic example of the multiple comparisons fallacy. </p>
<p>In a group of 23 people (assuming each of their birthdays is an independently chosen day of the year with all days equally likely), it is more likely than not that at least two of the group have the same birthday.</p>
<p>People often disbelieve this, recalling that it is rare that they meet someone who shares their own birthday. If you just pick two people, the chance they share a birthday is, of course, low (roughly 1 in 365, which is less than 0.3%).</p>
<p>However, with 23 people there are 253 (23x22/2) pairs of people who might have a common birthday. So by looking across the whole group you are testing to see if any one of these 253 pairings, each of which independently has a 0.3% chance of coinciding, does indeed match. These many possibilities of a pair actually make it statistically very likely for coincidental matches to arise.</p>
<p>For a group of as few as 40 people, it is almost nine times as likely that there is a shared birthday than not.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/163084/original/image-20170329-1664-1tb8sti.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/163084/original/image-20170329-1664-1tb8sti.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=529&fit=crop&dpr=1 600w, https://images.theconversation.com/files/163084/original/image-20170329-1664-1tb8sti.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=529&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/163084/original/image-20170329-1664-1tb8sti.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=529&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/163084/original/image-20170329-1664-1tb8sti.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=665&fit=crop&dpr=1 754w, https://images.theconversation.com/files/163084/original/image-20170329-1664-1tb8sti.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=665&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/163084/original/image-20170329-1664-1tb8sti.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=665&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">The probability of no shared birthdays drops as the number of people in a group increases.</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><img src="https://counter.theconversation.com/content/74440/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Stephen Woodcock 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>Sometimes statistics and probability can produce unexpected or counter-intuitive results. If we’re hoping to use numbers to make good decisions, we should be wary of the traps.Stephen Woodcock, Senior Lecturer in Mathematics, University of Technology SydneyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/746902017-03-29T19:21:16Z2017-03-29T19:21:16ZWorried about shark attacks or terrorism? Here’s how to think about the real risk of rare events<figure><img src="https://images.theconversation.com/files/162588/original/image-20170327-3268-1819ykz.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">How risky is it to swim?</span> <span class="attribution"><span class="source">Christine Cabalo/Wikimedia</span></span></figcaption></figure><p><em>Statistics is a useful tool for understanding the patterns in the world around us. But our intuition often lets us down when it comes to interpreting those patterns. In this series we look at some of the common mistakes we make and how to avoid them when thinking about <a href="https://theconversation.com/au/topics/statistics-probability-and-risk-37151">statistics, probability and risk</a>.</em></p>
<hr>
<p>The world can feel like a scary place. </p>
<p>Today, Australia’s National Terrorism Threat Level is “<a href="https://www.nationalsecurity.gov.au/Securityandyourcommunity/Pages/National-Terrorism-Threat-Advisory-System.aspx">Probable</a>”. Shark attacks are on the rise; the number of people attacked by sharks in 2000-2009 has almost doubled since <a href="http://www.publish.csiro.au/mf/MF10181">1990-1999</a>. Travellers are at a high risk of getting the Zika virus in places where the disease is <a href="http://www.health.gov.au/internet/main/publishing.nsf/Content/ohp-zika-factsheet-basics.htm#toc03">present</a>, such as Brazil and Mexico. </p>
<p>However, despite their tragic outcomes, these events are all extremely rare. </p>
<p>Since 1996, only eight people have been killed by terrorism attacks in <a href="http://www.start.umd.edu/gtd/search/Results.aspx?page=1&casualties_type=b&casualties_max=&start_yearonly=1996&end_yearonly=2015&dtp2=all&country=14&charttype=line&chart=overtime&expanded=no&ob=TotalNumberOfFatalities&od=desc#results-table">Australia</a>. There have been 186 shark attacks in the 20 years from <a href="http://www.publish.csiro.au/mf/MF10181">1990 to 2009</a>. Best estimates indicate that only 1.8 people for each million tourists would have <a href="http://www.vox.com/2016/5/25/11760228/zika-virus-risk-rio-olympics-2016">contracted Zika at the Rio Olympics</a>. </p>
<p>To be fair, it is extremely difficult to judge the incidence of rare events. So how should we think about these risks?</p>
<h2>Default to safe</h2>
<p>Decision scientists study rare events by bringing people into the lab and asking them to make choices. For example, in their Nobel Prize-winning work, researchers Daniel Kahneman and Amos Tversky had people <a href="https://www.princeton.edu/%7Ekahneman/docs/Publications/prospect_theory.pdf">make choices between two options</a>: one safe, one risky. </p>
<p>A typical choice might involve a safe option where you’d walk away with $5, guaranteed. Alternatively, you could choose to take a gamble and receive $15 with 90% probability. However, if you lost the gamble, you would have to pay $35. </p>
