tag:theconversation.com,2011:/ca/topics/graphs-39500/articlesGraphs – The Conversation2024-01-07T19:04:19Ztag:theconversation.com,2011:article/2145762024-01-07T19:04:19Z2024-01-07T19:04:19ZHere’s why you should (almost) never use a pie chart for your data<figure><img src="https://images.theconversation.com/files/558554/original/file-20231109-25-j7ehuz.jpg?ixlib=rb-1.1.0&rect=810%2C436%2C4761%2C3377&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/lemon-pie-flat-lay-on-blue-1663719415">YesPhotographers/Shutterstock</a></span></figcaption></figure><p>Our lives are becoming increasingly data driven. Our phones monitor our time and internet usage and online surveys discern our opinions and likes. These data harvests are used for telling us how well we’ve slept or what we might like to buy. </p>
<p>Numbers are becoming more important for everyday life, yet people’s numerical skills are falling behind. For example, the percentage of Year 12 schoolchildren in Australia taking higher and intermediate mathematics <a href="https://amsi.org.au/?publications=year-12-participation-in-calculus-based-mathematics-subjects-takes-a-dive-2">has been declining for decades</a>. </p>
<p>To help the average person understand big data and numbers, we often use visual summaries, such as pie charts. But while non-numerate folk will avoid numbers, most numerate folk will avoid pie charts. Here’s why.</p>
<h2>What is a pie chart?</h2>
<p>A pie chart is a circular diagram that represents numerical percentages. The circle is divided into slices, with the size of each slice proportional to the category it represents. It is named because it resembles a sliced pie and can be “served” in many different ways. </p>
<p>An example pie chart below shows Australia’s two-party preferred vote before the last election, with Labor on 55% and the the Coalition on 45%. The two near semi-circles show the relatively tight race – this is a useful example of a pie chart. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/560670/original/file-20231121-23-sgp640.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="55% for labor, 45% for coalition on a red and blue pie chart" src="https://images.theconversation.com/files/560670/original/file-20231121-23-sgp640.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/560670/original/file-20231121-23-sgp640.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=360&fit=crop&dpr=1 600w, https://images.theconversation.com/files/560670/original/file-20231121-23-sgp640.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=360&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/560670/original/file-20231121-23-sgp640.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=360&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/560670/original/file-20231121-23-sgp640.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=452&fit=crop&dpr=1 754w, https://images.theconversation.com/files/560670/original/file-20231121-23-sgp640.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=452&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/560670/original/file-20231121-23-sgp640.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=452&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">A simple pie chart showing the percentages for the two major Australian parties in an opinion poll.</span>
<span class="attribution"><span class="source">Victor Oguoma</span></span>
</figcaption>
</figure>
<h2>What’s wrong with pie charts?</h2>
<p>Once we have more than two categories, pie charts can easily misrepresent percentages and become hard to read.</p>
<p>The three charts below are a good example – it is very hard to work out which of the five areas is the largest. The pie chart’s circularity means the areas lack a common reference point. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/556782/original/file-20231031-27-3dz8ta.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/556782/original/file-20231031-27-3dz8ta.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/556782/original/file-20231031-27-3dz8ta.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=208&fit=crop&dpr=1 600w, https://images.theconversation.com/files/556782/original/file-20231031-27-3dz8ta.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=208&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/556782/original/file-20231031-27-3dz8ta.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=208&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/556782/original/file-20231031-27-3dz8ta.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=261&fit=crop&dpr=1 754w, https://images.theconversation.com/files/556782/original/file-20231031-27-3dz8ta.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=261&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/556782/original/file-20231031-27-3dz8ta.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=261&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Three example pie charts, each with five similar categories. Can you quickly tell which colour is the largest in each pie?</span>
<span class="attribution"><a class="source" href="https://commons.wikimedia.org/wiki/File:Piecharts.svg">Schutz/Wikimedia Commons</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<p>Pie charts also do badly when there are lots of categories. For example, this chart from a study on data sources used for COVID data visualisation shows hundreds of categories in one pie. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/556770/original/file-20231031-19-uurqzu.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/556770/original/file-20231031-19-uurqzu.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/556770/original/file-20231031-19-uurqzu.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=340&fit=crop&dpr=1 600w, https://images.theconversation.com/files/556770/original/file-20231031-19-uurqzu.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=340&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/556770/original/file-20231031-19-uurqzu.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=340&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/556770/original/file-20231031-19-uurqzu.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=428&fit=crop&dpr=1 754w, https://images.theconversation.com/files/556770/original/file-20231031-19-uurqzu.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=428&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/556770/original/file-20231031-19-uurqzu.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=428&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">A pie chart with dozens of categories. Not every category has a label, it’s not clear what the total number of categories is and what the unlabelled slices refer to.</span>
<span class="attribution"><a class="source" href="https://doi.org/10.3390/informatics7030035">Trajkova et al., Informatics (2020)</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<p>The tiny slices, lack of clear labelling and the kaleidoscope of colours make interpretation difficult for anyone.</p>
<p>It’s even harder for a colour blind person. For example, this is a simulation of what the above chart would look like to a person with deuteranomaly or reduced sensitivity to green light. This is the most common type of colour blindness, affecting roughly <a href="https://wearecolorblind.com/articles/a-quick-introduction-to-color-blindness/">4.6% of the population</a>. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/558560/original/file-20231109-27-4714o0.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/558560/original/file-20231109-27-4714o0.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/558560/original/file-20231109-27-4714o0.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=449&fit=crop&dpr=1 600w, https://images.theconversation.com/files/558560/original/file-20231109-27-4714o0.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=449&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/558560/original/file-20231109-27-4714o0.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=449&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/558560/original/file-20231109-27-4714o0.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=564&fit=crop&dpr=1 754w, https://images.theconversation.com/files/558560/original/file-20231109-27-4714o0.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=564&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/558560/original/file-20231109-27-4714o0.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=564&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">The same data chart as above, but run through a simulation filter to demonstrate what it would look like for someone with a common type of colour blindness.</span>
<span class="attribution"><a class="source" href="https://doi.org/10.3390/informatics7030035">Trajkova et al., Informatics (2020); modified.</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<p>It can get even worse if we take pie charts and make them three-dimensional. This can lead to egregious misrepresentations of data.</p>
<p>Below, the yellow, red and green areas are all the same size (one-third), but appear to be different based on the angle and which slice is placed at the bottom of the pie.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/556772/original/file-20231031-25-bdpq56.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/556772/original/file-20231031-25-bdpq56.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/556772/original/file-20231031-25-bdpq56.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=196&fit=crop&dpr=1 600w, https://images.theconversation.com/files/556772/original/file-20231031-25-bdpq56.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=196&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/556772/original/file-20231031-25-bdpq56.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=196&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/556772/original/file-20231031-25-bdpq56.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=246&fit=crop&dpr=1 754w, https://images.theconversation.com/files/556772/original/file-20231031-25-bdpq56.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=246&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/556772/original/file-20231031-25-bdpq56.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=246&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">A standard two-dimensional pie chart and two three-dimensional pie charts. In every chart the proportions are one-third but there appear to be differences between states in the three-dimensional versions.</span>
<span class="attribution"><span class="source">Victor Oguoma</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<h2>So why are pie charts everywhere?</h2>
<p>Despite the well known problems with pie charts, they are everywhere. They are in journal articles, PhD theses, political polling, books, newspapers and government reports. They’ve even been used by the Australian Bureau of Statistics.</p>
<p>While statisticians have criticised them for decades, it’s hard to argue with this logic: “if pie charts are so bad, why are there so many of them?”</p>
<p>Possibly they are popular because they are popular, which is a circular argument that suits a pie chart.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/556781/original/file-20231031-17-hfvpgr.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/556781/original/file-20231031-17-hfvpgr.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/556781/original/file-20231031-17-hfvpgr.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=395&fit=crop&dpr=1 600w, https://images.theconversation.com/files/556781/original/file-20231031-17-hfvpgr.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=395&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/556781/original/file-20231031-17-hfvpgr.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=395&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/556781/original/file-20231031-17-hfvpgr.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=496&fit=crop&dpr=1 754w, https://images.theconversation.com/files/556781/original/file-20231031-17-hfvpgr.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=496&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/556781/original/file-20231031-17-hfvpgr.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=496&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">A collection of terrible pie charts gathered from various open access sources, including ‘exploded’ pie charts and 3D pie charts.</span>
<span class="attribution"><span class="source">Adrian Barnett and Victor Oguoma</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<h2>What’s a good alternative to pie charts?</h2>
<p>There’s a simple fix that can effectively summarise big data in a small space and still allow creative colour schemes. </p>
<p>It’s the humble bar chart. Remember the brain-aching pie chart example above with the five categories? Here’s the same example using bars – we can now instantly see which category is the largest.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/556773/original/file-20231031-25-9vdsm4.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/556773/original/file-20231031-25-9vdsm4.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/556773/original/file-20231031-25-9vdsm4.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=430&fit=crop&dpr=1 600w, https://images.theconversation.com/files/556773/original/file-20231031-25-9vdsm4.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=430&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/556773/original/file-20231031-25-9vdsm4.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=430&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/556773/original/file-20231031-25-9vdsm4.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=541&fit=crop&dpr=1 754w, https://images.theconversation.com/files/556773/original/file-20231031-25-9vdsm4.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=541&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/556773/original/file-20231031-25-9vdsm4.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=541&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Three pie charts, each with five similar categories, and the same data presented using bar charts.</span>
<span class="attribution"><a class="source" href="https://commons.wikimedia.org/wiki/File:Piecharts.svg">Schutz/Wikimedia Commons</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<p>Linear bars are easier on the eye than the non-linear segments of a pie chart. But beware the temptation to make a humble bar chart look more interesting by adding a 3D effect. As you already saw, 3D charts distort perception and make it harder to find a reference point.</p>
<p>Below is a standard bar chart and a 3D alternative of the number of voters in the 1992 US presidential election split by family income (from under US$15K to over $75k). Using the 3D version, can you tell the number of voters for each candidate in the highest income category? Not easily. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/556775/original/file-20231031-17-dscfue.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/556775/original/file-20231031-17-dscfue.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/556775/original/file-20231031-17-dscfue.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=157&fit=crop&dpr=1 600w, https://images.theconversation.com/files/556775/original/file-20231031-17-dscfue.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=157&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/556775/original/file-20231031-17-dscfue.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=157&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/556775/original/file-20231031-17-dscfue.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=197&fit=crop&dpr=1 754w, https://images.theconversation.com/files/556775/original/file-20231031-17-dscfue.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=197&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/556775/original/file-20231031-17-dscfue.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=197&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">The same voter data presented as a standard two-dimensional bar chart and an unhelpful three-dimensional version.</span>
<span class="attribution"><span class="source">Victor Oguoma</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<h2>Is it ever okay to use a pie chart?</h2>
<p>We’ve shown some of the worst examples of pie charts to make a point. Pie charts can be okay when there are just a few categories and the percentages are dissimilar, for example with one large and one small category.</p>
<p>Overall, it is best to use pie charts sparingly, especially when there is a more “digestible” alternative – the bar chart.</p>
<p>Whenever we see pie charts, we think one of two things: their creators don’t know what they’re doing, or they know what they are doing and are deliberately trying to mislead.</p>
<p>A graphical summary aims to easily and quickly communicate the data. If you feel the need to spruce it up, you’re likely reducing understanding without meaning to do so.</p>
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Read more:
<a href="https://theconversation.com/3-questions-to-ask-yourself-next-time-you-see-a-graph-chart-or-map-141348">3 questions to ask yourself next time you see a graph, chart or map</a>
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<img src="https://counter.theconversation.com/content/214576/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Adrian Barnett is a member of the Statistical Society of Australia.</span></em></p><p class="fine-print"><em><span>Victor Oguoma is a member of the Statistical Society of Australia.</span></em></p>They are popular because they are popular, which is a circular argument that suits a pie chart. But there are some serious downsides to using the humble pie.Adrian Barnett, Professor of Statistics, Queensland University of TechnologyVictor Oguoma, Senior Research Fellow, Poche Centre for Indigenous Health, The University of QueenslandLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/2183832023-11-28T12:02:17Z2023-11-28T12:02:17ZCOVID inquiry heard Boris Johnson ‘struggled’ with graphs – if you do too, here are some tips<p>In March 2020, the UK government’s chief scientific adviser, Patrick Vallance, presented to the nation a graph showing “<a href="https://youtu.be/cAE8-e5_EKY?t=530">the shape of an epidemic</a>”. The red line depicting the number of predicted COVID cases rose to a steep peak before falling again. Vallance explained that delaying and reducing the height of that peak was essential to ease the strain on Britain’s healthcare system. Boris Johnson, then prime minister, put it much more succinctly: “Squash that sombrero.”</p>
<p>In the two years that followed, both men must have spent many hours discussing graphs like this. But as we’re now learning through Vallance’s testimony in the COVID inquiry, it seems the prime minister <a href="https://www.independent.co.uk/news/uk/boris-johnson-patrick-vallance-chris-whitty-government-god-b2450446.html">struggled to understand</a> what was shown in these graphs, despite his daily exposure to them.</p>
<p>Inquiry chair Baroness Hallet spoke up for the former prime minister: “He wouldn’t be the only person to struggle with graphs. I confess to struggling with graphs myself on occasion.”</p>
<p>Her point is an important one: communication is a two-way street. It’s not always fair to blame the person looking at a graph if they misunderstand it, it must be made intelligible in the first place.</p>
<p>During the inquiry, much has been made of the need for policymakers to <a href="https://www.ft.com/content/c8b36b76-0550-4568-8dcc-5f60ae59b2ef">grasp basic statistics</a> in order to make informed decisions, especially when the stakes are high. So how can scientists create better data visualisations to help solve this problem?</p>
<p>To find the answer to this, we can look back 160 years to Florence Nightingale, namesake of the temporary hospitals created in the early days of the pandemic. Nightingale was <a href="https://www.scientificamerican.com/article/how-florence-nightingale-changed-data-visualization-forever/">a pioneer</a> of using effective data graphics to change policies during a time of crisis.</p>
<p>Following her experience nursing soldiers dying from preventable diseases in the Crimean war (1853-1856), she waged her own battle against the British military. To convince them of the need for sanitary reform, Nightingale worked with other statisticians to create graphs that were sent out to key establishment figures, including Queen Victoria, with Nightingale hoping “she may look at it because it has pictures”.</p>
<figure class="align-center ">
<img alt="A chart from 1858 showing multicoloured wedge graphs depicting the causes of mortality in the British Army, with deaths from preventable or mitigatable diseases far outstripping those from wounds and other causes." src="https://images.theconversation.com/files/561341/original/file-20231123-23-7wi6rp.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/561341/original/file-20231123-23-7wi6rp.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=391&fit=crop&dpr=1 600w, https://images.theconversation.com/files/561341/original/file-20231123-23-7wi6rp.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=391&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/561341/original/file-20231123-23-7wi6rp.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=391&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/561341/original/file-20231123-23-7wi6rp.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=491&fit=crop&dpr=1 754w, https://images.theconversation.com/files/561341/original/file-20231123-23-7wi6rp.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=491&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/561341/original/file-20231123-23-7wi6rp.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=491&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Florence Nightingale’s charts are a model for science communicators.</span>
<span class="attribution"><a class="source" href="https://wellcomecollection.org/works/jxwtskzc/images?id=ub3n8egf">Wellcome Collection</a></span>
</figcaption>
</figure>
<p>Her charts visually separated the stats on monthly deaths before and after sanitary reform, and showed how few deaths were caused by the wounds of battle. Nightingale left readers in no doubt that poor living conditions were killing soldiers in their barracks. This inspired reforms that saved countless soldiers from dying from preventable diseases.</p>
<h2>How scientists can better communicate data</h2>
<p>Since Nightingale’s time, there has been a great deal of progress in the use of statistics to improve public health. Here are two very simple improvements to charts that can make a huge difference to their readers: better colours and more considered use of text.</p>