<p>If you’d just take the $5, then you’re not alone. Despite the gamble being clearly better than taking $5, in terms of what you would win on average (0.9 x $15 – 0.1 x $35 = $10), the loss of $35 looms so large in the mind that many of us tend to choose the safe option.</p>
<p>In this scenario, the loss of $35 is a relatively rare event: it will only occur 10% of the time. Yet we treat the rare event as if it were much more likely to occur than in reality. Kahneman and Tversky termed this the “overweighting” of small probabilities.</p>
<p>Of course, real-world rare events, such as disease control, shark attacks and terrorism threats, are much more complex than this fictitious gamble. But from a purely statistical point of view, it may be that we are disproportionately worried about such events, given their rarity. </p>
<p>For example, a poll conducted by Chapman University in the United States suggests that 38.5% of people were “afraid” or “very afraid” of being a victim of <a href="https://qz.com/898207/the-psychology-of-why-americans-are-more-scared-of-terrorism-than-guns-though-guns-are-3210-times-likelier-to-kill-them/">terrorism</a>. This is despite the fact that only 71 people in the US were killed by terrorism between <a href="https://www.newamerica.org/in-depth/terrorism-in-america/what-threat-united-states-today/#americas-layered-defenses">2005 and 2015</a>. To put that into perspective, PolitiFact reports that <a href="http://www.politifact.com/truth-o-meter/statements/2015/oct/05/viral-image/fact-checking-comparison-gun-deaths-and-terrorism-/">301,797 people have died from gun violence</a> in the US over a similar period.</p>
<p>So is it fear that drives us to believe that rare events are likely to happen?</p>
<p>According to David Landy, a researcher at Indiana University, who spoke on this very issue at the 2016 meeting of the <a href="http://www.sjdm.org/">Society for Judgment and Decision Making</a>, the answer is no. </p>
<p>One question in Landy’s survey asked people to estimate the proportion of the US population that was Muslim. The true proportion is slightly less than 1%. People’s estimates tended to be <a href="http://www.sjdm.org/programs/2016-program.pdf">higher</a>, at around 10%. </p>
<p>It is typically the case that people overestimate the population of Muslims in the <a href="http://www.nbcnews.com/news/us-news/most-americans-overestimate-muslim-population-17x-poll-shows-n696071">US</a>. The overestimate is often interpreted in terms of fear. The idea is that people are more likely to pay attention to things that scare them, and this leads them to believe they are more common than they really are.</p>
<p>The “fear” explanation is intuitively plausible, but it may not be true. In a critical comparison, Landy also asked about the probability of other events that also had a small probability, but would be unlikely to make people scared (such as what proportion of the US population had served in the military). </p>
<p>It turned out that people also overestimated the probability of these rare but uninteresting events. In fact, the degree to which they overestimated these other events was practically identical to how much they overestimated the population of Muslims. </p>
<p>Landy’s result suggests that we simply have trouble in thinking about small probabilities, regardless of the topic. It may not be that some people overestimate the proportion of Muslims out of fear. Rather, it seems that we will overestimate the incidence of any rare event. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/162586/original/image-20170327-3303-9wjrd7.JPG?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/162586/original/image-20170327-3303-9wjrd7.JPG?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/162586/original/image-20170327-3303-9wjrd7.JPG?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=336&fit=crop&dpr=1 600w, https://images.theconversation.com/files/162586/original/image-20170327-3303-9wjrd7.JPG?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=336&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/162586/original/image-20170327-3303-9wjrd7.JPG?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=336&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/162586/original/image-20170327-3303-9wjrd7.JPG?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=422&fit=crop&dpr=1 754w, https://images.theconversation.com/files/162586/original/image-20170327-3303-9wjrd7.JPG?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=422&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/162586/original/image-20170327-3303-9wjrd7.JPG?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=422&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Are you worried about getting struck?</span>
<span class="attribution"><span class="source">Wikimedia</span></span>
</figcaption>
</figure>
<h2>How to think about rare events</h2>
<p>So how should we think about and respond to rare events? </p>
<p>One remedy might be to use what some researchers refer to as “<a href="https://en.wikipedia.org/wiki/Metacognition">metacognitive awareness</a>”. This is being aware of how cognitive processes, like memory, work when we try to think about and estimate the frequency with which things happen. </p>
<p>One metacognitive cue you might use is how easy it is to remember a particular event, such as hearing about shark attacks. But simply reading-off the ease of recall is likely to be <a href="http://psiexp.ss.uci.edu/research/teaching/Tversky_Kahneman_1974.pdf">misleading</a>. This is because your memory is biased by positive instances: going swimming and not being attacked by sharks is not surprising so it is not particularly memorable.</p>
<p>This failure of memory to deliver representative samples of evidence suggests a need to think carefully, not only about the bias in memory retrieval, but also in the samples available to us in the world. </p>
<p>Perversely, it suggests that when you want to work out how rare an event is (and an appropriate response), you should try to think about all the times it didn’t happen (negative instances) rather than those when it did!</p>
<p>So next time you are at the beach and contemplating taking a dip, just think of the millions of swimmers who have never been attacked by a shark, and <em>not</em> the relatively few who have.</p><img src="https://counter.theconversation.com/content/74690/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Ben Newell receives funding from the Australian Research Council. </span></em></p><p class="fine-print"><em><span>Chris Donkin receives funding from the Australian Research Council. </span></em></p><p class="fine-print"><em><span>Dan Navarro receives funding from the Australian Research Council. </span></em></p>We naturally overestimate the risk of rare events, like shark attacks or terrorism. But there are things you can do to think more rationally about the real risk.Ben Newell, Professor of Cognitive Psychology, UNSW SydneyChris Donkin, Senior Lecturer in Psychology, UNSW SydneyDan Navarro, Associate Professor of Cognitive Science, UNSW SydneyLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/743062017-03-28T19:04:21Z2017-03-28T19:04:21ZThe seven deadly sins of statistical misinterpretation, and how to avoid them<figure><img src="https://images.theconversation.com/files/162827/original/image-20170328-21243-6xrdpk.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Where are the error bars?</span> <span class="attribution"><span class="source">Shutterstock</span></span></figcaption></figure><p><em>Statistics is a useful tool for understanding the patterns in the world around us. But our intuition often lets us down when it comes to interpreting those patterns. In this series we look at some of the common mistakes we make and how to avoid them when thinking about <a href="https://theconversation.com/au/topics/statistics-probability-and-risk-37151">statistics, probability and risk</a>.</em></p>
<hr>
<h2>1. Assuming small differences are meaningful</h2>
<p>Many of the daily fluctuations in the stock market represent chance rather than anything meaningful. Differences in polls when one party is ahead by a point or two are often just statistical noise.</p>
<p>You can avoid drawing faulty conclusions about the causes of such fluctuations by demanding to see the “margin of error” relating to the numbers. </p>
<p>If the difference is smaller than the margin of error, there is likely no meaningful difference, and the variation is probably just down to random fluctuations.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/162565/original/image-20170327-18974-kee9sg.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/162565/original/image-20170327-18974-kee9sg.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/162565/original/image-20170327-18974-kee9sg.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=338&fit=crop&dpr=1 600w, https://images.theconversation.com/files/162565/original/image-20170327-18974-kee9sg.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=338&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/162565/original/image-20170327-18974-kee9sg.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=338&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/162565/original/image-20170327-18974-kee9sg.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=424&fit=crop&dpr=1 754w, https://images.theconversation.com/files/162565/original/image-20170327-18974-kee9sg.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=424&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/162565/original/image-20170327-18974-kee9sg.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">Error bars illustrate the degree of uncertainty in a score. When such margins of error overlap, the difference is likely to be due to statistical noise.</span>
</figcaption>
</figure>
<hr>
<h2>2. Equating statistical significance with real-world significance</h2>
<p>We often hear generalisations about how two groups differ in some way, such as that women are more nurturing while men are physically stronger. </p>
<p>These differences often draw on stereotypes and folk wisdom but often ignore the similarities in people between the two groups, and the variation in people within the groups.</p>
<p>If you pick two men at random, there is likely to be quite a lot of difference in their physical strength. And if you pick one man and one woman, they may end up being very similar in terms of nurturing, or the man may be more nurturing than the woman.</p>
<p>You can avoid this error by asking for the “effect size” of the differences between groups. This is a measure of how much the average of one group differs from the average of another. </p>
<p>If the effect size is small, then the two groups are very similar. Even if the effect size is large, the two groups will still likely have a great deal of variation within them, so not all members of one group will be different from all members of another group.</p>
<hr>
<h2>3. Neglecting to look at extremes</h2>
<p>The flipside of effect size is relevant when the thing that you’re focusing on follows a “<a href="https://en.wikipedia.org/wiki/Normal_distribution">normal distribution</a>” (sometimes called a “bell curve”). This is where most people are near the average score and only a tiny group is well above or well below average. </p>
<p>When that happens, a small change in performance for the group produces a difference that means nothing for the average person (see point 2) but that changes the character of the extremes more radically. </p>