<p>An entry in Vallance’s notebook details Johnson’s confusion over the colours in a line graph. Scientists <a href="https://theconversation.com/how-rainbow-colour-maps-can-distort-data-and-be-misleading-167159">can be prone</a> to using unclear colours in their visualisations. Colour choice has been shown to affect how accurately users read maps, with <a href="https://pubmed.ncbi.nlm.nih.gov/33417558/">recent research</a> suggesting it can be confusing to use “cheery” colours to visualise grim data. </p>
<p>There are <a href="https://lisacharlottemuth.com/2016/04/22/Colors-for-DataVis/">many guides</a> on how to avoid poor colour choices hindering important decisions or making data inaccessible to people with colour blindness.</p>
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Read more:
<a href="https://theconversation.com/why-so-many-people-have-had-enough-of-experts-and-how-to-win-back-trust-206134">Why so many people have had enough of experts – and how to win back trust</a>
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<p>Vallance told the inquiry he was also concerned that Johnson was not retaining messages from the graphs. Very little can be done if the audience is not paying attention, but <a href="https://ieeexplore.ieee.org/document/7192646">a 2016 study</a> found that people were more likely to remember the message of a visualisation if it contained titles and annotations that spelled out information already shown in the graphic. </p>
<p>Time is of the essence, since readers can form their impression of a graphic <a href="https://dl.acm.org/doi/10.1145/2702123.2702545">within 500 milliseconds</a>. Alan Smith, head of visual and data journalism at the Financial Times, encourages his team to use active verbs in their titles. As he writes in his book How Charts Work, this approach will “give a chart focus, providing a real narrative sense of purpose”. </p>
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<iframe width="440" height="260" src="https://www.youtube.com/embed/2moJvFVM50M?wmode=transparent&start=0" frameborder="0" allowfullscreen=""></iframe>
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<h2>How you can be a better graph reader</h2>
<p>There are also things that we, as readers, can do to better understand the graphs, charts and data visualisations that are part of daily life. Here are a few things to look out for.</p>
<p>Some charts <a href="https://uksa.statisticsauthority.gov.uk/correspondence/response-from-sir-robert-chote-to-andrew-gwynne-mp-dhsc-chart-on-nurses-pay/">can mislead</a> by being selective in the values used on their axes. A common trick – which <a href="https://www.independent.co.uk/news/uk/politics/general-election-lib-dem-bar-charts-tories-labour-jacob-rees-mogg-a9184046.html">politicians have mastered</a> – is that they don’t start at zero in order to exaggerate an increase or decrease in something. There may be good reasons for this approach, but not always. </p>
<p>You should also look out for a source, and confirm that it’s a reputable one such as the Office for National Statistics. If the source isn’t shown, ask. If there is no credit at all, then you are right to be sceptical.</p>
<p>Finally, be just as curious about what the graph doesn’t show. Is there data missing, or does the plot only show one aspect of a problem? Do other charts of the same data show something different? </p>
<p>Often there are no perfect answers to these questions. But they are important conversation starters – especially if, like Vallance and Johnson, the person who can explain the graph is right in front of you.</p><img src="https://counter.theconversation.com/content/218383/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>James Cheshire receives funding from the ESRC.</span></em></p><p class="fine-print"><em><span>Rob Davidson receives funding from the ESRC and The Health Foundation.</span></em></p>Communication is a two-way street.James Cheshire, Professor of Geographic Information and Cartography, UCLRob Davidson, Postgraduate Researcher in Human Geography, UCLLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1991272023-04-13T14:38:43Z2023-04-13T14:38:43ZVenn: the man behind the famous diagrams – and why his work still matters today<figure><img src="https://images.theconversation.com/files/507859/original/file-20230202-16-eghiz9.png?ixlib=rb-1.1.0&rect=0%2C2%2C1974%2C1105&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption"></span> <span class="attribution"><span class="license">Author provided</span></span></figcaption></figure><p>April 2023 marks the 100th anniversary of the death of mathematician and philosopher John Venn. You may well be familiar with Venn diagrams – the ubiquitous pictures of typically two or three intersecting circles, illustrating the relationships between two or three collections of things. </p>
<p>For example, during the pandemic, Venn diagrams <a href="https://www.childrens.com/health-wellness/allergies-or-covid-19">helped to illustrate symptoms</a> of COVID-19 that are distinct from seasonal allergies. They are also often taught to school children and are typically part of the early curriculum for logic and databases in higher education.</p>
<figure class="align-right zoomable">
<a href="https://images.theconversation.com/files/520557/original/file-20230412-18-o440sw.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="John Venn." src="https://images.theconversation.com/files/520557/original/file-20230412-18-o440sw.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/520557/original/file-20230412-18-o440sw.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=815&fit=crop&dpr=1 600w, https://images.theconversation.com/files/520557/original/file-20230412-18-o440sw.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=815&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/520557/original/file-20230412-18-o440sw.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=815&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/520557/original/file-20230412-18-o440sw.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1025&fit=crop&dpr=1 754w, https://images.theconversation.com/files/520557/original/file-20230412-18-o440sw.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1025&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/520557/original/file-20230412-18-o440sw.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1025&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">John Venn.</span>
<span class="attribution"><span class="source">wikipedia</span>, <a class="license" href="http://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA</a></span>
</figcaption>
</figure>
<p>Venn <a href="https://www.britannica.com/biography/John-Venn">was born in Hull, UK,</a> in 1834. His early life in Hull was influenced by his father, an Anglican priest – it was expected John would follow in his footstep. He did initially begin a career in the Anglican church, but later moved into academia at the University of Cambridge. </p>
<p>One of Venn’s major achievements was to find a way to visualise a mathematical area called set theory. Set theory is an area of mathematics which can help to formally describe properties of collections of objects.</p>
<p>For example, we could have a set of cars, C. Within this set, there could be subsets such as the set of electric cars, E, the set of petrol based cars, say P, and the set of diesel powered cars, D. Given these, we can operate on them, for example, to apply car charges to the sets P and D, and a discount to the set E. </p>
<p>These sorts of operations form the basis of databases, as well as being used in many fundamental areas of science. Other major works of Venn’s include probability theory and symbolic logic. Venn had initially used diagrams developed by the Swiss <a href="https://mathshistory.st-andrews.ac.uk/Biographies/Euler/">mathematician Leonard Euler</a> to <a href="https://doi.org/10.1007/s10516-022-09642-2">show some relationships between sets</a>, which he then developed into his famous Venn diagrams. </p>
<p>Venn used the diagrams to prove a form of logical statement known as a categorical syllogism. This can be used to model reasoning. Here’s an example: “All computers need power. All AI systems are computers.” We can chain these together to the conclusion that “all AI systems need power”. </p>
<p>Today, we are familiar with such reasoning to illustrate how different collections relate to each other. For example, the SmartArt tool in Microsoft products lets you create a Venn diagram to illustrate the relationships between different sets. In our earlier car example, we could have a diagram showing electric cars, E, and petrol powered cars, P. The set of hybrid cars that have a petrol engine would be in the intersection of P and E.</p>
<h2>Logic and computing</h2>
<p>The visualisation of sets (and databases) is helpful, but the importance of Venn’s work then – and now – is the way they allowed proof of <a href="https://plato.stanford.edu/entries/boole/">George Boole’s ideas</a> of logic as a formal science. </p>
<p>Venn used his diagrams to illustrate and explore such “<a href="https://www.tandfonline.com/doi/full/10.1080/01445340.2020.1758387">symbolic logic</a>” – defending and extending it. Symbolic logic underpins modern computing, and Boolean logic is a key part of the design of modern computer systems – making his work relevant today. </p>
<p>Venn’s work was also crucial to the work of philosopher <a href="https://www.nobelprize.org/prizes/literature/1950/russell/biographical/">Bertrand Russell</a>, showing that there are problems that are unsolvable. We can express such problems with sets, in which each is an unsolvable problem. One such unsolvable problem can be expressed with the “<a href="https://www.britannica.com/topic/barber-paradox">Barber paradox</a>”. Suppose we had an article in Wikipedia containing all the articles that don’t contain themselves – a set. Is this new article itself in that set? </p>
<p>Luckily we can visualise that with a Venn diagram with two circles, where one circle is the set of entries that don’t include themselves, A, and the other circle is the set of entries that do include themselves, B. </p>
<p>We can then ask the question: where do we put the article that contains all the articles that don’t contain themselves? Have a think about it, then see where you would put it. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/519094/original/file-20230403-28-a4koz4.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/519094/original/file-20230403-28-a4koz4.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=350&fit=crop&dpr=1 600w, https://images.theconversation.com/files/519094/original/file-20230403-28-a4koz4.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=350&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/519094/original/file-20230403-28-a4koz4.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=350&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/519094/original/file-20230403-28-a4koz4.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=440&fit=crop&dpr=1 754w, https://images.theconversation.com/files/519094/original/file-20230403-28-a4koz4.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=440&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/519094/original/file-20230403-28-a4koz4.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=440&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">A Venn diagram of two sets - a set A of articles that do contain themselves, and a set B of articles that don’t.</span>
</figcaption>
</figure>
<p>The problem is that it cannot be on the left, as it would contain itself, and would therefore be inconsistent. And it cannot be on the right, as then it would be missing, or incomplete. And it can’t be in both. It must be in one or the other. This paradox illustrates how unsolvable statements can arise – they are valid in terms of expressing them within the logical system, but ultimately unanswerable. We could possibly extend our system to solve this, but then we would end up with another unanswerable question. </p>
<p>Venn’s diagrams were crucial in understanding this. And this area of science is still important, for example when <a href="https://doi.org/10.1038/d41586-019-00083-3">considering the limitations</a> of machine learning and AI, where we may ask questions that cannot be answered. </p>
<p>Venn also had an interest in building mechanical machines – <a href="https://mathshistory.st-andrews.ac.uk/Biographies/Venn/">including a bowling machine</a> which proved so effective it was able to bowl out some top Australian batsmen of the day.</p>
<p>Following his abstract work on logic, he developed the concept of a logical-diagram machine with a lot of processing power: though this brilliant idea from 1881 would take many decades to appear as modern computers. </p>
<p>We remember Venn here in Hull, with a bridge close to his birthplace decorated with Venn circle inspired artwork. At the University of Hull’s main administration building, there’s an intersection of management and academia which is called the Venn building.</p><img src="https://counter.theconversation.com/content/199127/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Neil Gordon 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>Venn diagrams have helped the development of logic and computing.Neil Gordon, Lecturer in Computer Science, University of HullLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1790642022-07-21T12:24:22Z2022-07-21T12:24:22ZFrom in-crowds to power couples, network science uncovers the hidden structure of community dynamics<figure><img src="https://images.theconversation.com/files/474376/original/file-20220715-26-7p5uhp.jpg?ixlib=rb-1.1.0&rect=0%2C9%2C6240%2C4138&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Can you tell who in this picture wields soft power? A new technique for analyzing networks can.</span> <span class="attribution"><a class="source" href="https://www.gettyimages.com/detail/photo/group-of-business-people-in-convention-center-royalty-free-image/1179435810">gremlin/E+ via Getty Images</a></span></figcaption></figure><p>The world is a networked place, literally and figuratively. The field of network science is used today to understand phenomena as diverse as the <a href="https://doi.org/10.1145/2872518.2890092">spread of misinformation</a>, <a href="https://www.brookings.edu/blog/africa-in-focus/2016/10/10/mapping-west-african-trade-networks/">West African trade</a> and <a href="https://doi.org/10.1038/nbt0108-69">protein-protein interactions</a> in cells.</p>
<p>Network science has uncovered several <a href="https://doi.org/10.1038/30918">universal properties</a> of complex social networks, which in turn has made it possible to learn details of particular networks. For example, the network consisting of the international financial corruption scheme uncovered by the <a href="https://panamapapers.org/">Panama Papers investigation</a> has an <a href="https://doi.org/10.1007/s41109-020-00313-y">unusual lack of connections among its parts</a>.</p>
<p>But understanding the hidden structures of key elements of social networks, such as subgroups, has remained elusive. My colleagues and I have found two complex patterns in these networks that can help researchers better understand the hierarchies and dynamics of these elements. We found a way to detect powerful “inner circles” in large organizations simply by studying networks that map emails being sent among employees. </p>
<p>We demonstrated the utility of our methods by applying them to the famous Enron network. Enron was an energy trading company that <a href="https://www.cnn.com/2013/07/02/us/enron-fast-facts/index.html">perpetrated fraud on a massive scale</a>. Our <a href="https://doi.org/10.48550/arXiv.2203.06491">study</a> further showed that the method can potentially be used to detect people who wield enormous soft power in an organization regardless of their official title or position. This could be useful for historical, sociological and economic research, as well as government, legal and media investigations.</p>
<h2>From pencil and paper to artificial intelligence</h2>
<p>Sociologists have been constructing and studying smaller social networks in careful field experiments for <a href="https://doi.org/10.2307/2785266">at least 80 years</a>, well before the advent of the internet and online social networks. The concept is so simple that it can be drawn on paper: Entities of interest – people, businesses, countries – are nodes represented as points, and relationships between pairs of nodes are links represented as lines drawn between the points. </p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/451706/original/file-20220312-14-o2rnnt.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Two sets of dots with lines connecting some of the dots" src="https://images.theconversation.com/files/451706/original/file-20220312-14-o2rnnt.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/451706/original/file-20220312-14-o2rnnt.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=313&fit=crop&dpr=1 600w, https://images.theconversation.com/files/451706/original/file-20220312-14-o2rnnt.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=313&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/451706/original/file-20220312-14-o2rnnt.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=313&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/451706/original/file-20220312-14-o2rnnt.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=393&fit=crop&dpr=1 754w, https://images.theconversation.com/files/451706/original/file-20220312-14-o2rnnt.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=393&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/451706/original/file-20220312-14-o2rnnt.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=393&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">An abstract network, at left, shows lines between points representing relationships. The network on the right shows a small fragment of a real-world network of West African traders, based on data from Oliver J. Walther. https://doi.org/10.1080/00220388.2015.1010152.</span>
<span class="attribution"><span class="source">Mayank Kejriwal</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<p>Using network science to study human societies and other complex systems took on new meaning in <a href="https://doi.org/10.1126/science.286.5439.509">the late 1990s</a> when researchers discovered some universal properties of networks. <a href="https://doi.org/10.1038/30918">Some of these universal properties</a> have since entered mainstream pop culture. One concept is the Six Degrees of Kevin Bacon, based on the famous empirical finding that any two people on Earth are <a href="https://doi.org/10.2307/2786545">six or fewer links apart</a>. Similarly, versions of statements such as “<a href="https://doi.org/10.1371/journal.pone.0086197">the rich get richer</a>” and “<a href="https://doi.org/10.2307/2786545">winner takes all</a>” have also been replicated in some networks. </p>
<p>These global properties, meaning ones applying to the entire network, seemingly emerge from the myopic and local actions of independent nodes. When I connect with someone on LinkedIn, I am certainly not thinking of the global consequences of my connection on the LinkedIn network. Yet my actions, along with those of many others, eventually lead to predictable, rather than random, outcomes about how the network will evolve. </p>
<p>My colleagues and I have used network science to study <a href="https://doi.org/10.1007/s41109-020-00275-1">human trafficking in the U.K.</a>, the <a href="https://doi.org/10.1007/s41109-019-0154-z">structure of noise</a> in artificial intelligence systems’ outputs, and <a href="https://doi.org/10.1007/s41109-020-00313-y">financial corruption</a> in the Panama Papers.</p>
<h2>Groups have their own structure</h2>
<p>Along with studying emergent properties like the Six Degrees of Kevin Bacon, researchers have also used network science to focus on problems such as <a href="https://senseable.mit.edu/community_detection/">community detection</a>. Stated simply, can a set of rules, otherwise known as an algorithm, automatically discover groups or communities within a collection of people?</p>
<p>Today there are hundreds, if not thousands, of <a href="https://doi.org/10.1016/j.jnca.2018.02.011">community detection algorithms</a>, some relying on advanced AI methods. They are used for many purposes, including finding communities of interest and uncovering malicious groups on social media. Such algorithms encode intuitive assumptions, such as the expectation that nodes belonging to the same group are more densely connected to one another than nodes belonging to different groups. </p>
<p>Although an exciting line of work, community detection does not study the internal structure of communities. Should communities be thought of only as collections of nodes in networks? And what about communities that are small but particularly influential, such as inner circles and in-crowds?</p>
<h2>Two hypothetical structures for influential groups</h2>
<p>In a manner of speaking, you likely already have some inkling of the structure of very small groups in social networks. The truth of the adage that “a friend of my friend is also my friend” can be tested statistically in friendship networks by counting the number of triangles in the network and determining whether this number is higher than chance alone could explain. And indeed, many social network studies have been used to <a href="https://doi.org/10.1126/sciadv.aax7310">verify the claim</a>. </p>
<p>Unfortunately, the concept starts breaking down when extended to groups with more than three members. Although motifs have been well studied in both algorithmic <a href="https://doi.org/10.1016/j.jpdc.2011.08.007">computer science</a> and <a href="https://doi.org/10.1016/B978-0-12-801213-0.00001-0">biology</a>, they have not been reliably linked to influential groups in real communication networks.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/451707/original/file-20220312-26-1xiy0uc.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="six sets of four dots each with different configurations of lines connecting the dots" src="https://images.theconversation.com/files/451707/original/file-20220312-26-1xiy0uc.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/451707/original/file-20220312-26-1xiy0uc.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=274&fit=crop&dpr=1 600w, https://images.theconversation.com/files/451707/original/file-20220312-26-1xiy0uc.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=274&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/451707/original/file-20220312-26-1xiy0uc.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=274&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/451707/original/file-20220312-26-1xiy0uc.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=344&fit=crop&dpr=1 754w, https://images.theconversation.com/files/451707/original/file-20220312-26-1xiy0uc.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=344&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/451707/original/file-20220312-26-1xiy0uc.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=344&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Six examples of motifs with four nodes.</span>
<span class="attribution"><span class="source">Mayank Kejriwal</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<p>Building on this tradition, my doctoral student <a href="https://scholar.google.com/citations?hl=en&user=-D05LWQAAAAJ&view_op=list_works&sortby=pubdate">Ke Shen</a> and I found and <a href="https://aaai.org/Conferences/AAAI-22/ws22workshops/#ws19">presented</a> <a href="https://doi.org/10.48550/arXiv.2203.06491">two structures that seem elaborate</a> but turn out to be quite common in real networks.</p>
<p>The first structure extends the triangle, not by adding more nodes, but by directly adding triangles. Specifically, there is a central triangle that is flanked by other peripheral triangles. Importantly, the third person in any peripheral triangle must not be linked to the third person on the central triangle, thereby excluding them from the true inner circle of influence. </p>
<p>The second structure is similar but assumes that there is no central triangle, and the inner circle is just a pair of nodes. A real-life example might be two co-founders of a startup like Sergey Brin and Larry Page of Google, or a power couple with joint interests, <a href="https://www.nytimes.com/interactive/2016/10/28/world/americas/president-spouses-politics-dynasty.html">common in global politics</a>, like Bill and Hillary Clinton.</p>
<h2>Understanding influential groups in an infamous network</h2>
<p>We tested our hypothesis on the <a href="https://doi.org/10.1080/10691898.2015.11889734">Enron email network</a>, which is well studied in network science, with nodes representing email addresses and links representing communication among those addresses. Despite being elaborate, not only were our proposed structures present in the network in greater numbers than chance alone would predict, but a qualitative analysis showed that there is merit to the claim that they represent influential groups.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/474985/original/file-20220719-10005-7ornip.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="Two diagrams of overlapping sets of triangles labeled with names of people" src="https://images.theconversation.com/files/474985/original/file-20220719-10005-7ornip.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/474985/original/file-20220719-10005-7ornip.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=248&fit=crop&dpr=1 600w, https://images.theconversation.com/files/474985/original/file-20220719-10005-7ornip.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=248&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/474985/original/file-20220719-10005-7ornip.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=248&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/474985/original/file-20220719-10005-7ornip.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=311&fit=crop&dpr=1 754w, https://images.theconversation.com/files/474985/original/file-20220719-10005-7ornip.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=311&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/474985/original/file-20220719-10005-7ornip.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=311&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Examples of the two structures found in the Enron network. More such structures are present in the network and cannot be explained by chance alone.</span>
<span class="attribution"><span class="source">Mayank Kejriwal</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<p>The main characters in the Enron saga are <a href="https://www.wsj.com/articles/SB114123416916986639">well</a> <a href="https://www.nytimes.com/2003/04/20/books/chapters/power-failure.html">documented</a> by now. Intriguingly, some of these characters do not seem to have had much official influence but may have wielded significant <a href="https://doi.org/10.2307/2390947">soft power</a>. An example is Sherri Reinartz-Sera, who was the longtime administrative assistant of Jeffrey K. Skilling, the former chief executive of Enron. Unlike Skilling, Sera was only mentioned in a <a href="https://www.nytimes.com/2006/01/19/business/exenron-chief-executive-prepares-for-trial.html">New York Times article</a> following investigative reporting that took place during the course of the scandal. However, our algorithm discovered an influential group with Sera occupying a central position.</p>
<h2>Dissecting power dynamics</h2>
<p>Society has intricate structures at the levels of individuals, friendships and communities. In-crowds are not just ragtag groups of characters talking to one another, or a single ringleader calling all the shots. Many in-crowds, or influential groups, have a sophisticated structure. </p>
<p>While much still remains to be discovered about such groups and their influence, network science can help uncover their complexity.</p><img src="https://counter.theconversation.com/content/179064/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Mayank Kejriwal receives funding from the Defense Advanced Research Projects Agency (DARPA). </span></em></p>A mathematical method of analyzing networks can spot hidden features such as people who wield soft power in organizations.Mayank Kejriwal, Research Assistant Professor of Industrial & Systems Engineering, University of Southern CaliforniaLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1732452021-12-26T20:28:27Z2021-12-26T20:28:27ZLike songs, the best graphs tell stories. Here are my 10 favourites from 2021<figure><img src="https://images.theconversation.com/files/436251/original/file-20211208-141213-1demhsp.png?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">sheetmusicdirect</span></span></figcaption></figure><p>“One of the first things you have to decide on with a musical is why should there be songs.”</p>
<p>The person speaking is <a href="https://www.nytimes.com/video/players/offsite/index.html?videoId=1248069062358">Stephen Sondheim</a>, the writer of some of the best songs for musicals in the 20th century, who died in November aged 91.</p>
<blockquote>
<p>You can put songs in any story, but what I think you have to look for is, why are songs necessary to this story? If it’s unnecessary, then the show generally turns out to be not very good.</p>
</blockquote>
<p>I’m no <a href="https://www.abc.net.au/news/2021-11-27/stephen-sondheim-dies/100655760">Sondheim</a>, but as an editor I won’t put a graph into any story unless it is absolutely necessary to tell the story.</p>
<p>When I do, the picture can be worth at least the 800 words that accompany it.</p>
<p>So here are my 10 favourites from the business and economy stories I edited for The Conversation in 2021.</p>
<h2>Some of the best graphs remove doubt</h2>
<p>This graph, from the Bureau of Statistics, leaves no doubt about what happens to consumer spending when lockdowns end.</p>
<p>Released in November, with the national accounts, it uses <a href="https://theconversation.com/sure-the-national-accounts-show-gdp-going-backwards-but-look-at-whats-to-come-172950">bank account data</a> to show what happened to spending on clothes, furnishings, recreation, transport and restaurants and hotels. </p>
<hr>
<p><strong>Selected Victorian spending data</strong></p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/434925/original/file-20211201-15-38vvlr.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/434925/original/file-20211201-15-38vvlr.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/434925/original/file-20211201-15-38vvlr.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=247&fit=crop&dpr=1 600w, https://images.theconversation.com/files/434925/original/file-20211201-15-38vvlr.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=247&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/434925/original/file-20211201-15-38vvlr.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=247&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/434925/original/file-20211201-15-38vvlr.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=310&fit=crop&dpr=1 754w, https://images.theconversation.com/files/434925/original/file-20211201-15-38vvlr.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=310&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/434925/original/file-20211201-15-38vvlr.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=310&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Aggregated bank data. Index for May 2020 = 100.</span>
<span class="attribution"><a class="source" href="https://www.abs.gov.au/articles/impact-lockdowns-household-consumption-insights-alternative-data-sources">ABS</a></span>
</figcaption>
</figure>
<hr>
<p>While the effect is clear, and beautifully illustrated, it can be interpreted in two ways. One is that lockdowns are to be avoided because they suppress ordinary life. </p>
<p>The other is that Victoria’s long lockdown was caused by the failure of the NSW government to lockdown <a href="https://www.abc.net.au/news/2021-12-02/policy-failures-caused-the-historical-decline-in-economic-growth/100664322">quickly enough</a> and hard enough as the Delta variant spread, meaning lockdowns are to be embraced, and quickly. </p>
<p>Another graph that removed doubt is this one showing what Australia’s July 2012 to July 2014 carbon price did to <a href="https://theconversation.com/vital-signs-marketing-is-getting-in-the-way-of-markets-that-could-get-us-to-net-zero-171602">greenhouse gas emissions</a>, excluding those related to land use and forestry that are subject to government directives.</p>
<hr>
<p><strong>Australian emissions excluding land use, land-use change and forestry</strong></p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/431464/original/file-20211111-27-mha6a7.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/431464/original/file-20211111-27-mha6a7.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/431464/original/file-20211111-27-mha6a7.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=285&fit=crop&dpr=1 600w, https://images.theconversation.com/files/431464/original/file-20211111-27-mha6a7.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=285&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/431464/original/file-20211111-27-mha6a7.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=285&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/431464/original/file-20211111-27-mha6a7.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=358&fit=crop&dpr=1 754w, https://images.theconversation.com/files/431464/original/file-20211111-27-mha6a7.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=358&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/431464/original/file-20211111-27-mha6a7.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=358&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Million tonnes of carbon dioxide equivalent per annum, updated quarterly.</span>
<span class="attribution"><a class="source" href="https://www.climatecouncil.org.au/wp-content/uploads/2019/04/Climate-Cuts-Cover-Ups-and-Censorship.pdf">Climate Council, Department of Industry</a></span>
</figcaption>
</figure>
<hr>
<p>Whatever else is said about the carbon price, its effect on emissions is clear. </p>
<p>Also clear, and enormous when you look at it, is what our current system of adjusting JobSeeker only in line with the consumer price index will do to it compared to the age pension, which is adjusted in line with wages.</p>
<p>The projections in this graph derive from the mid-year intergenerational report which looks forward 40 years. </p>
<p>After 40 years – unless there’s an extra increase, and one wasn’t allowed for in the intergenerational report – JobSeeker will be a <a href="https://theconversation.com/when-covid-is-behind-us-australians-are-going-to-have-to-pay-more-tax-164707">mere fraction</a> of the pension.</p>
<hr>
<p><strong>JobSeeker and age pension as projected in intergenerational report</strong></p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/412051/original/file-20210720-15-jrjreu.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/412051/original/file-20210720-15-jrjreu.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/412051/original/file-20210720-15-jrjreu.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=247&fit=crop&dpr=1 600w, https://images.theconversation.com/files/412051/original/file-20210720-15-jrjreu.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=247&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/412051/original/file-20210720-15-jrjreu.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=247&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/412051/original/file-20210720-15-jrjreu.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=310&fit=crop&dpr=1 754w, https://images.theconversation.com/files/412051/original/file-20210720-15-jrjreu.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=310&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/412051/original/file-20210720-15-jrjreu.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=310&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Payment for a single person, dollars per fortnight. JobSeeker, pension indexed to intergenerational report inflation projections.</span>
</figcaption>
</figure>
<hr>
<p>Also shrinking, with unfortunate consequences for <a href="https://theconversation.com/paying-off-a-home-loan-used-to-be-easier-than-it-looked-its-now-harder-heres-why-161873">Australians with mortgages</a> and Australians trying to get them, has been wage growth.</p>
<p>The government has been forecasting a return to the 3-4% wage growth we once had in <a href="https://theconversation.com/its-the-budget-cash-splash-that-reaches-back-in-time-114188">every budget</a> since 2012, save for the last two.</p>
<p>Right now public sector wages growth, which used to lead private sector growth, is well below 2%. Private sector growth has started to climb, but it is well short of where it was.</p>
<hr>
<p><strong>Wage price index</strong></p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/436258/original/file-20211208-25-idgl6u.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/436258/original/file-20211208-25-idgl6u.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/436258/original/file-20211208-25-idgl6u.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=247&fit=crop&dpr=1 600w, https://images.theconversation.com/files/436258/original/file-20211208-25-idgl6u.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=247&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/436258/original/file-20211208-25-idgl6u.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=247&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/436258/original/file-20211208-25-idgl6u.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=310&fit=crop&dpr=1 754w, https://images.theconversation.com/files/436258/original/file-20211208-25-idgl6u.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=310&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/436258/original/file-20211208-25-idgl6u.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=310&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Annual seasonally adjusted growth in total hourly rates of pay excluding bonuses.</span>
<span class="attribution"><a class="source" href="https://www.abs.gov.au/statistics/economy/price-indexes-and-inflation/wage-price-index-australia/sep-2021">ABS</a></span>
</figcaption>
</figure>
<hr>
<p>Up until the year 2000, buying a home cost between two and three times household after tax-income. </p>
<p>Then, after the headline rate of capital gains tax was halved and investors dived into the market, prices climbed to between three and four times income.</p>
<p>Six years ago they jumped again to between four and five times income, and in 2021 they climbed once again to more than <a href="https://theconversation.com/paying-off-a-home-loan-used-to-be-easier-than-it-looked-its-now-harder-heres-why-161873">six times</a> disposable income.</p>
<hr>
<p><strong>Home prices as proportion of household disposable income</strong></p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/394394/original/file-20210411-15-8ofvv7.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/394394/original/file-20210411-15-8ofvv7.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/394394/original/file-20210411-15-8ofvv7.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=240&fit=crop&dpr=1 600w, https://images.theconversation.com/files/394394/original/file-20210411-15-8ofvv7.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=240&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/394394/original/file-20210411-15-8ofvv7.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=240&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/394394/original/file-20210411-15-8ofvv7.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=302&fit=crop&dpr=1 754w, https://images.theconversation.com/files/394394/original/file-20210411-15-8ofvv7.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=302&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/394394/original/file-20210411-15-8ofvv7.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=302&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Household disposable income after tax, before the deduction of interest payments, including income of unincorporated enterprises.</span>
<span class="attribution"><a class="source" href="https://www.rba.gov.au/chart-pack/pdf/chart-pack.pdf">Core Logic, ABS, RBA</a></span>
</figcaption>
</figure>
<hr>
<p>While low wage growth should make it harder to pay off a loan than it used to be, just at the moment ultra-low interest rates are making it <a href="https://theconversation.com/as-home-prices-soar-beyond-reach-we-have-a-government-inquiry-almost-designed-not-to-tell-us-why-168959">easier to service</a> mortgages than it has been in decades.</p>
<p>But what the Reserve Bank calls <a href="https://theconversation.com/as-home-prices-soar-beyond-reach-we-have-a-government-inquiry-almost-designed-not-to-tell-us-why-168959">housing accessibility</a> (to distinguish it from housing affordability) is much worse.</p>
<p>Astounding price growth and a decade of weak wages growth have pushed up the cost of an average first home deposit from 70% of income to more than 80%.</p>
<hr>
<p><strong>Average first home buyer deposit</strong></p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/425847/original/file-20211012-26-1kbvg9c.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/425847/original/file-20211012-26-1kbvg9c.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/425847/original/file-20211012-26-1kbvg9c.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=238&fit=crop&dpr=1 600w, https://images.theconversation.com/files/425847/original/file-20211012-26-1kbvg9c.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=238&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/425847/original/file-20211012-26-1kbvg9c.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=238&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/425847/original/file-20211012-26-1kbvg9c.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=299&fit=crop&dpr=1 754w, https://images.theconversation.com/files/425847/original/file-20211012-26-1kbvg9c.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=299&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/425847/original/file-20211012-26-1kbvg9c.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=299&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Owner-occupier; estimated as a share of average annual household disposable income using average first home buyer commitment size and assuming 20 per cent deposit. Seasonally adjusted and break-adjusted.</span>
<span class="attribution"><a class="source" href="https://www.rba.gov.au/publications/submissions/housing-and-housing-finance/inquiry-into-housing-affordability-and-supply-in-australia/pdf/inquiry-into-housing-affordability-and-supply-in-australia.pdf">RBA, ABS</a></span>
</figcaption>
</figure>
<hr>
<h2>Other graphs surprise</h2>
<p>If we start building more houses, it stands to reason that we will get more houses.</p>
<p>That’ll doubtless be the case eventually, but if you are expecting it to happen any time soon, you will be disappointed.</p>
<p>In the space of a year, the number of Australian houses (not apartments) under construction has jumped from 56,060 to 88,445 — the most ever. </p>
<p>But bizarrely, as has been the case for half a century, the number of houses completed each quarter has <a href="https://theconversation.com/building-more-houses-quickly-is-harder-than-it-looks-australia-hasnt-done-it-in-decades-170223">barely moved</a>. </p>
<p>It’s as if homebuilding can’t scale up. </p>
<hr>
<p><strong>Houses under construction, houses completed, quarterly</strong></p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/439030/original/file-20211227-117041-xttokw.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/439030/original/file-20211227-117041-xttokw.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/439030/original/file-20211227-117041-xttokw.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=321&fit=crop&dpr=1 600w, https://images.theconversation.com/files/439030/original/file-20211227-117041-xttokw.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=321&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/439030/original/file-20211227-117041-xttokw.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=321&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/439030/original/file-20211227-117041-xttokw.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=404&fit=crop&dpr=1 754w, https://images.theconversation.com/files/439030/original/file-20211227-117041-xttokw.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=404&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/439030/original/file-20211227-117041-xttokw.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=404&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption"></span>
<span class="attribution"><a class="source" href="https://www.abs.gov.au/statistics/industry/building-and-construction/building-activity-australia/latest-release#data-download">Australian Bureau of Statistics</a></span>
</figcaption>
</figure>
<hr>
<p>Another surprising graph shows the disconnect between crime and our desire to lock people up.</p>
<p>Nonviolent crime has plummeted. Between 2000 and 2020, armed robberies fell from 9,480 to 4,746, unarmed robberies fell from 13,850 to 4,666, and motor vehicle vehicle theft fell from 138,915 to 48,056.</p>
<p>Violent crime is falling too. The Productivity Commission believes homicide gives the best read on crime because almost all homicides are reported. </p>
<p>It found that while homicide has plummeted, imprisonment has <a href="https://theconversation.com/more-prison-time-for-less-crime-our-swelling-prisons-are-costing-us-dearly-170792">doubled</a>. </p>
<hr>