<p>Avoid this error by reflecting on whether you’re dealing with extremes or not. When you’re dealing with average people, small group differences often don’t matter. When you care a lot about the extremes, small group differences can matter heaps.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/162567/original/image-20170327-18998-1s1jqcj.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/162567/original/image-20170327-18998-1s1jqcj.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/162567/original/image-20170327-18998-1s1jqcj.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=312&fit=crop&dpr=1 600w, https://images.theconversation.com/files/162567/original/image-20170327-18998-1s1jqcj.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=312&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/162567/original/image-20170327-18998-1s1jqcj.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=312&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/162567/original/image-20170327-18998-1s1jqcj.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=392&fit=crop&dpr=1 754w, https://images.theconversation.com/files/162567/original/image-20170327-18998-1s1jqcj.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=392&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/162567/original/image-20170327-18998-1s1jqcj.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=392&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">When two populations follow a normal distribution, the differences between them will be more apparent at the extremes than in the averages.</span>
</figcaption>
</figure>
<hr>
<h2>4. Trusting coincidence</h2>
<p>Did you know there’s a <a href="http://www.tylervigen.com/spurious-correlations">correlation</a> between the number of people who drowned each year in the United States by falling into a swimming pool and number of films Nicholas Cage appeared in?</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/162122/original/image-20170323-25751-2a2g8r.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/162122/original/image-20170323-25751-2a2g8r.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/162122/original/image-20170323-25751-2a2g8r.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=237&fit=crop&dpr=1 600w, https://images.theconversation.com/files/162122/original/image-20170323-25751-2a2g8r.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=237&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/162122/original/image-20170323-25751-2a2g8r.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=237&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/162122/original/image-20170323-25751-2a2g8r.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=297&fit=crop&dpr=1 754w, https://images.theconversation.com/files/162122/original/image-20170323-25751-2a2g8r.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=297&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/162122/original/image-20170323-25751-2a2g8r.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=297&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">But is there a causal link?</span>
<span class="attribution"><a class="source" href="http://www.tylervigen.com/spurious-correlations">tylervigen.com</a></span>
</figcaption>
</figure>
<p>If you look hard enough you can find interesting patterns and correlations that are merely due to coincidence. </p>
<p>Just because two things happen to change at the same time, or in similar patterns, does not mean they are related.</p>
<p>Avoid this error by asking how reliable the observed association is. Is it a one-off, or has it happened multiple times? Can future associations be predicted? If you have seen it only once, then it is likely to be due to random chance.</p>
<hr>
<h2>5. Getting causation backwards</h2>
<p>When two things are correlated – say, unemployment and mental health issues – it might be tempting to see an “obvious” causal path – say that mental health problems lead to unemployment. </p>
<p>But sometimes the causal path goes in the other direction, such as unemployment causing mental health issues.</p>
<p>You can avoid this error by remembering to think about reverse causality when you see an association. Could the influence go in the other direction? Or could it go both ways, creating a feedback loop? </p>
<hr>
<h2>6. Forgetting to consider outside causes</h2>
<p>People often fail to evaluate possible “third factors”, or outside causes, that may create an association between two things because both are actually outcomes of the third factor.</p>
<p>For example, there might be an association between eating at restaurants and better cardiovascular health. That might lead you to believe there is a causal connection between the two.</p>
<p>However, it might turn out that those who can afford to eat at restaurants regularly are in a high socioeconomic bracket, and can also afford better health care, and it’s the health care that affords better cardiovascular health. </p>
<p>You can avoid this error by remembering to think about third factors when you see a correlation. If you’re following up on one thing as a possible cause, ask yourself what, in turn, causes that thing? Could that third factor cause both observed outcomes? </p>
<hr>
<h2>7. Deceptive graphs</h2>
<p>A lot of mischief occurs in the scaling and labelling of the vertical axis on graphs. The labels should show the full meaningful range of whatever you’re looking at. </p>
<p>But sometimes the graph maker chooses a narrower range to make a small difference or association look more impactful. On a scale from 0 to 100, two columns might look the same height. But if you graph the same data only showing from 52.5 to 56.5, they might look drastically different.</p>