<p><strong>Homicides and imprisonment per 100,000 Australians</strong></p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/428992/original/file-20211028-27-1u1evql.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/428992/original/file-20211028-27-1u1evql.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/428992/original/file-20211028-27-1u1evql.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=314&fit=crop&dpr=1 600w, https://images.theconversation.com/files/428992/original/file-20211028-27-1u1evql.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=314&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/428992/original/file-20211028-27-1u1evql.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=314&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/428992/original/file-20211028-27-1u1evql.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=395&fit=crop&dpr=1 754w, https://images.theconversation.com/files/428992/original/file-20211028-27-1u1evql.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=395&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/428992/original/file-20211028-27-1u1evql.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=395&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Number of prisoners per 100,000 population aged 18 years and over, number of homicides per 100,000 persons.</span>
<span class="attribution"><a class="source" href="https://www.pc.gov.au/research/completed/prison-dilemma">Productivity Commission</a></span>
</figcaption>
</figure>
<hr>
<p>Another surprise is that the “<a href="https://theconversation.com/australias-great-resignation-is-a-myth-we-are-changing-jobs-less-than-ever-before-170784">great resignation</a>” – the jump in the proportion of workers quitting their jobs in the United States – hasn’t been seen here.</p>
<p>It seems to be a real phenomenon in the US, where low vaccination rates have made public-facing jobs dangerous, but not here where resignations have been falling for decades.</p>
<p>Australians seem increasingly resigned to staying in the jobs they are in.</p>
<hr>
<p><strong>Proportion of Australians who changed jobs in the past year</strong></p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/435827/original/file-20211206-23-1h2uj0y.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/435827/original/file-20211206-23-1h2uj0y.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/435827/original/file-20211206-23-1h2uj0y.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=307&fit=crop&dpr=1 600w, https://images.theconversation.com/files/435827/original/file-20211206-23-1h2uj0y.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=307&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/435827/original/file-20211206-23-1h2uj0y.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=307&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/435827/original/file-20211206-23-1h2uj0y.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=386&fit=crop&dpr=1 754w, https://images.theconversation.com/files/435827/original/file-20211206-23-1h2uj0y.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=386&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/435827/original/file-20211206-23-1h2uj0y.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=386&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption"></span>
<span class="attribution"><a class="source" href="https://www.abs.gov.au/statistics/labour/employment-and-unemployment/job-mobility/feb-2021">Australian Bureau of Statistics</a></span>
</figcaption>
</figure>
<hr>
<h2>The very best graphs tell an entire story</h2>
<p>When COVID took off in the first half of 2020 there was concern that many more people would die as a result of COVID than were recorded as COVID deaths.</p>
<p>Some of these “<a href="https://www.economist.com/graphic-detail/coronavirus-excess-deaths-tracker">excess deaths</a>” would be COVID deaths that were not classified as COVID; some would be extra deaths caused by measures such as lockdowns; and some would be caused by crowded medical facilities turning away patients. </p>
<p>Worldwide, there have been <a href="https://ourworldindata.org/excess-mortality-covid">millions</a> of excess deaths.</p>
<p>But not in Australia. In several months Australia’s excess deaths have been <a href="https://www.economist.com/graphic-detail/coronavirus-excess-deaths-tracker">negative</a>, with more deaths avoided than usual, in part because better health practices prevented deaths from the flu.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/you-cant-fix-it-if-you-cant-see-it-how-the-abs-became-our-secret-weapon-156637">You can't fix it if you can't see it: how the ABS became our secret weapon</a>
</strong>
</em>
</p>
<hr>
<p>To track excess deaths the Bureau of Statistics has <a href="https://www.abs.gov.au/statistics/health/causes-death/provisional-mortality-statistics/jan-2020-aug-2021">graphed</a> the number of doctor certified deaths actually recorded each week against the number that would be expected for that week given the average over the past five years.</p>
<hr>
<p><strong>Weekly deaths vs 2015-2019 average</strong></p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/439022/original/file-20211226-23072-1tsjblq.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/439022/original/file-20211226-23072-1tsjblq.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/439022/original/file-20211226-23072-1tsjblq.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=214&fit=crop&dpr=1 600w, https://images.theconversation.com/files/439022/original/file-20211226-23072-1tsjblq.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=214&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/439022/original/file-20211226-23072-1tsjblq.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=214&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/439022/original/file-20211226-23072-1tsjblq.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=269&fit=crop&dpr=1 754w, https://images.theconversation.com/files/439022/original/file-20211226-23072-1tsjblq.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=269&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/439022/original/file-20211226-23072-1tsjblq.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=269&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Doctor certified deaths.</span>
<span class="attribution"><a class="source" href="https://www.abs.gov.au/statistics/health/causes-death/provisional-mortality-statistics/jan-2020-aug-2021">ABS Provisional Mortality Statistics</a></span>
</figcaption>
</figure>
<hr>
<p>What is apparent is that in most weeks Australian deaths have been little more than would be expected given five-year averages, and in many weeks less.</p>
<p>If COVID has been killing people in ways we can’t see, the effect has been offset by the measures we have taken to combat COVID – saving lives in other ways we can’t see.</p>
<p>It’s an important finding, not at all foreseeable, and illustrated beautifully.</p><img src="https://counter.theconversation.com/content/173245/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Peter Martin 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>The Conversation’s best graphs have removed doubt, surprised, and told entire stories.Peter Martin, Visiting Fellow, Crawford School of Public Policy, Australian National UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1705562021-11-01T18:38:23Z2021-11-01T18:38:23ZThe science everyone needs to know about climate change, in 6 charts<figure><img src="https://images.theconversation.com/files/428635/original/file-20211026-23-1ky80w7.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Scientific instruments in space today can monitor hurricane strength, sea level rise, ice sheet loss and much more.</span> <span class="attribution"><a class="source" href="https://www.flickr.com/photos/gsfc/48698288003">Christina Koch/NASA</a></span></figcaption></figure><p><em><a href="https://theconversation.com/las-nociones-cientificas-sobre-el-cambio-climatico-que-todos-deberiamos-conocer-en-seis-graficos-171149">Leer en español</a></em></p>
<p>With the United Nations’ climate conference in Scotland turning a spotlight on climate change policies and the impact of global warming, it’s useful to understand what the science shows.</p>
<p>I’m an <a href="https://cires.colorado.edu/research/research-groups/elizabeth-weatherhead-group">atmospheric scientist</a> who has worked on global climate science and assessments for most of my career. Here are six things you should know, in charts.</p>
<h2>What’s driving climate change</h2>
<p>The primary focus of the negotiations is on carbon dioxide, a greenhouse gas that is released when fossil fuels – coal, oil and natural gas – are burned, as well as by forest fires, land use changes and natural sources.</p>
<p>The Industrial Revolution of the late 1800s started an enormous increase in the burning of fossil fuels. It powered homes, industries and opened up the planet to travel. That same century, scientists <a href="https://theconversation.com/scientists-understood-physics-of-climate-change-in-the-1800s-thanks-to-a-woman-named-eunice-foote-164687">identified carbon dioxide’s potential</a> to <a href="https://www.rsc.org/images/Arrhenius1896_tcm18-173546.pdf">increase global temperatures</a>, which at the time was considered a possible benefit to the planet. Systematic measurements started in the mid-1900s and have shown a steady increase in carbon dioxide, with <a href="https://www.ipcc.ch/assessment-report/ar6/">the majority of it directly traceable</a> to the combustion of fossil fuels.</p>
<p><iframe id="kkVw7" class="tc-infographic-datawrapper" src="https://datawrapper.dwcdn.net/kkVw7/23/" height="400px" width="100%" style="border: none" frameborder="0"></iframe></p>
<p>Once in the atmosphere, carbon dioxide tends to stay there for a very long time. A portion of the carbon dioxide released through human activities is taken up by plants, and some is absorbed directly into the ocean, but <a href="https://public.wmo.int/en/media/press-release/greenhouse-gas-bulletin-another-year-another-record">roughly half</a> of all carbon dioxide emitted by human activities today stays in the atmosphere — and it <a href="https://tos.org/oceanography/article/an-accounting-of-the-observed-increase-in-oceanic-and-atmospheric-co2-and-a">likely will remain there for hundreds of years</a>, influencing the climate globally.</p>
<p>During the <a href="https://www.iea.org/articles/global-energy-review-co2-emissions-in-2020">first year of the pandemic in 2020</a>, when fewer people were driving and some industries briefly stopped, carbon dioxide emissions from fuels fell by roughly 6%. But it <a href="https://essd.copernicus.org/articles/12/3269/2020/">didn’t stop the rise in the concentration of carbon dioxide</a> because the amount released into the atmosphere by human activities far exceeded what nature could absorb.</p>
<p>If civilization stopped its carbon dioxide-emitting activities today, it would <a href="https://tos.org/oceanography/article/an-accounting-of-the-observed-increase-in-oceanic-and-atmospheric-co2-and-a">still take many hundreds of years</a> for the concentration of carbon dioxide in the atmosphere to fall enough naturally to bring the planet’s carbon cycle back into balance because of carbon dioxide’s long life in the atmosphere.</p>
<p><iframe id="dE1UL" class="tc-infographic-datawrapper" src="https://datawrapper.dwcdn.net/dE1UL/8/" height="400px" width="100%" style="border: none" frameborder="0"></iframe></p>
<h2>How we know greenhouse gases can change the climate</h2>
<p>Multiple lines of scientific evidence point to the increase in greenhouse emissions over the past century and a half as a driver of long-term climate change around the world. For example:</p>
<ul>
<li><p>Laboratory measurements <a href="https://www.rsc.org/images/Arrhenius1896_tcm18-173546.pdf">since the 1800s</a> have repeatedly verified and quantified the absorptive properties of carbon dioxide that allow it to trap heat in the atmosphere.</p></li>
<li><p><a href="https://esd.copernicus.org/articles/12/545/2021/esd-12-545-2021-discussion.html">Simple models</a> based on the warming impact of carbon dioxide in the atmosphere <a href="https://agupubs.onlinelibrary.wiley.com/doi/full/10.1002/2017MS001038">match historical changes in temperature</a>.</p></li>
<li><p>Complex climate models, recently acknowledged in <a href="https://theconversation.com/winners-of-2021-nobel-prize-in-physics-built-mathematics-of-climate-modeling-making-predictions-of-global-warming-and-modern-weather-forecasting-possible-169329">the Nobel Prize for Physics</a>, not only indicate a warming of the Earth due to increases in carbon dioxide but also <a href="https://gmd.copernicus.org/articles/9/3461/2016/">offer details of the areas of greatest warming</a>.</p></li>
</ul>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/429261/original/file-20211029-26-whwkeu.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/429261/original/file-20211029-26-whwkeu.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/429261/original/file-20211029-26-whwkeu.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=353&fit=crop&dpr=1 600w, https://images.theconversation.com/files/429261/original/file-20211029-26-whwkeu.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=353&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/429261/original/file-20211029-26-whwkeu.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=353&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/429261/original/file-20211029-26-whwkeu.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=444&fit=crop&dpr=1 754w, https://images.theconversation.com/files/429261/original/file-20211029-26-whwkeu.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=444&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/429261/original/file-20211029-26-whwkeu.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=444&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 carbon dioxide levels have been high in the past, evidence shows temperatures have also been high.</span>
<span class="attribution"><a class="source" href="https://link.springer.com/chapter/10.1007/978-3-319-46939-3_1">Based on Salawitch et al., 2017, updated with data to the end of 2020</a>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<ul>
<li><p>Long-term records from <a href="https://doi.org/10.1038/s41586-018-0172-5">ice cores</a>, <a href="https://www.nytimes.com/2019/04/30/science/tree-rings-climate.html">tree rings</a> and <a href="https://www.aims.gov.au/docs/research/climate-change/climate-history/climate-history.html">corals</a> show that when carbon dioxide levels have been high, temperatures have also been high.</p></li>
<li><p>Our neighboring planets also offer evidence. Venus’ atmosphere is thick with carbon dioxide, and it is the <a href="https://doi.org/10.1029/95JE03862">hottest planet</a> in our solar system as a result, even though Mercury is closer to the sun. </p></li>
</ul>
<h2>Temperatures are rising on every continent</h2>
<p>The rising temperatures are evident in records from every continent and over the oceans.</p>
<p>The temperatures aren’t rising at the same rate everywhere, however. A variety of factors affect local temperatures, including land use that influences how much solar energy is absorbed or reflected, local heating sources like <a href="https://scied.ucar.edu/learning-zone/climate-change-impacts/urban-heat-islands">urban heat islands</a>, and pollution.</p>
<p>The Arctic, for example, is warming about <a href="https://www.nilu.com/2021/05/amap-increase-in-arctic-temperature-is-three-times-higher-than-the-global-average/">three times faster than the global average</a> in part because as the planet warms, snow and ice melt makes the surface more likely to absorb, rather than reflect, the sun’s radiation. Snow cover and sea ice recede even more rapidly as a result. </p>
<p><iframe id="yV1Al" class="tc-infographic-datawrapper" src="https://datawrapper.dwcdn.net/yV1Al/12/" height="400px" width="100%" style="border: none" frameborder="0"></iframe></p>
<h2>What climate change is doing to the planet</h2>
<p>Earth’s climate system is interconnected and complex, and even small temperature changes can have large impacts – for instance, with snow cover and sea levels.</p>
<p>Changes are already happening. Studies show that rising temperatures are <a href="https://www.ipcc.ch/assessment-report/ar6/">already affecting</a> precipitation, glaciers, weather patterns, tropical cyclone activity and severe storms. A number of studies show that the <a href="https://www.epa.gov/climate-indicators/climate-change-indicators-heat-waves">increases in frequency</a>, severity and duration of heat waves, for example, <a href="https://www.science.org/doi/10.1126/science.1098704">affect ecosystems, human lives</a>, commerce and agriculture.</p>
<p>Historical records of ocean water level have shown mostly consistent increases over the past 150 years as glacier ice melts and rising temperatures expand ocean water, with some local deviations due to sinking or rising land.</p>
<p><iframe id="AYpRq" class="tc-infographic-datawrapper" src="https://datawrapper.dwcdn.net/AYpRq/6/" height="400px" width="100%" style="border: none" frameborder="0"></iframe></p>
<p>While extreme events are often due to complex sets of causes, some are exacerbated by climate change. Just as coastal flooding can be made worse by rising ocean levels, heat waves are more damaging with higher baseline temperatures.</p>
<p>Climate scientists work hard to estimate future changes as a result of increased carbon dioxide and other expected changes, such as world population. It’s clear that temperatures will increase and precipitation will change. The exact magnitude of change depends on many interacting factors. </p>
<figure class="align-center ">
<img alt="Models of future temperature and precipitation in map form" src="https://images.theconversation.com/files/429867/original/file-20211103-21-1omk71v.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/429867/original/file-20211103-21-1omk71v.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=721&fit=crop&dpr=1 600w, https://images.theconversation.com/files/429867/original/file-20211103-21-1omk71v.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=721&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/429867/original/file-20211103-21-1omk71v.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=721&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/429867/original/file-20211103-21-1omk71v.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=906&fit=crop&dpr=1 754w, https://images.theconversation.com/files/429867/original/file-20211103-21-1omk71v.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=906&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/429867/original/file-20211103-21-1omk71v.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=906&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Based on SSP3-7.0, a high-emissions scenario.</span>
<span class="attribution"><a class="source" href="https://esd.copernicus.org/articles/12/253/2021/">Claudia Tebaldi, et al., 2021</a></span>
</figcaption>
</figure>
<h2>A few reasons for hope</h2>
<p>On a hopeful note, scientific research is improving our understanding of climate and the complex Earth system, identifying the most vulnerable areas and guiding efforts to reduce the drivers of climate change. Work on renewable energy and alternative energy sources, as well as ways to capture carbon from industries or from the air, are producing more options for a better prepared society. </p>
<p>At the same time, people are learning about how they can reduce their own impact, with the growing understanding that a globally coordinated effort is required to have a significant impact. <a href="https://www.bts.gov/data-spotlight/electric-vehicle-use-grows">Electric vehicles, as well as solar and wind power, are growing</a> at previously unthinkable rates. More people are showing a <a href="https://theconversation.com/pews-new-global-survey-of-climate-change-attitudes-finds-promising-trends-but-deep-divides-167847">willingness to adopt new strategies</a> to use energy more efficiently, consume more sustainably and choose renewable energy. </p>
<p>Scientists increasingly recognize that shifting away from fossil fuels has <a href="https://www.sciencedirect.com/science/article/abs/pii/S0269749107002849">additional benefits</a>, including <a href="https://books.google.com/books?hl=en&lr=&id=YmNnDwAAQBAJ&oi=fnd&pg=PP4&dq=World+Health+Organization,+2018,+Health,+environment+and+climate+change:+report+by+the+Director-General&ots=zQRnV6VGzD&sig=hsqdBTGjE45iZB-ECYP4HNlIQWc">improved air quality</a> for human health and ecosystems.</p>
<figure class="align-right ">
<img alt="COP26: the world’s biggest climate talks" src="https://images.theconversation.com/files/424739/original/file-20211005-17-cgrf2z.png?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/424739/original/file-20211005-17-cgrf2z.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=600&fit=crop&dpr=1 600w, https://images.theconversation.com/files/424739/original/file-20211005-17-cgrf2z.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=600&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/424739/original/file-20211005-17-cgrf2z.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=600&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/424739/original/file-20211005-17-cgrf2z.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=754&fit=crop&dpr=1 754w, https://images.theconversation.com/files/424739/original/file-20211005-17-cgrf2z.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=754&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/424739/original/file-20211005-17-cgrf2z.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=754&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption"></span>
</figcaption>
</figure>
<p><strong>This story is part of The Conversation’s coverage of COP26, the Glasgow climate conference, by experts from around the world.</strong>
<br><em>Amid a rising tide of climate news and stories, The Conversation is here to clear the air and make sure you get information you can trust. <a href="https://theconversation.com/us/cop26">Read more of our U.S.</a> and <a href="https://page.theconversation.com/cop26-glasgow-2021-climate-change-summit/">global coverage</a>.</em></p><img src="https://counter.theconversation.com/content/170556/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Betsy Weatherhead 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>Take a closer look at what’s driving climate change and how scientists know CO2 is involved, in a series of charts examining the evidence in different ways.Betsy Weatherhead, Senior Scientist, University of Colorado BoulderLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1621752021-06-18T04:50:26Z2021-06-18T04:50:26ZConcerned about the latest AstraZeneca news? These 3 graphics help you make sense of the risk<p>Yesterday’s <a href="https://www.health.gov.au/news/atagi-statement-on-revised-recommendations-on-the-use-of-covid-19-vaccine-astrazeneca-17-june-2021">announcement</a> the AstraZeneca COVID vaccine would now only be recommended for the over 60s has highlighted the many ways we think about risk.</p>
<p>The decision reflects a greater understanding of the real, but extremely low, risk of the clotting disorder called thrombosis with thrombocytopenia (TTS) for people aged 50-59, who are now recommended to have the Pfizer vaccine.</p>
<p><div data-react-class="Tweet" data-react-props="{"tweetId":"1405351450666967045"}"></div></p>
<p>But errors in the way we perceive these extremely small risks, called <a href="https://www.bookdepository.com/Thinking-Fast-Slow-Daniel-Kahneman/9780141033570">cognitive biases</a>, reflect the fact that when our brains evolved we did not have to grapple with risks this small. So we struggle to make sense of them and perceive these events as being much more likely than they actually are. </p>
<p>This can lead us to make decisions, such as not having a vaccine that could potentially save our life. And the misperception of the likelihood of TTS is one of the main reasons many are hesitant about receiving the AstraZeneca vaccine.</p>
<p>So let’s start with what we know about the risk of dying from TTS associated with the AstraZeneca vaccine, expressed the traditional way, with words and numbers. Then we’ll present the same numbers graphically.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/australians-under-60-will-no-longer-receive-the-astrazeneca-vaccine-so-whats-changed-162930">Australians under 60 will no longer receive the AstraZeneca vaccine. So what's changed?</a>
</strong>
</em>
</p>
<hr>
<h2>What’s the risk of dying from TTS?</h2>
<p>Initially, we thought about 25% of people with TTS associated with the vaccine would die. But as we learnt more about how to recognise and treat these rare blood clots, the risk of dying from it has changed. In Australia, mortality is now down to <a href="https://theconversation.com/how-rare-are-blood-clots-after-the-astrazeneca-vaccine-what-should-you-look-out-for-and-how-are-they-treated-161280">around 4%</a>.</p>
<p>This is a low risk of dying from a syndrome with a small likelihood of occurring. So we can express TTS risk in another way. </p>
<p>Two people in Australia have died from TTS after <a href="https://www.health.gov.au/ministers/the-hon-greg-hunt-mp/media/press-conference-in-canberra-on-17-june-2021-about-updated-atagi-covid-19-advice">3.8 million doses</a> of the AstraZeneca vaccine delivered. This makes the likelihood of dying from this syndrome about 0.5 in a million, or if you prefer whole numbers, about 1 in 2 million.</p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/a-balancing-act-between-benefits-and-risks-making-sense-of-the-latest-vaccine-news-158634">A balancing act between benefits and risks: making sense of the latest vaccine news</a>
</strong>
</em>
</p>
<hr>
<h2>And now, with graphics</h2>
<p>Here’s one way of representing 1 in 2 million visually. This figure shows just how small this risk is. Are you ready for some scrolling?</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/407164/original/file-20210618-30-szzxgt.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/407164/original/file-20210618-30-szzxgt.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=1466&fit=crop&dpr=1 600w, https://images.theconversation.com/files/407164/original/file-20210618-30-szzxgt.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=1466&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/407164/original/file-20210618-30-szzxgt.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=1466&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/407164/original/file-20210618-30-szzxgt.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1843&fit=crop&dpr=1 754w, https://images.theconversation.com/files/407164/original/file-20210618-30-szzxgt.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1843&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/407164/original/file-20210618-30-szzxgt.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1843&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>As you can see, the risk of TTS is so small it is almost too small to communicate effectively in this format.</p>
<p>Perhaps even more visually powerful is to compare the risk of dying from TTS to other risks we face in our lives, using a risk scale. This allows you to compare a range of risks and put them into perspective. </p>
<p>As the risk of TTS is a one-off risk normally associated with the first dose of the AstraZeneca vaccine, one interesting comparison is with other one-off risks, such as adventure sports.</p>
<hr>
<iframe src="https://flo.uri.sh/visualisation/6452610/embed" title="Interactive or visual content" class="flourish-embed-iframe" frameborder="0" scrolling="no" style="width:100%;height:550px;" sandbox="allow-same-origin allow-forms allow-scripts allow-downloads allow-popups allow-popups-to-escape-sandbox allow-top-navigation-by-user-activation" width="100%" height="400"></iframe>
<div style="width:100%!;margin-top:4px!important;text-align:right!important;"><a class="flourish-credit" href="https://public.flourish.studio/visualisation/6452610/?utm_source=embed&utm_campaign=visualisation/6452610" target="_top"><img alt="Made with Flourish" src="https://public.flourish.studio/resources/made_with_flourish.svg"> </a></div>
<hr>
<p>As you can see, the risk of dying from TTS is far lower than many activities some of us get up to at the weekend.</p>
<p>But not all of us spend our weekends scuba diving or rock climbing. So let’s look at the more common risks we take in our everyday lives but do not pay much attention to.</p>
<p>This is not a perfect comparison, as the risks are averaged across the whole population, across the entire year. But it’s useful nevertheless.</p>
<hr>
<iframe src="https://flo.uri.sh/visualisation/6451291/embed" title="Interactive or visual content" class="flourish-embed-iframe" frameborder="0" scrolling="no" style="width:100%;height:450px;" sandbox="allow-same-origin allow-forms allow-scripts allow-downloads allow-popups allow-popups-to-escape-sandbox allow-top-navigation-by-user-activation" width="100%" height="400"></iframe>
<div style="width:100%!;margin-top:4px!important;text-align:right!important;"><a class="flourish-credit" href="https://public.flourish.studio/visualisation/6451291/?utm_source=embed&utm_campaign=visualisation/6451291" target="_top"><img alt="Made with Flourish" src="https://public.flourish.studio/resources/made_with_flourish.svg"> </a></div>
<hr>
<p>So the risk of dying from TTS after the first dose of the AstraZeneca vaccine is similar to the risk of being killed by lightning in a year in Australia. And this pales in comparison when compared to other risks, such as the risk of dying in a car accident. </p>
<h2>So what happens next?</h2>
<p>One of the challenges for public health has always been putting the risks and benefits of our health choices into perspective. This task is even harder when the risks involved are so small.</p>
<p>Using visualisations like these is one way to effectively communicate just how small the risk of TTS is and also put this risk into perspective by comparing it to other risks we incur in our lives. </p>
<p>When you fully appreciate how small the risk of TTS is, the decision to have the AstraZeneca vaccine to protect yourself and others becomes a much easier one to make.</p><img src="https://counter.theconversation.com/content/162175/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Hassan Vally 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>Our brains cannot easily understand tiny risks so we tend to overestimate them. That’s when we need a little extra help to make the best decisions about our health.Hassan Vally, Associate Professor, La Trobe UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1521922020-12-18T15:15:39Z2020-12-18T15:15:39ZWhat children can teach governments about making graphs<figure><img src="https://images.theconversation.com/files/375637/original/file-20201217-19-15xd5b3.jpg?ixlib=rb-1.1.0&rect=0%2C0%2C5898%2C3998&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Kids know...</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/kid-write-graph-on-wall-by-303639425"> PathomP</a></span></figcaption></figure><p>Thanks to the COVID-19 pandemic, the year 2020 has been dominated by data. But with great amounts of data comes great responsibility to communicate it properly. Unfortunately, the accurate and clear communication of complex information has been an area where many have fallen short this year. The UK government in particular has been <a href="https://theconversation.com/next-slide-please-data-visualisation-expert-on-whats-wrong-with-the-uk-governments-coronavirus-charts-149329">criticised</a> for the graphs used in its coronavirus briefings.</p>
<p>How can we do better? Adults could learn a thing or two from children about how to make graphs that people can easily read and understand.</p>
<p>As part of <a href="https://mathsweekengland.co.uk">Maths Week England</a>, we challenged primary school children to create graphs about the things that were important to them. We received more than <a href="https://statsyss.wordpress.com/2020/11/06/check-out-our-chart-competition-for-maths-week-england-2020/">75 entries</a> of amazing charts relating to sport, sweets, toys, pets and almost everything in between. </p>
<p>Many of the graphs were so beautiful, colourful, and informative that we thought they could be used to teach media organisations and government bodies a few lessons about displaying data.</p>
<p>Here we present some of the children’s excellent examples to provide a list of dos and don'ts when it come to graph making.</p>
<h2>Do: label your axes and provide a scale</h2>
<p>The main purpose of a graph is to provide a clear, concise and accurate representation of your data. An important, but often overlooked, part of this is making sure that your graph actually tells your reader what they are looking at. Producing a graph without proper labels is a bit like building a car without an engine – it might look good, but it’s not going to get you anywhere.</p>
<p>Nine-year-old TaoHai used Lego to produce an excellent representation of the population of each of the world’s continents. The y-axis (vertical axis) is very easy to understand – each large check mark on this axis represents one billion people.</p>
<figure class="align-center ">
<img alt="Image of a lego graph of the world's population" src="https://images.theconversation.com/files/375635/original/file-20201217-17-4oq8y5.png?ixlib=rb-1.1.0&rect=93%2C76%2C840%2C640&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/375635/original/file-20201217-17-4oq8y5.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=460&fit=crop&dpr=1 600w, https://images.theconversation.com/files/375635/original/file-20201217-17-4oq8y5.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=460&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/375635/original/file-20201217-17-4oq8y5.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=460&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/375635/original/file-20201217-17-4oq8y5.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=578&fit=crop&dpr=1 754w, https://images.theconversation.com/files/375635/original/file-20201217-17-4oq8y5.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=578&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/375635/original/file-20201217-17-4oq8y5.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=578&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Tahoi, nine.</span>
<span class="attribution"><span class="source">Royal Statistical Society</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>In contrast, <a href="https://au.news.yahoo.com/boris-johnson-coronavirus-parliament-professor-covid19-170215230.html">the graph in this story</a> by the Press Association uses a line graph to display the number of global COVID-19 cases and deaths in which neither axis has a labelled scale, This makes it impossible to interpret the lines. Another issue with this plot is that it tries to put both cases and deaths on the same numerical scale, despite them being an order of magnitude apart.</p>
<h2>Don’t: hide the origin</h2>
<p>If you’re using a bar chart to compare a set of values which are quite close together, it can be tempting to start the numerical scale at a number other than zero in order to highlight their differences more clearly. However, this can often be misleading - making the numbers seem smaller than they actually are.</p>
<p>Farhan, aged eight, compared the speed of their favourite cars from the computer game “Asphalt 8”. The lowest speed is 290.1km/h, but they nonetheless opted to draw each of the bars from zero – ensuring that the relative differences in size can be compared fairly. </p>
<figure class="align-center ">
<img alt="Bar graphs representing speeds in a video game." src="https://images.theconversation.com/files/375482/original/file-20201216-17-1kkfhcf.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/375482/original/file-20201216-17-1kkfhcf.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=454&fit=crop&dpr=1 600w, https://images.theconversation.com/files/375482/original/file-20201216-17-1kkfhcf.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=454&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/375482/original/file-20201216-17-1kkfhcf.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=454&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/375482/original/file-20201216-17-1kkfhcf.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=570&fit=crop&dpr=1 754w, https://images.theconversation.com/files/375482/original/file-20201216-17-1kkfhcf.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=570&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/375482/original/file-20201216-17-1kkfhcf.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=570&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Farhan, eight.</span>
<span class="attribution"><span class="source">Royal Statistical Society</span>, <a class="license" href="http://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA</a></span>
</figcaption>
</figure>
<p>This is something several graphs relating to the pandemic has failed to do. For example, <a href="https://youtu.be/1-Fv2i2VoYs?t=543">the graph in this video from Balkan TV station N1</a> shows the proportions of mask-wearing in different regions of Croatia (mask wearers in blue). </p>
<p>At first glance, you might think that more than half of the people in each region do not wear masks, but when you look more closely at the actual figures provided, you realise that the scale on the x-axis has started at 75% rather than 0%.</p>
<figure class="align-center ">
<img alt="Image of a graph from the Balkan TV station N1." src="https://images.theconversation.com/files/375634/original/file-20201217-23-sbmmbr.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/375634/original/file-20201217-23-sbmmbr.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=352&fit=crop&dpr=1 600w, https://images.theconversation.com/files/375634/original/file-20201217-23-sbmmbr.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=352&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/375634/original/file-20201217-23-sbmmbr.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=352&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/375634/original/file-20201217-23-sbmmbr.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=442&fit=crop&dpr=1 754w, https://images.theconversation.com/files/375634/original/file-20201217-23-sbmmbr.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=442&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/375634/original/file-20201217-23-sbmmbr.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=442&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Confusing graph.</span>
<span class="attribution"><a class="source" href="https://www.youtube.com/watch?t=543&v=1-Fv2i2VoYs&feature=youtu.be">N1/youtube</a>, <a class="license" href="http://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA</a></span>
</figcaption>
</figure>
<p>This case is likely just a misguided attempt to differentiate between the regions, but many unscrupulous graph makers use this technique in order to deliberately mislead.</p>
<h2>Do: keep it simple</h2>
<p>The whole point of providing people with a graph is that it’s easier to digest than lots of big tables of numbers. A well-designed graph will allow the reader to glance at it and immediately understand the key take-home point. If your graph is too cluttered or provides too much information, then it’s going to confuse the reader.</p>
<p>Our school children did a good job of following this important rule. Most of the entries focused on presenting the count of a single variable, which left the reader in no doubt as to the main findings of their investigation. Holly, aged 10, raided the treat cupboard to count the frequency of each type of chocolate in a standard box of Celebrations. You can immediately tell that there are more Milky Ways than anything else.</p>
<figure class="align-center ">
<img alt="Bar graph using chocolate from a celebration box." src="https://images.theconversation.com/files/375452/original/file-20201216-15-1xs1fs8.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/375452/original/file-20201216-15-1xs1fs8.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=448&fit=crop&dpr=1 600w, https://images.theconversation.com/files/375452/original/file-20201216-15-1xs1fs8.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=448&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/375452/original/file-20201216-15-1xs1fs8.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=448&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/375452/original/file-20201216-15-1xs1fs8.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=563&fit=crop&dpr=1 754w, https://images.theconversation.com/files/375452/original/file-20201216-15-1xs1fs8.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=563&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/375452/original/file-20201216-15-1xs1fs8.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=563&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Holly, 10.</span>
<span class="attribution"><span class="source">Royal Statistical Society.</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>Compare this to the slide below from the English Chief Medical Officer’s press conference on October 31. There is an overload of information here – we’re being asked to compare positive test rates in nine different regions of England across five different age groups over 24 days.</p>
<p>This plot also breaches another golden rule of presenting data by having a series of numbers on the graph which are too small to read.</p>
<figure class="align-center ">
<img alt="Image of confusing graphs from the UK government.." src="https://images.theconversation.com/files/375450/original/file-20201216-13-wk18qv.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/375450/original/file-20201216-13-wk18qv.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=349&fit=crop&dpr=1 600w, https://images.theconversation.com/files/375450/original/file-20201216-13-wk18qv.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=349&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/375450/original/file-20201216-13-wk18qv.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=349&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/375450/original/file-20201216-13-wk18qv.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=438&fit=crop&dpr=1 754w, https://images.theconversation.com/files/375450/original/file-20201216-13-wk18qv.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=438&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/375450/original/file-20201216-13-wk18qv.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=438&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Graph from UK government briefing.</span>
<span class="attribution"><span class="source">UK government/COBR</span>, <a class="license" href="http://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA</a></span>
</figcaption>
</figure>
<h2>Don’t try to reinvent the wheel…</h2>
<p>When statistics is taught at school, we tend to focus on tried and tested data visualisation techniques such as bar graphs, line graphs and pie charts. These classical methods are popular and have stood the test of time for a reason – they’re clear, simple to produce and easy to understand. Of course, there is always room for innovation.</p>
<p>Professional statisticians tend not to recommend pie charts much in general because they can tend to lead to <a href="https://www.data-to-viz.com/caveat/pie.html">less exact interpretations</a> compared to a bar chart. But we will make an exception for nine year-old Elise, who took the concept of a pie chart literally to display their friends’ and family’s favourite types of jam.</p>
<figure class="align-center ">
<img alt="A pie chart that's actually a pie." src="https://images.theconversation.com/files/375448/original/file-20201216-19-yqrium.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/375448/original/file-20201216-19-yqrium.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=331&fit=crop&dpr=1 600w, https://images.theconversation.com/files/375448/original/file-20201216-19-yqrium.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=331&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/375448/original/file-20201216-19-yqrium.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=331&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/375448/original/file-20201216-19-yqrium.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=416&fit=crop&dpr=1 754w, https://images.theconversation.com/files/375448/original/file-20201216-19-yqrium.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=416&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/375448/original/file-20201216-19-yqrium.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=416&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Elsie, nine.</span>
<span class="attribution"><span class="source">Royal Statistical Society</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>The main reason the pie chart worked is that it was still straightforward to understand the information being conveyed. That isn’t always the case though, as we can see from <a href="https://www.bbc.co.uk/news/resources/idt-7464500a-6368-4029-aa41-ab94e0ee09fb">this BBC visualisation</a>, which tries to use an animated flower to count COVID-19 deaths. </p>
<h2>…but rules exist to be broken</h2>
<p>Ultimately, however, each individual graph is judged on its own merits, and sometimes you can break some of the rules and still produce something fantastic. </p>
<p>Our competition winner was 10-year-old Lola, who constructed a wonderful 3D infographic displaying her daily exercise over a five-day period. </p>
<figure class="align-center ">