<p>You can avoid this error by taking care to note graph’s labels along the axes. Be especially sceptical of unlabelled graphs.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/161027/original/image-20170315-20495-1jjsvtm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/161027/original/image-20170315-20495-1jjsvtm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/161027/original/image-20170315-20495-1jjsvtm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=183&fit=crop&dpr=1 600w, https://images.theconversation.com/files/161027/original/image-20170315-20495-1jjsvtm.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=183&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/161027/original/image-20170315-20495-1jjsvtm.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=183&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/161027/original/image-20170315-20495-1jjsvtm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=229&fit=crop&dpr=1 754w, https://images.theconversation.com/files/161027/original/image-20170315-20495-1jjsvtm.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=229&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/161027/original/image-20170315-20495-1jjsvtm.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=229&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Graphs can tell a story – making differences look bigger or smaller depending on scale.</span>
</figcaption>
</figure><img src="https://counter.theconversation.com/content/74306/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Winnifred Louis receives funding from the Australian Research Council and the Social Sciences and Humanities Research Council of Canada. She is a teacher of statistics in the University of Queensland, as well as a social psychologist, a peace psychologist, and a longstanding activist for causes such as enviromental sustainability and anti-racism. </span></em></p><p class="fine-print"><em><span>Cassandra Chapman receives funding in the form of a PhD scholarship from the Department of Education and Training of the Australian government. She previously worked in marketing and fundraising for various not-for-profits and still collaborates with organisations in that sector.</span></em></p>Here are some all-too-common errors when it comes to interpreting statistics, and how to avoid them.Winnifred Louis, Associate Professor, Social Psychology, The University of QueenslandCassandra Chapman, PhD Candidate in Social Psychology, The University of QueenslandLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/746942017-03-26T19:02:59Z2017-03-26T19:02:59ZRegression to the mean, or why perfection rarely lasts<figure><img src="https://images.theconversation.com/files/162333/original/image-20170324-4938-1b2swbm.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">A perfect night out involves a lot of chance.</span> <span class="attribution"><span class="source">Shutterstock</span></span></figcaption></figure><p><em>Statistics is a useful tool for understanding the patterns in the world around us. But our intuition often lets us down when it comes to interpreting those patterns. In this series we look at some of the common mistakes we make and how to avoid them when thinking about <a href="https://theconversation.com/au/topics/statistics-probability-and-risk-37151">statistics, probability and risk</a>.</em></p>
<hr>
<p>Have you ever experienced the perfect evening out? The weather was great, you got the best table in the house at your favourite restaurant, the food was delicious and the wine superb, and the conversation was sparkling.</p>
<p>Then have you made the mistake of trying to repeat the experience and ended up disappointed? This is because your perfect evening was due to a series of chance events that all fell in your favour. A great experience is like tossing a coin and getting a long run of heads – unusual and difficult to repeat. </p>
<p>When you try to repeat a perfect experience, at least one thing is likely to be imperfect the second time around. The couple at the next table are loud and boorish, the waiter gets your order wrong, your jokes fall flat, and so on. </p>
<p>Happily, it works both ways. So if you’re forced to repeat a terrible experience, it’s likely that it won’t be so bad the second time around.</p>
<p>This phenomenon is called “regression to the mean” or “reversion to mediocrity”, which sums up how unusual events are likely to be followed by more typical ones. </p>
<p>The polymath <a href="https://www.britannica.com/biography/Francis-Galton">Sir Francis Galton</a> coined the term when he noticed that tall parents tended to have children shorter than them, whereas short parents often had children who were taller than themselves. </p>
<p>For a parent to be unusually tall, the genetic coin had to be “heads” many times in a row. Repeating that feat of chance for their children is not impossible, but it is unlikely. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/162341/original/image-20170324-12149-1us9uhh.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/162341/original/image-20170324-12149-1us9uhh.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/162341/original/image-20170324-12149-1us9uhh.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=415&fit=crop&dpr=1 600w, https://images.theconversation.com/files/162341/original/image-20170324-12149-1us9uhh.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=415&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/162341/original/image-20170324-12149-1us9uhh.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=415&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/162341/original/image-20170324-12149-1us9uhh.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=521&fit=crop&dpr=1 754w, https://images.theconversation.com/files/162341/original/image-20170324-12149-1us9uhh.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=521&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/162341/original/image-20170324-12149-1us9uhh.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=521&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Outliers in a population, such as very short or tall parents, will tend to gravitate towards the mean, such as by having children that are closer to the average height in that population.</span>