<img alt="3D image of exercise habits." src="https://images.theconversation.com/files/375446/original/file-20201216-19-91k5ct.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/375446/original/file-20201216-19-91k5ct.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=462&fit=crop&dpr=1 600w, https://images.theconversation.com/files/375446/original/file-20201216-19-91k5ct.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=462&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/375446/original/file-20201216-19-91k5ct.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=462&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/375446/original/file-20201216-19-91k5ct.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=580&fit=crop&dpr=1 754w, https://images.theconversation.com/files/375446/original/file-20201216-19-91k5ct.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=580&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/375446/original/file-20201216-19-91k5ct.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=580&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Lola, 10.</span>
<span class="attribution"><span class="source">Royal Statistical Society</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>The beauty of this entry is that it is both simple and complex simultaneously – the lollipop sticks provide a straightforward representation of steps and exercise time, but for those who want to dig deeper, the actual data is also included elsewhere.</p>
<p><em>Acknowledegements: We would like to provide a massive thank you to all the children who participated.</em></p><img src="https://counter.theconversation.com/content/152192/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Emily Granger is supported by the Medical Research Council. </span></em></p><p class="fine-print"><em><span>Lucy Teece is supported by the UK National Institute for Health Research (NIHR) Applied Research Collaboration East Midlands (ARC EM).</span></em></p><p class="fine-print"><em><span>Craig Anderson and Maria Dunbar do not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>There have been some shockingly bad graphs circulating during the pandemic.Craig Anderson, Lecturer in Statistics, University of GlasgowEmily Granger, Research Fellow in Medical Statistics, London School of Hygiene & Tropical MedicineLucy Teece, Research Fellow in Medical Statistics, University of LeicesterMaria Dunbar, PhD candidate in Statistics, University of ZurichLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1413482020-07-24T12:22:49Z2020-07-24T12:22:49Z3 questions to ask yourself next time you see a graph, chart or map<figure><img src="https://images.theconversation.com/files/349233/original/file-20200723-23-1c9tv31.jpg?ixlib=rb-1.1.0&rect=167%2C5%2C3464%2C2454&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">White House Coronavirus Task Force members reference a misleading chart in a press briefing.</span> <span class="attribution"><a class="source" href="http://www.apimages.com/metadata/Index/Virus-Outbreak-Trump/f2c5f8d116a24062b563a32cea88235e/1/0">AP Photo/Alex Brandon</a></span></figcaption></figure><p>Since the days of painting on cave walls, people have been representing information through figures and images. Nowadays, data visualization experts know that <a href="https://www.forbes.com/sites/evamurray/2019/01/28/how-data-visualization-supports-communication">presenting information visually</a> <a href="https://ed.ted.com/lessons/david-mccandless-the-beauty-of-data-visualization">helps people better understand</a> <a href="https://doi.org/10.1016/j.envsoft.2010.12.006">complicated data</a>. The problem is that data visualizations can also leave you with the wrong idea – whether the images are sloppily made or intentionally misleading. </p>
<p>Take for example the bar graph presented at an <a href="https://www.c-span.org/video/?470990-1/president-trump-coronavirus-task-force-briefing">April 6 press briefing</a> by members of the White House Coronavirus Task Force. It’s titled “COVID-19 testing in the U.S.” and illustrates almost 2 million coronavirus tests completed up to that point. President Trump used the graph to support his assertion that testing was “<a href="https://www.whitehouse.gov/briefings-statements/remarks-president-trump-vice-president-pence-members-coronavirus-task-force-press-briefing-21/">going up at a rapid rate</a>.” Based on this graphic many viewers likely took away the same conclusion – but it is incorrect.</p>
<p>The graph shows the total cumulative number of tests performed over months, not the number of new tests each day.</p>
<p><iframe id="pG025" class="tc-infographic-datawrapper" src="https://datawrapper.dwcdn.net/pG025/2/" height="400px" width="100%" style="border: none" frameborder="0"></iframe></p>
<p>When you graph the number of new tests by date, you can see the number of COVID-19 tests performed between March and April did increase through time, but not rapidly. This instance is one of many when important information was not properly understood or well communicated.</p>
<p>As a <a href="https://scholar.google.com/citations?user=T7vRKkQAAAAJ&hl=en">researcher of hazard and risk communication</a>, I think a lot about how people interpret the charts, graphs <a href="https://doi.org/10.1016/j.ijdrr.2020.101487">and maps</a> they encounter daily.</p>
<p>Whether they show COVID-19 cases, global warming trends, high-risk tsunami zones, or utility usage, being able to correctly assess and interpret figures allows you to make informed decisions. Unfortunately, not all figures are created equal.</p>
<p>If you can spot a figure’s pitfalls you can avoid the bad ones. Consider the following three key questions the next time you see a graph, map or other data visual so you can confidently decide what to do with that new nugget of information.</p>
<h2>What is this figure trying to tell me?</h2>
<p>Start by reading the title, looking at the labels and checking the caption. If these are not available – be very wary. Labels will be on the horizontal and vertical axes on graphs or in a legend on maps. People often overlook them, but this information is crucial for putting everything you see in the visualization into context.</p>
<p>Look at the units of measure – are they in days or years, Celsius or Fahrenheit, counts, age, or what? Are they evenly spaced along the axis? Many of the recent COVID-19 cumulative case graphs use a logarithmic scale, where the the intervals along the vertical axis are not equally spaced. <a href="https://www.youtube.com/watch?v=O-3Mlj3MQ_Q">This creates confusion for people</a> unfamiliar with this format.</p>
<iframe width="100%" height="315" src="https://www.msnbc.com/msnbc/embedded-video/mmvo80534597724" scrolling="no" frameborder="0" allowfullscreen=""></iframe>
<figure><figcaption><span class="caption">A March 12 broadcast of ‘The Rachel Maddow Show’ included a graph with unlabeled numbers and a tricky horizontal axis.</span></figcaption></figure>
<p>For instance, a graph from “<a href="https://www.msnbc.com/rachel-maddow/watch/u-s-unprepared-for-expected-explosion-in-coronavirus-cases-80534597724?cid=sm_fb_maddow">The Rachel Maddow Show” on MSNBC</a>, showed coronavirus cases in the United States between Jan. 21 and March 11. The x-axis units on the horizontal are time (in a month-day format) and the y-axis units on the vertical are presumably cumulative case counts, though it does not specify.</p>
<p>The main issue with this graph is that the time periods between consecutive dates are uneven.</p>
<p><iframe id="yzUp1" class="tc-infographic-datawrapper" src="https://datawrapper.dwcdn.net/yzUp1/5/" height="400px" width="100%" style="border: none" frameborder="0"></iframe></p>
<p>In a revised graph, with dates properly spaced through time, and coronavirus diagnoses plotted as a line graph, you can see more clearly what <a href="https://theconversation.com/coronavirus-cases-are-growing-exponentially-heres-what-that-means-135181">exponential growth</a> in the rate of infection really looks like. It took the first 30 days to add 33 cases, but only the last four to add 584 cases.</p>
<p>What may seem like a slight difference could help people understand how quickly exponential growth can go sky high and maybe change how they perceive the importance of curbing it.</p>
<h2>How are color, shape, size and perspective used?</h2>
<p><a href="https://eos.org/features/visualizing-science-how-color-determines-what-we-see">Color plays an important role</a> in how people interpret information. Color choices can make you notice particular patterns or draw your eye to certain aspects of a graphic.</p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/349252/original/file-20200723-23-wgpj48.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/349252/original/file-20200723-23-wgpj48.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=196&fit=crop&dpr=1 600w, https://images.theconversation.com/files/349252/original/file-20200723-23-wgpj48.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=196&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/349252/original/file-20200723-23-wgpj48.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=196&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/349252/original/file-20200723-23-wgpj48.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=246&fit=crop&dpr=1 754w, https://images.theconversation.com/files/349252/original/file-20200723-23-wgpj48.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=246&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/349252/original/file-20200723-23-wgpj48.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=246&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">Oregon landslide susceptibility.</span>
<span class="attribution"><span class="source">Oregon Department of Geology and Mineral Industries</span></span>
</figcaption>
</figure>
<p>Consider two maps depicting landslide susceptibility, which are exactly the same except for reversed color schemes. Your eye may be be drawn to darker shades, intuitively seeing those areas as at higher risk. After looking at the legend, which color order do you think best represents the information? By paying attention to <a href="https://www.khanacademy.org/humanities/hass-storytelling/storytelling-pixar-in-a-box/ah-piab-visual-language/v/color-visual">how color is used</a>, you can better understand how it influences what stands out to you and what you perceive.</p>
<p>Shape, size and orientation of features can also influence <a href="https://doi.org/10.1111/j.1756-8765.2011.01150.x">how you interpret a figure</a>. </p>
<figure class="align-right zoomable">
<a href="https://images.theconversation.com/files/348978/original/file-20200722-32-o99maq.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="confusing pie chart of employment data" src="https://images.theconversation.com/files/348978/original/file-20200722-32-o99maq.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/348978/original/file-20200722-32-o99maq.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=608&fit=crop&dpr=1 600w, https://images.theconversation.com/files/348978/original/file-20200722-32-o99maq.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=608&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/348978/original/file-20200722-32-o99maq.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=608&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/348978/original/file-20200722-32-o99maq.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=764&fit=crop&dpr=1 754w, https://images.theconversation.com/files/348978/original/file-20200722-32-o99maq.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=764&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/348978/original/file-20200722-32-o99maq.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=764&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">What industries employ Coloradans?</span>
<span class="attribution"><a class="source" href="https://dossier.ink-live.com/html5/reader/production/default.aspx?pubname=&edid=5f3a495a-fdef-463f-b826-6b92609f04c5">Hemispheres</a></span>
</figcaption>
</figure>
<p>Pie charts, like this one showing employment breakdown for a region, are notoriously difficult to parse. Notice how hard it is to pull out which employment category is highest or how they rank. The pie chart’s wedges are not organized by size, there are too many categories (11!), the 3D perspective distorts the wedge sizes, and some wedges are separate from others making size comparisons almost impossible.</p>
<p><iframe id="yCDTo" class="tc-infographic-datawrapper" src="https://datawrapper.dwcdn.net/yCDTo/2/" height="400px" width="100%" style="border: none" frameborder="0"></iframe></p>
<p>A bar chart is a better option for an informative display and helps show which industries people are employed in.</p>
<h2>Where do the data come from?</h2>
<figure class="align-right zoomable">
<a href="https://images.theconversation.com/files/345601/original/file-20200703-33935-elrvg1.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="screen shot of Twitter poll about Trump's performance" src="https://images.theconversation.com/files/345601/original/file-20200703-33935-elrvg1.png?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/345601/original/file-20200703-33935-elrvg1.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=361&fit=crop&dpr=1 600w, https://images.theconversation.com/files/345601/original/file-20200703-33935-elrvg1.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=361&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/345601/original/file-20200703-33935-elrvg1.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=361&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/345601/original/file-20200703-33935-elrvg1.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=453&fit=crop&dpr=1 754w, https://images.theconversation.com/files/345601/original/file-20200703-33935-elrvg1.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=453&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/345601/original/file-20200703-33935-elrvg1.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=453&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Survey posted on ‘Lou Dobbs Tonight,’ requesting viewers vote on Twitter about Trump’s performance.</span>
<span class="attribution"><a class="source" href="https://www.mediaite.com/tv/lou-dobbs-invites-viewers-to-vote-on-trumps-coronavirus-leadership-superb-great-or-very-good/">Fox Business Network</a></span>
</figcaption>
</figure>
<p>The source of data matters in terms of quality and reliability. This is especially true for partisan or politicized data. If the data are collected from a group that isn’t a good approximation of the population as a whole, then it may be biased.</p>
<p>For example, on March 18, Fox Business Network host Lou Dobbs polled his audience with the question “How would you grade President Trump’s leadership in the nation’s fight against the Wuhan Virus?” </p>
<p><div data-react-class="Tweet" data-react-props="{"tweetId":"1240421216692961284"}"></div></p>
<p>Imagine if only Republicans were asked this question and how the results would compare if only Democrats were asked. In this case, respondents were part of a self-selecting group who already chose to watch Dobbs’ show. The poll can only tell you about that group’s opinions, not people in the U.S. generally, for instance.</p>
<p>[<em>Get facts about coronavirus and the latest research.</em> <a href="https://theconversation.com/us/newsletters/the-daily-3?utm_source=TCUS&utm_medium=inline-link&utm_campaign=newsletter-text&utm_content=coronavirus-facts">Sign up for The Conversation’s newsletter.</a>]</p>
<p>Then consider that Dobbs provided only positive responses in his multiple choice options – “superb, great or very good” – and it is clear that this data has a bias.</p>
<p>Spotting bias and improper data collection methods allows you to decide which information is trustworthy. </p>
<h2>Think through what you see</h2>
<p>During this pandemic, information is emerging hour by hour. Media consumers are inundated with facts, charts, graphs and maps every day. If you can take a moment to ask yourself a few questions about what you see in these data visualizations, you may walk away with a completely different conclusion than you might have had at first glance.</p><img src="https://counter.theconversation.com/content/141348/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Carson MacPherson-Krutsky receives funding from The National Science Foundation. She is the co-owner of HazardReady, LLC. </span></em></p>Visualizations can help you understand data better – but they can also confuse or mislead. Here, some tips on what to watch out for.Carson MacPherson-Krutsky, PhD Candidate in Geosciences, Boise State UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1356982020-04-16T23:05:12Z2020-04-16T23:05:12ZMore testing will give us a better picture of the coronavirus spread and its slowdown<p><a href="https://7news.com.au/lifestyle/health-wellbeing/coronavirus-australia-infection-rate-continues-to-decline-as-australia-ponders-exit-strategy-c-979164">Many states</a> are <a href="https://www.abc.net.au/news/2020-04-15/sa-broadens-coronavirus-testing-with-two-week-covid-blitz/12150524">now</a> <a href="https://www.abc.net.au/news/2020-04-14/victoria-expands-coronavirus-testing-criteria/12146166">ramping up the number of tests</a> by relaxing the criteria for who can get tested for COVID-19. This should give us a better idea of whether the spread is easing or getting worse.</p>
<p>We get regular updates about COVID-19 with lots of data, figures and graphs with some interpretations to see if we are flattening the curve on the number of new cases.</p>
<p>But most of these are based on using only the total or the daily number of confirmed new cases. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/how-much-has-australia-really-flattened-the-curve-of-coronavirus-until-we-keep-better-records-we-dont-know-136252">How much has Australia really flattened the curve of coronavirus? Until we keep better records, we don't know</a>
</strong>
</em>
</p>
<hr>
<p>This does not provide enough information about whether the situation is improving, stabilising or getting worse. That is why we also need to consider the number of people tested daily for COVID-19.</p>
<p>For example, in percentage terms there is no actual difference between getting 20 positive cases out of 1,000 tests one day and 100 positive cases out of 5,000 tests the next. Both lead to the conclusion we have 2% reported infected people of those tested.</p>
<p>If we are only given the number of new cases, getting 100 in a day sounds a lot worse than getting 20. The 2% percentage figure here tells us things are pretty much the same over the two days.</p>
<h2>Curves and trends</h2>
<p>Take Victoria, if we look at the total number of confirmed cases we see it followed an exponential trend for a while – one that was increasingly rising – and then started to divert on April 3.</p>
<hr>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/328279/original/file-20200416-140745-urr91b.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/328279/original/file-20200416-140745-urr91b.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/328279/original/file-20200416-140745-urr91b.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=558&fit=crop&dpr=1 600w, https://images.theconversation.com/files/328279/original/file-20200416-140745-urr91b.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=558&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/328279/original/file-20200416-140745-urr91b.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=558&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/328279/original/file-20200416-140745-urr91b.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=701&fit=crop&dpr=1 754w, https://images.theconversation.com/files/328279/original/file-20200416-140745-urr91b.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=701&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/328279/original/file-20200416-140745-urr91b.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=701&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption"></span>
<span class="attribution"><span class="source">The Conversation</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<hr>
<p>In the daily number of confirmed cases we see high jumps and large fluctuations going back and forth.</p>
<hr>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/328281/original/file-20200416-140719-npy0fk.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/328281/original/file-20200416-140719-npy0fk.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/328281/original/file-20200416-140719-npy0fk.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=527&fit=crop&dpr=1 600w, https://images.theconversation.com/files/328281/original/file-20200416-140719-npy0fk.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=527&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/328281/original/file-20200416-140719-npy0fk.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=527&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/328281/original/file-20200416-140719-npy0fk.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=662&fit=crop&dpr=1 754w, https://images.theconversation.com/files/328281/original/file-20200416-140719-npy0fk.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=662&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/328281/original/file-20200416-140719-npy0fk.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=662&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption"></span>
<span class="attribution"><span class="source">The Conversation</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<hr>
<p>When the daily number of applied tests is considered, we can calculate the actual percentage of new cases each day. Now we have a way flatter curve (below) with different fluctuations.</p>
<hr>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/328284/original/file-20200416-140729-sfncn1.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/328284/original/file-20200416-140729-sfncn1.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/328284/original/file-20200416-140729-sfncn1.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=838&fit=crop&dpr=1 600w, https://images.theconversation.com/files/328284/original/file-20200416-140729-sfncn1.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=838&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/328284/original/file-20200416-140729-sfncn1.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=838&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/328284/original/file-20200416-140729-sfncn1.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=1054&fit=crop&dpr=1 754w, https://images.theconversation.com/files/328284/original/file-20200416-140729-sfncn1.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=1054&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/328284/original/file-20200416-140729-sfncn1.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=1054&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption"></span>
<span class="attribution"><span class="source">The Conversation</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<hr>
<p>The peak is now on March 24 when the number of tests is included. If we just look at the daily count, the highest number of confirmed cases was on March 27. When we look at the percentage, it shows a decrease rather than an increase with more than 2,300 tests.</p>
<p>From the daily new cases data it looks like there is a strongly decreasing trend in the number of confirmed cases between April 2 and 6. </p>
<p>But we do not see the same strong downward movement in the percentage data on the number of tests. Although both figures go down, then up slightly, the percentage trend downward is not as strong as the daily trend.</p>
<p>This is a good example of the discrepancy between the inferences from the raw and percentage data. When we consider the number of tested people, we get a different view on the progress of the pandemic.</p>
<h2>More tests needed</h2>
<p>In using the number of tests to get a more reliable picture of the situation, there is an important point to consider. That’s were the purple error bars in the graph (above) come in.</p>
<p>They show the margin of error where each percentage estimate swings for the daily number of applied tests, so the actual number could be higher or lower but within those purple bars.</p>
<p>When we have a larger number of applied tests, we get a reduced margin of error, and that gives us a clearer picture of what is happening. </p>
<hr>
<p>
<em>
<strong>
Read more:
<a href="https://theconversation.com/even-in-a-pandemic-continue-with-routine-health-care-and-dont-ignore-a-medical-emergency-136246">Even in a pandemic, continue with routine health care and don't ignore a medical emergency</a>
</strong>
</em>
</p>
<hr>
<p>Since the peak on March 24 is backed up by only 500 tests, it has the largest margin of error. The figure on March 28 is based on 8,900 tests with a very small amount of error. </p>
<p>To get a more reliable picture of the situation, the number of applied tests has to be expanded, which it is what is happening in some states. This should reduce the margin of error.</p>
<h2>Out in the community</h2>
<p>After getting some signals of flattening the curve in <a href="https://www.theage.com.au/national/victoria/wonderful-success-optimism-that-victoria-has-started-to-flatten-the-curve-20200405-p54h9v.html">Victoria</a> and <a href="https://www.theguardian.com/world/2020/apr/05/health-officials-hopeful-australia-is-flattening-coronavirus-curve-but-warn-against-complacency">Australia</a> as well, do we see an exponential increase in just the community transmission? </p>
<p>Community transmission is where someone has caught the virus locally, not an infected traveller who’s returned from a cruise or overseas. At the moment they are <a href="https://www.health.gov.au/news/health-alerts/novel-coronavirus-2019-ncov-health-alert/coronavirus-covid-19-current-situation-and-case-numbers">the minority of cases</a> and authorities would like it to stay that way to <a href="https://www.abc.net.au/news/2020-04-11/what-is-community-transmission-of-coronavirus-covid-19/12142638">contain the spread of the virus</a>.</p>
<p>Again, we need to consider the number of tests to answer this question clearly. The raw numbers of community transmission in Victoria looked like they were increasing exponentially.</p>
<hr>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/328296/original/file-20200416-140741-12r4ldn.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/328296/original/file-20200416-140741-12r4ldn.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/328296/original/file-20200416-140741-12r4ldn.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=453&fit=crop&dpr=1 600w, https://images.theconversation.com/files/328296/original/file-20200416-140741-12r4ldn.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=453&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/328296/original/file-20200416-140741-12r4ldn.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=453&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/328296/original/file-20200416-140741-12r4ldn.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=569&fit=crop&dpr=1 754w, https://images.theconversation.com/files/328296/original/file-20200416-140741-12r4ldn.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=569&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/328296/original/file-20200416-140741-12r4ldn.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=569&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption"></span>
<span class="attribution"><span class="source">The Conversation</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<hr>
<p>But the numbers as a percentage of the number tested tell a different story. Although there is some increase in the rate of community transmissions recently, it still shows a way flatter behaviour far from the exponential curve.</p>
<hr>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/328287/original/file-20200416-140735-15sxjj3.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/328287/original/file-20200416-140735-15sxjj3.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/328287/original/file-20200416-140735-15sxjj3.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=514&fit=crop&dpr=1 600w, https://images.theconversation.com/files/328287/original/file-20200416-140735-15sxjj3.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=514&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/328287/original/file-20200416-140735-15sxjj3.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=514&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/328287/original/file-20200416-140735-15sxjj3.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=646&fit=crop&dpr=1 754w, https://images.theconversation.com/files/328287/original/file-20200416-140735-15sxjj3.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=646&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/328287/original/file-20200416-140735-15sxjj3.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=646&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption"></span>
<span class="attribution"><span class="source">The Conversation</span>, <a class="license" href="http://creativecommons.org/licenses/by-nd/4.0/">CC BY-ND</a></span>
</figcaption>
</figure>
<hr>
<p>That is why it is important to understand the impact of the number of tests on the figures displaying the progress of the pandemic. Understanding this relationship could reassure people about new numbers.</p><img src="https://counter.theconversation.com/content/135698/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Haydar Demirhan does not work for, consult, own shares in or receive funding from any company or organisation that would benefit from this article, and has disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Don’t just tell us how many new cases of COVID-19 have been confirmed, tell us how many people you tested as well. That helps us to know if things are getting better or worse.Haydar Demirhan, Senior Lecturer in Analytics, RMIT UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/1357562020-04-07T10:31:27Z2020-04-07T10:31:27ZThree graphs that show a global slowdown in COVID-19 deaths<figure><img src="https://images.theconversation.com/files/326222/original/file-20200407-36858-pa4svp.jpg?ixlib=rb-1.1.0&rect=95%2C2%2C710%2C424&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">
</span> <span class="attribution"><span class="source">Danny Dorling. Illustration by Kirsten McClure</span>, <span class="license">Author provided</span></span></figcaption></figure><p>Almost as soon as the COVID-19 pandemic began, graphs and many other visualisations charting the rise of the virus started to multiply. Many show the cumulative number of deaths attributed to the virus. This number, of course, will always rise, but will also – eventually – plateau. A cumulative total can never fall.</p>
<p>Other <a href="https://www.worldometers.info/coronavirus/coronavirus-cases/#daily-cases">published graphs</a> have shown the number of deaths reported each day for various countries. These are more useful, but the reader is still left trying to discern the extent to which the rise from one day to the next is larger or smaller.</p>
<p>The graph below is different. It shows both the number of deaths each day and the rate of change in that number. Most importantly, it uses smoothed data – a moving average from the day before to the day after each date shown. This method of showing change is explored in my forthcoming book, <a href="http://www.dannydorling.org/books/SLOWDOWN/">Slowdown</a>, which I worked on with illustrator Kirsten McClure who turned my crude Excel graphs into clearer visuals. It’s a useful way to look at data when it is <a href="http://www.dannydorling.org/books/SLOWDOWN/Animations.html">change that is of the greatest interest</a>.</p>
<p>The first graph (below) shows the rise in mortality in seven countries up until Thursday, April 2, 2020. At that point, the number of deaths was still rising every day in the US, France and the UK. The increases in mortality had begun to slow in Spain and Italy. Germany and China were reporting far lower numbers of deaths.</p>
<p><strong>Mortality in seven countries attributed to COVID-19 (January 23 to April 2, 2020).</strong></p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/326025/original/file-20200407-31007-dits9d.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/326025/original/file-20200407-31007-dits9d.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/326025/original/file-20200407-31007-dits9d.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=370&fit=crop&dpr=1 600w, https://images.theconversation.com/files/326025/original/file-20200407-31007-dits9d.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=370&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/326025/original/file-20200407-31007-dits9d.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=370&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/326025/original/file-20200407-31007-dits9d.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=464&fit=crop&dpr=1 754w, https://images.theconversation.com/files/326025/original/file-20200407-31007-dits9d.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=464&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/326025/original/file-20200407-31007-dits9d.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=464&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption"></span>
<span class="attribution"><span class="source">Danny Dorling/Kirsten McClure</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>The picture began to change very markedly on Friday, April 3 and Saturday, April 4. As the graph below shows, the number of deaths in the US stayed the same (when smoothed). France was now reporting falling mortality, as was Spain and Italy. So too, for the first time, was the UK. The three-day smoothed daily number of deaths in Germany was also now falling. The graph is worth interpreting in the light of when the various national lockdowns began.</p>
<p><strong>Mortality in seven countries attributed to COVID-19 (January 23 to April 4, 2020).</strong></p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/326026/original/file-20200407-18916-1tzb4wb.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/326026/original/file-20200407-18916-1tzb4wb.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/326026/original/file-20200407-18916-1tzb4wb.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=366&fit=crop&dpr=1 600w, https://images.theconversation.com/files/326026/original/file-20200407-18916-1tzb4wb.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=366&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/326026/original/file-20200407-18916-1tzb4wb.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=366&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/326026/original/file-20200407-18916-1tzb4wb.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=460&fit=crop&dpr=1 754w, https://images.theconversation.com/files/326026/original/file-20200407-18916-1tzb4wb.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=460&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/326026/original/file-20200407-18916-1tzb4wb.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=460&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption"></span>
<span class="attribution"><span class="source">Danny Dorling/Kirsten McClure</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>It is worth emphasising that both graphs above show a smoothed estimate of the number of deaths occurring on each day. This estimate is made by working out a three-day moving average of the number of deaths and it is shown on the vertical axis. The horizontal axis of the graph then shows the rate of change in that measure. Once a curve crosses to the left of the central axis, the number of deaths is falling. As I write, the number is not yet falling in the US, but it is about to.</p>
<p>When that graph was drawn just two days earlier, the picture it showed was less optimistic for France and the US, although even by April 2 it was evident that they too were swinging leftwards.</p>
<h2>Reliability of the numbers</h2>
<p>The numbers that are reported each day cannot be terribly reliable. For example, the daily tally of deaths are not those that have actually happened in the last 24-hour period, <a href="https://www.theguardian.com/world/2020/apr/04/why-what-we-think-we-know-about-the-uks-coronavirus-death-toll-is-wrong">but rather the deaths that were reported in that period</a>. In the early days of the pandemic, there were concerns about lower numbers being reported on Sundays as deaths then were not registered until Monday. Because of <a href="https://www.prospectmagazine.co.uk/politics/what-is-austerity-marmot-report-deaths-uk">spending cuts</a>, over the course of the past two decades in the UK <a href="https://www.ons.gov.uk/peoplepopulationandcommunity/birthsdeathsandmarriages/deaths/articles/impactofregistrationdelaysonmortalitystatisticsinenglandandwales/2018">there was an increase</a> “in the median delay between occurrence and registration for deaths registered by a coroner from five days in 2001 to 18 days in 2018”.</p>
<p>In recent weeks, the registration of deaths has hopefully been faster than this; but additionally, the definition of what a death associated with COVID-19 is, has changed over the preceding weeks. The sources of data, however, tend to be very similar, including <a href="https://github.com/CSSEGISandData/COVID-19/blob/master/csse_covid_19_data/csse_covid_19_time_series/time_series_covid19_deaths_global.csv">the data used here</a>.</p>
<p>Because the numbers of deaths that have occurred in China <a href="https://theconversation.com/coronavirus-why-is-germanys-fatality-rate-so-low-135496">and Germany</a> are so much lower than in other countries, the graph below highlights this data. Mortality began to fall in China by February 14 and in Germany by April 2. However, wherever mortality falls it can rise again, as is shown by the various loops in China.</p>
<p><strong>Mortality in China and Germany attributed to COVID-19 (January 23 to April 4, 2020)</strong></p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/326027/original/file-20200407-110267-5g3bsv.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/326027/original/file-20200407-110267-5g3bsv.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/326027/original/file-20200407-110267-5g3bsv.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=389&fit=crop&dpr=1 600w, https://images.theconversation.com/files/326027/original/file-20200407-110267-5g3bsv.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=389&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/326027/original/file-20200407-110267-5g3bsv.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=389&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/326027/original/file-20200407-110267-5g3bsv.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=488&fit=crop&dpr=1 754w, https://images.theconversation.com/files/326027/original/file-20200407-110267-5g3bsv.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=488&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/326027/original/file-20200407-110267-5g3bsv.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=488&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption"></span>
<span class="attribution"><span class="source">Danny Dorling/Kirsten McClure</span>, <span class="license">Author provided</span></span>
</figcaption>
</figure>
<p>While all the graphs above show that the rise in the number of deaths per day from COVID-19 may be abruptly slowing, they don’t confirm that this trend will continue. It has almost certainly been the social distancing measures put in place that have resulted in each of these seven trends altering as and when they did.</p>
<p>As modellers know all too well, the number of cases could conceivably rise again – and China appears to be the only country that has so far fully brought the novel coronavirus under control. On April 6, for the first time since January 2020, China <a href="https://www.theguardian.com/world/2020/apr/07/china-reports-zero-daily-deaths-from-coronavirus-for-the-first-time-since-january">reported</a> no new COVID-19 deaths.</p><img src="https://counter.theconversation.com/content/135756/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>Danny Dorling 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>These graphs reveal something you may have not seen illustrated before.Danny Dorling, Halford Mackinder Professor of Geography, University of OxfordLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/886212017-12-21T14:19:52Z2017-12-21T14:19:52ZFrom internet trolls to college dropouts: Our 6 favorite charts from 2017<figure><img src="https://images.theconversation.com/files/199289/original/file-20171214-27597-7qg88l.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Where we've been in 2017.</span> <span class="attribution"><a class="source" href="https://www.shutterstock.com/image-photo/destinations-pinned-on-map-761527345?src=73Ra-hKwDpnPnLaTs6-6rw-1-18">rawpixel.com/shutterstock.com</a></span></figcaption></figure><p><em>Editor’s Note: As the year comes to an end, we rounded up some of our favorite graphs and maps from archival articles The Conversation published in 2017.</em></p>
<h2>1. Invisible inequality</h2>
<p>America may be getting richer, but who’s reaping the reward? The economic gap in the U.S. has widened over the past few decades. Today, the top 10 percent of U.S. households control over three-quarters of the country’s wealth.</p>
<p>But as inequality gets worse, something curious happens: <a href="https://theconversation.com/inequality-is-getting-worse-but-fewer-people-than-ever-are-aware-of-it-76642">More and more people think that they actually live in a meritocracy</a>.</p>
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<p>“People on either side of the income divide cannot see the breadth of the gap that separates their lives from those of others,” explains Jonathan J.B. Mijs at Harvard University. “As the gap grows wider, other people’s lives are harder to view. Rising inequality prevents people from seeing its full extent.”</p>
<h2>2. Don’t ditch the degree</h2>
<p>What do Steve Jobs, Bill Gates and Mark Zuckerberg have in common? They’re all massively successful tech icons – and they all dropped out of college. </p>
<p>Dropping out is a well-worn trope in modern stories of business success. But a study of 11,745 U.S. leaders shows that <a href="https://theconversation.com/the-myth-of-the-college-dropout-75760">dropouts like Zuckerberg are outliers</a>. Ninety-four percent of the leaders attended college, about half at an elite school like Princeton. </p>
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<p>“Perhaps in the future, college may not be as important to employers,” write the researchers at Duke University and Chemnitz University of Technology. “But for now, college dropouts who rule the world are rare exceptions – not the rule.”</p>
<h2>3. Hollywood’s diversity problem</h2>
<p>Hollywood has fielded criticism in recent years for a lack of diversity on the silver screen. In 2016, 7 in 10 speaking roles <a href="http://variety.com/2017/film/news/hollywood-diversity-little-rise-study-1202510809/">went to white actors</a>. </p>
<p>What’s more, a study of over 800 top movies suggests that the best earners at the domestic and international box offices tend to have white leads and majority-white casts. </p>
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<p>Roberto Pedace at Scripps College suggests that studios may be pandering to prejudiced consumers, as <a href="https://theconversation.com/why-arent-hollywood-films-more-diverse-the-international-box-office-might-be-to-blame-86905">movies with diverse casts can struggle abroad</a>: “The revenue implications of international audience preferences are simply too large for studios to ignore.” </p>
<h2>4. Big business in the Big House</h2>
<p>The number of prisons in the U.S. has more than tripled since 1970. Roughly 70 percent have been built in rural communities – largely in southern states like Florida, Georgia, Oklahoma and Texas. </p>
<p><img width="100%" src="https://media.giphy.com/media/xUOxfaTdBpycKlYYP6/giphy.gif"></p>
<p>Prisons can be <a href="https://theconversation.com/why-prison-building-will-continue-booming-in-rural-america-71920">a means of survival for struggling communities</a>, writes John Eason at Texas A&M University. “Prisons provide a short-term boost to the local economy by increasing median family income and home value while reducing unemployment and poverty.”</p>
<h2>5. Opioids by the numbers</h2>
<p>About 64,000 people died of drug overdose in the U.S. in 2016 – many from heroin, fentanyl and other opioids. </p>
<p>Oxycodone, a semi-synthetic pain medication, is one of the most commonly prescribed opioids in the U.S. In fact, U.S. per capita oxycodone consumption is much higher than other developed nations.</p>
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<p>Andrew Kolodny at Brandeis University says that overprescription is <a href="https://theconversation.com/the-opioid-epidemic-in-6-charts-81601">one of the driving causes of the epidemic</a>. “Until opioids are prescribed more cautiously and until effective opioid addiction treatment becomes easier to access, overdose deaths will likely remain at record high levels.”</p>
<h2>6. The trolls among us</h2>
<p>The internet can be a nasty place. Take a trip into the comments section under a news article or YouTube video, and you might see name-calling, graphic threats or even hate speech. </p>
<p>Who’s posting this stuff? A study of millions of comments on CNN.com suggests that <a href="https://theconversation.com/our-experiments-taught-us-why-people-troll-72798">almost anyone can be pushed to troll others</a> – under the right circumstances.</p>
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<p>According to the team’s research, negative comments peak late at night and on Mondays. </p>
<p>What’s more, the more troll comments there are in a particular discussion, the more likely future participants will also troll. As the authors at Stanford University and Cornell University write, “Many ‘trolls’ are just people like ourselves who are having a bad day.”</p><img src="https://counter.theconversation.com/content/88621/count.gif" alt="The Conversation" width="1" height="1" />