<span class="attribution"><a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<h2>Is that a trend?</h2>
<p>Regression to the mean is driven by chance, and so it occurs wherever chance occurs, which means it occurs almost everywhere. It is prevalent in sport and can explain the “<a href="https://www.theguardian.com/football/blog/2014/oct/19/manager-of-the-month">manager of the month curse</a>” in football. This award is usually won by managers who have had four or more wins in a row, often because of a combination of skill and luck. When the luck runs out, the “curse” strikes.</p>
<p>Regression to the mean will even occur in this article as unusually long sentences will tend to be followed by shorter ones. Check if you don’t believe me. It occurs in the published literature on regression to the mean, as years with many published papers on the phenomenon tend to be followed by years with fewer papers. </p>
<p>This article will itself cause some regression to the mean if it spikes interest in the <a href="https://en.wikipedia.org/wiki/Regression_toward_the_mean">Wikipedia page</a>, but that interest will inevitably wane. </p>
<p>Regression to the mean is mostly harmless, but it becomes a problem when the change it creates is misinterpreted. </p>
<p>For example, imagine you ran a hospital and were told that hospital-acquired infections were five times higher than average last month. A colleague tells you they know the cause and it can solved by using more prophylactic antibiotics. </p>
<p>You agree and in the following month you’re told that prophylactic antibiotic use is through the roof and infections have come down. Your mind makes a causal connection and you’re now convinced of the need for widespread prophylactic antibiotics, a potentially dangerous connection given that the unusual infection rate could have been due to chance events. </p>
<p>Now your hospital budget will be tighter because of the costs of using more antibiotics, and you’re contributing to serious problem of antibiotic resistance.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/162342/original/image-20170324-12132-1y5b4wl.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/162342/original/image-20170324-12132-1y5b4wl.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/162342/original/image-20170324-12132-1y5b4wl.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=415&fit=crop&dpr=1 600w, https://images.theconversation.com/files/162342/original/image-20170324-12132-1y5b4wl.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=415&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/162342/original/image-20170324-12132-1y5b4wl.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=415&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/162342/original/image-20170324-12132-1y5b4wl.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=521&fit=crop&dpr=1 754w, https://images.theconversation.com/files/162342/original/image-20170324-12132-1y5b4wl.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=521&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/162342/original/image-20170324-12132-1y5b4wl.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=521&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 you track the quality of your nights out, they might fluctuate up and down, but will still hover around the mean.</span>
<span class="attribution"><a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<h2>Making sham treatments look good</h2>
<p>Regression to the mean is unwittingly exploited by quacks who often see patients when they are at their lowest. As many diseases have a natural ebb and flow, seeing patients when they are at their worst is the best time to exploit regression to the mean, because any treatment will appear to cause improvements in enough patients to make it look broadly effective. </p>
<p>Telling the difference between regression to the mean and a real change can be difficult. A chronically ill patient may have a very bad day, but is that the early warning of a downward trajectory or just a blip due to a random cluster of events, such as a bad meal, poor sleep, or an ill-judged sprint for the bus? </p>
<p>Gathering more data using watchful waiting can be useful, as once a clear pattern emerges in a patient’s well-being, it is less likely to be the random ups and downs of regression to the mean.</p>
<p>Regression to the mean is everywhere. Being aware of it might help you avoid overreacting to unusual events. However, if you didn’t find this article interesting or useful then why not read another one on The Conversation – the chances are you’ll enjoy it more.</p><img src="https://counter.theconversation.com/content/74694/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Adrian Barnett receives funding from the National Health and Medical Research Council. </span></em></p>Things tend to revert back to their typical state over time, so we should be careful not to mistake that for some other trend.Adrian Barnett, Professor of Public Health, Queensland University of TechnologyLicensed as Creative Commons – attribution, no derivatives.