How do diverse movies fare in the international box office? What time do trolls like to post their comments? We look back on some of this year’s most intriguing graphs and maps.Aviva Rutkin, Data EditorLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/802562017-08-02T01:20:25Z2017-08-02T01:20:25ZThis math puzzle will help you plan your next party<figure><img src="https://images.theconversation.com/files/179645/original/file-20170725-30152-1sg6hk3.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Mapping connections at your next shindig.</span> <span class="attribution"><a class="source" href="https://www.flickr.com/photos/unclibraries_commons/23109914111/in/photolist-Bd9mk2-4id8ef-9b3RB-7qFUhu-8ETfQv-kUVHxH-5ENkBs-4aWEEf-kUVF2v-kYPf5X-kYPdvK-8Y91FT-pKLRm-4aSCNx-bt2FqY-kYQmxU-5NXrDW-5QKVRi-668pD-iDChA-bS7NkP-7Qm21B-axnNjC-9fw57s-4jAkj1-kYQAZQ-aigLLX-8nwh4d-wrhJb-kYPqdv-6YW7NP-aigLEx-6Z199Q-ixZBQg-HyAgcu-kYPqZR-9v1r5W-ddzLaV-derxa6-5eiWhs-9cD5ss-auQjZo-cBiqX-9X9PGL-3JChmw-89RRvG-51s3TR-9P7eTG-7jhz8Z-4aSD1t/">unclibraries_commons</a></span></figcaption></figure><p>Let’s say you’re planning your next party and agonizing over the guest list. To whom should you send invitations? What combination of friends and strangers is the right mix? </p>
<p>It turns out mathematicians have been working on a version of this problem for nearly a century. Depending on what you want, the answer can be complicated. </p>
<p>Our book, <a href="http://press.princeton.edu/titles/10314.html">“The Fascinating World of Graph Theory</a>,” explores puzzles like these and shows how they can be solved through graphs. A question like this one might seem small, but it’s a beautiful demonstration of how graphs can be used to solve mathematical problems in such diverse fields as the sciences, communication and society.</p>
<h1>A puzzle is born</h1>
<p>While it’s well-known that Harvard is one of the top academic universities in the country, you might be surprised to learn that there was a time when Harvard had one of the nation’s best football teams. But in 1931, led by <a href="http://www.thecrimson.com/article/1971/3/12/barry-wood-31-was-star-for/">All–American quarterback Barry Wood</a>, such was the case. </p>
<p>That season Harvard played Army. At halftime, unexpectedly, Army led Harvard 13–0. Clearly upset, Harvard’s president told Army’s commandant of cadets that while Army may be better than Harvard in football, Harvard was superior in a more scholarly competition.</p>
<p>Though Harvard came back to defeat Army 14-13, the commandant accepted the challenge to compete against Harvard in something more scholarly. It was agreed that the two would compete – in mathematics. This led to Army and Harvard selecting mathematics teams; the showdown occurred in West Point in 1933. To Harvard’s surprise, Army won. </p>
<p>The Harvard–Army competition eventually led to an annual mathematics competition for undergraduates in 1938, called the <a href="https://www.maa.org/programs/maa-awards/putnam-competition-individual-and-team-winners">Putnam exam</a>, named for William Lowell Putnam, a relative of Harvard’s president. This exam was designed to stimulate a healthy rivalry in mathematics in the United States and Canada. Over the years and continuing to this day, this exam has contained many interesting and often challenging problems – including the one we describe above.</p>
<h1>Red and blue lines</h1>
<p>The 1953 exam contained the following problem (reworded a bit): There are six points in the plane. Every point is connected to every other point by a line that’s either blue or red. Show that there are three of these points between which only lines of the same color are drawn. </p>
<p>In math, if there is a collection of points with lines drawn between some pairs of points, that structure is called a graph. The study of these graphs is called graph theory. In graph theory, however, the points are called vertices and the lines are called edges.</p>
<p>Graphs can be used to represent a wide variety of situations. For example, in this Putnam problem, a point can represent a person, a red line can mean the people are friends and a blue line means that they are strangers.</p>
<figure class="align-center zoomable">
<a href="https://images.theconversation.com/files/179639/original/file-20170725-30149-in14d6.png?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/179639/original/file-20170725-30149-in14d6.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/179639/original/file-20170725-30149-in14d6.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=266&fit=crop&dpr=1 600w, https://images.theconversation.com/files/179639/original/file-20170725-30149-in14d6.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=266&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/179639/original/file-20170725-30149-in14d6.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=266&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/179639/original/file-20170725-30149-in14d6.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=335&fit=crop&dpr=1 754w, https://images.theconversation.com/files/179639/original/file-20170725-30149-in14d6.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=335&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/179639/original/file-20170725-30149-in14d6.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=335&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px"></a>
<figcaption>
<span class="caption">Show that there are three points connected by lines of the same color.</span>
<span class="attribution"><span class="source">Gary Chartrand</span></span>
</figcaption>
</figure>
<p>For example, let’s call the points A, B, C, D, E, F and select one of them, say A. Of the five lines drawn from A to the other five points, there must be three lines of the same color. </p>
<p>Say the lines from A to B, C, D are all red. If a line between any two of B, C, D is red, then there are three points with only red lines between them. If no line between any two of B, C, D is red, then they are all blue.</p>
<p>What if there were only five points? There may not be three points where all lines between them are colored the same. For example, the lines A–B, B–C, C–D, D–E, E–A may be red, with the others blue.</p>
<p>From what we saw, then, the smallest number of people who can be invited to a party (where every two people are either friends or strangers) such that there are three mutual friends or three mutual strangers is six. </p>
<p>What if we would like four people to be mutual friends or mutual strangers? What is the smallest number of people we must invite to a party to be certain of this? This question has been answered. It’s 18. </p>
<p>What if we would like five people to be mutual friends or mutual strangers? In this situation, the smallest number of people to invite to a party to be guaranteed of this is – unknown. Nobody knows. While this problem is easy to describe and perhaps sounds rather simple, it is notoriously difficult.</p>
<h1>Ramsey numbers</h1>
<p>What we have been discussing is a type of number in graph theory called a Ramsey number. These numbers are named for the British philosopher, economist and mathematician <a href="https://www.repository.cam.ac.uk/bitstream/handle/1810/3484/RamseyText.html?sequence=5">Frank Plumpton Ramsey</a>. </p>
<p>Ramsey died at the age of 26 but obtained at his very early age a very curious theorem in mathematics, which gave rise to our question here. Say we have another plane full of points connected by red and blue lines. We pick two positive integers, named r and s. We want to have exactly r points where all lines between them are red or s points where all lines between them are blue. What’s the smallest number of points we can do this with? That’s called a Ramsey number. </p>
<p>For example, say we want our plane to have at least three points connected by all red lines and three points connected by all blue lines. The Ramsey number – the smallest number of points we need to make this happen – is six. </p>
<p>When mathematicians look at a problem, they often ask themselves: Does this suggest another question? This is what has happened with Ramsey numbers – and party problems. </p>
<p>For example, here’s one: Five girls are planning a party. They have decided to invite some boys to the party, whether they know the boys or not. How many boys do they need to invite to be certain that there will always be three boys among them such that three of the five girls are either friends with all three boys or are not acquainted with all three boys? It’s probably not easy to make a good guess at the answer. It’s 41!</p>
<p>Very few Ramsey numbers are known. However, this doesn’t stop mathematicians from trying to solve such problems. Often, failing to solve one problem can lead to an even more interesting problem. Such is the life of a mathematician.</p><img src="https://counter.theconversation.com/content/80256/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The authors do not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Let’s say you want the perfect mix of friends and strangers at your next party. Mathematicians have been working on a version of this problem for nearly a century, and the answer is complicated.Gary Chartrand, Professor Emeritus of Mathematics, Western Michigan UniversityArthur Benjamin, Professor of Mathematics, Harvey Mudd CollegePing Zhang, Professor of Mathematics, Western Michigan UniversityLicensed as Creative Commons – attribution, no derivatives.tag:theconversation.com,2011:article/780172017-06-14T02:23:21Z2017-06-14T02:23:21ZThe rise – and possible fall – of the graphing calculator<figure><img src="https://images.theconversation.com/files/172964/original/file-20170608-32318-zz67zc.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=496&fit=clip" /><figcaption><span class="caption">Graphing calculators – like the ones used in this seventh grade Dallas classroom – have become ubiquitous in U.S. education.</span> <span class="attribution"><a class="source" href="http://www.apimages.com/metadata/Index/AP-A-TX-USA-F-MATH-INITIATIVE/77d11887816444b08f34dd2e0e50289a/9/0">AP Photo/Tony Gutierrez</a></span></figcaption></figure><p>The first handheld graphing calculator, <a href="http://americanhistory.si.edu/collections/object-groups/handheld-electronic-calculators">the Casio fx-7000G</a>, appeared in 1985. </p>
<p>Since then, graphing calculators have become a common – and controversial – tool for learning mathematics. These devices can do all of the calculations of a scientific calculator, plus graph equations, make function tables and solve equations. Many have the ability to do statistical analysis and even some calculus.</p>
<p>Advocates claim that the calculators provide students access to more powerful mathematics. Critics worry that they might hurt students’ fluency in basic math and standard algorithms. </p>
<p>Today, some teachers are replacing expensive graphing calculators with free apps that can do more. But even after decades of use, graphing technology of any sort in the classroom <a href="https://www.theatlantic.com/education/archive/2016/12/the-conundrum-of-calculators-in-the-classroom/493961/">still sparks debate</a>.</p>
<p>As mathematics educators, we think the graphing calculator transformed American classrooms for the better. Whether teachers continue to use these tools or ditch them in favor of new ones, graphing technology will likely always have a place in secondary math education. </p>
<h1>Understanding math</h1>
<p>Math educators often talk about <a href="http://www.davidtall.com/skemp/pdfs/instrumental-relational.pdf">two kinds of understanding</a>.</p>
<p>“Instrumental understanding” comes from mastering a procedure or memorizing a fact, without really understanding the mathematics behind it. It’s knowing how, but not why. The saying “It is not ours to wonder why, just invert and multiply!” – which is sometimes used to teach division of fractions – captures this sort of understanding.</p>
<figure class="align-right ">
<img alt="" src="https://images.theconversation.com/files/173422/original/file-20170612-2090-9483pa.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/173422/original/file-20170612-2090-9483pa.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=791&fit=crop&dpr=1 600w, https://images.theconversation.com/files/173422/original/file-20170612-2090-9483pa.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=791&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/173422/original/file-20170612-2090-9483pa.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=791&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/173422/original/file-20170612-2090-9483pa.jpg?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=994&fit=crop&dpr=1 754w, https://images.theconversation.com/files/173422/original/file-20170612-2090-9483pa.jpg?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=994&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/173422/original/file-20170612-2090-9483pa.jpg?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=994&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">The first scientific graphing calculator.</span>
<span class="attribution"><a class="source" href="https://www.flickr.com/photos/51764518@N02/15810483905/in/photolist-q67S36">51764518@N02/flickr</a>, <a class="license" href="http://creativecommons.org/licenses/by-sa/4.0/">CC BY-SA</a></span>
</figcaption>
</figure>
<p>In contrast, “relational understanding” is a kind of connected, conceptual understanding. People with a relational understanding don’t just know how to invert and multiply, they know why such a procedure results in the quotient of two fractions.</p>
<p>Advocates for graphing calculators in school saw promise in the tool’s ability to <a href="http://www.nctm.org/Standards-and-Positions/More-NCTM-Standards/An-Agenda-for-Action-(1980s)/">help students develop relational understanding</a>. While the calculator takes care of the “how,” students can focus on “why.” </p>
<p>The impact is quite clear in the Advanced Placement (AP) calculus program, which started to require graphing calculators in their courses and on their exams <a href="http://www.andover.edu/gpgconference/documents/four-decades.pdf">in 1995</a>. Prior to 1995, AP calculus exam questions probed almost solely for the students’ ability to use rules to find derivatives and integrals of functions. After 1995, there was a marked shift away from this instrumental understanding and toward questions that probed for relational understanding.</p>
<p>As exams evolved, so too did teaching <a href="https://www.macalester.edu/%7Ebressoud/pub/launchings/launchings_06_10.html">philosophies</a>. The AP program required teachers to use graphing calculators in their courses. This was not just so students would learn how to use the calculator. Rather, the focus of instruction shifted so that students could learn mathematics through the graphing calculator. </p>
<p>For example, by using the graphing and zoom features of the graphing calculator, students could compare and contrast the local and global behavior of functions such as <em>y</em> = <em>x</em>² and <em>y</em> = <em>x</em>² + 2. By zooming in, students can see that in any local area, the graphs are clearly different. By zooming out, students can see that globally, the graphs are basically identical. Through exploration such as this, students gained relational understanding of infinite limits. </p>
<figure class="align-center ">
<img alt="" src="https://images.theconversation.com/files/173424/original/file-20170612-10795-15jqaok.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&fit=clip" srcset="https://images.theconversation.com/files/173424/original/file-20170612-10795-15jqaok.png?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=201&fit=crop&dpr=1 600w, https://images.theconversation.com/files/173424/original/file-20170612-10795-15jqaok.png?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=201&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/173424/original/file-20170612-10795-15jqaok.png?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=201&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/173424/original/file-20170612-10795-15jqaok.png?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=252&fit=crop&dpr=1 754w, https://images.theconversation.com/files/173424/original/file-20170612-10795-15jqaok.png?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=252&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/173424/original/file-20170612-10795-15jqaok.png?ixlib=rb-1.1.0&q=15&auto=format&w=754&h=252&fit=crop&dpr=3 2262w" sizes="(min-width: 1466px) 754px, (max-width: 599px) 100vw, (min-width: 600px) 600px, 237px">
<figcaption>
<span class="caption">In the local area (-6 < x < 6) shown at left, the graphs of y = x² + 5 and y = x² are clearly different. But zooming out (at right), the graphs of the two functions are basically identical.</span>
<span class="attribution"><span class="source">Frederick Peck</span>, <a class="license" href="http://creativecommons.org/licenses/by/4.0/">CC BY</a></span>
</figcaption>
</figure>
<h1>Does the tech help or hurt?</h1>
<p>Still, <a href="https://doi.org/10.1111/j.1949-8594.2007.tb17776.x">some teachers wondered</a> whether <a href="https://www.jstor.org/stable/27968919">this shift in instruction</a> in AP calculus and across the K-12 curriculum would have a negative effect on students’ instrumental understanding. After all, if a machine is doing the calculating for you, why bother to learn it?</p>
<p>After more than three decades of research, the findings are clear. Graphing calculators have a positive effect on <a href="https://doi.org/10.1111/j.1949-8594.2006.tb18067.x">students’ relational understanding</a> and a slight positive effect <a href="https://doi.org/10.1007/978-0-387-73315-9_60">on their instrumental understanding</a>.</p>
<p><a href="http://www.ti-researchlibrary.com/Lists/TI%20Education%20Technology%20%20Research%20Library/Attachments/122/GC%20in%20secondary%20math%20-%20research%20findings%20and%20implications%20-%20Burrill%202002%20-%20(yellow%20book)%20CL2872,%20review.pdf">Another review</a>, conducted by respected researchers in math education (but funded by a calculator company), came to a similar conclusion.</p>
<p>In other words, students who use graphing calculators in school know at least as many basic facts and are at least as good at doing standard algorithms as students who do not use graphing calculators. However, students who use graphing calculators have a deeper understanding of the “whys” behind those algorithms. </p>
<p>Of course, there are many individual studies that show negligible or even negative effects of graphing calculators. But overall, when the technology is paired with appropriate instructional techniques, the result is more and better mathematics learning.</p>
<h1>The rise of graph apps</h1>
<p>Today, online and app-based technology, such as <a href="https://www.desmos.com/calculator">Desmos</a> and <a href="https://www.geogebra.org/graphing">GeoGebra</a>, <a href="https://www.bloomberg.com/news/articles/2017-05-12/startup-targets-the-ti-calculators-your-kid-lugs-to-class">aim to replace</a> the role of stand-alone graphing calculators in school.</p>
<p>As with graphing calculators, for these new technologies to have a positive effect on student learning, teachers have to <a href="http://blog.desmos.com/post/150453765267/the-desmos-guide-to-building-great-digital-math">adapt their instruction</a>, changing <a href="https://theconversation.com/how-math-education-can-catch-up-to-the-21st-century-77129">what they teach and how they teach it</a>. </p>
<p>For example, technology can help students connect graphical representations with algebraic equations. We recently observed seventh grade students in Missoula, Montana doing that using Desmos. Students graphed three different linear equations, each with a different coefficient for the <em>x</em>-term. Based on this exploration, students made conjectures about the role of the coefficient, and used the app to test their conjectures – for example, <a href="https://www.desmos.com/calculator/ylc2sdigoi">by using a “slider” to dynamically vary the coefficient</a>. The flexibility of the technology also encouraged students to pose and explore their own questions.</p>
<figure class="align-left zoomable">
<a href="https://images.theconversation.com/files/172758/original/file-20170607-29588-mbwaim.PNG?ixlib=rb-1.1.0&q=45&auto=format&w=1000&fit=clip"><img alt="" src="https://images.theconversation.com/files/172758/original/file-20170607-29588-mbwaim.PNG?ixlib=rb-1.1.0&q=45&auto=format&w=237&fit=clip" srcset="https://images.theconversation.com/files/172758/original/file-20170607-29588-mbwaim.PNG?ixlib=rb-1.1.0&q=45&auto=format&w=600&h=338&fit=crop&dpr=1 600w, https://images.theconversation.com/files/172758/original/file-20170607-29588-mbwaim.PNG?ixlib=rb-1.1.0&q=30&auto=format&w=600&h=338&fit=crop&dpr=2 1200w, https://images.theconversation.com/files/172758/original/file-20170607-29588-mbwaim.PNG?ixlib=rb-1.1.0&q=15&auto=format&w=600&h=338&fit=crop&dpr=3 1800w, https://images.theconversation.com/files/172758/original/file-20170607-29588-mbwaim.PNG?ixlib=rb-1.1.0&q=45&auto=format&w=754&h=424&fit=crop&dpr=1 754w, https://images.theconversation.com/files/172758/original/file-20170607-29588-mbwaim.PNG?ixlib=rb-1.1.0&q=30&auto=format&w=754&h=424&fit=crop&dpr=2 1508w, https://images.theconversation.com/files/172758/original/file-20170607-29588-mbwaim.PNG?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">On the Desmos app, students can test their questions by dynamically varying the coefficient using a slider.</span>
<span class="attribution"><span class="source">David Erickson</span></span>
</figcaption>
</figure>
<p>Even as these cloud- and app-based tools provide powerful technology for free on smartphones and other personal devices, the expensive graphing calculator (which typically costs between US$80 and $150) <a href="https://www.washingtonpost.com/news/innovations/wp/2014/09/02/the-unstoppable-ti-84-plus-how-an-outdated-calculator-still-holds-a-monopoly-on-classrooms/">continues to be a stalwart in K-12 math classes</a>, with year-over-year units sales <a href="http://www.cbs58.com/news/digital-calculators-replacing-ti-84-graphing-calculator">increasing in 2015 and 2016</a>.</p>
<p>There has recently been <a href="https://mic.com/articles/125829/your-old-texas-instruments-graphing-calculator-still-costs-a-fortune-heres-why">much</a> <a href="http://money.cnn.com/2017/05/12/technology/ti-84-graphing-calculator/index.html">online</a> <a href="http://www.popularmechanics.com/technology/apps/a26520/free-online-tool-graphic-calculator/">hand-wringing</a> over this state of affairs, with commentators aghast at the continued dominance of graphing calculators when compared to inexpensive or free apps. The debate even provoked <a href="https://education.ti.com/en/success-story/why-graphing-calculators-add-up">a response</a> from the president of Texas Instruments, the dominant graphing calculator company in the U.S. </p>
<p>We agree with many of the points in favor of the new apps. But there is no doubt that, when properly used, graphing technology – whether on a calculator, computer screen, tablet or smartphone – is a powerful tool for helping students learn mathematics.</p><img src="https://counter.theconversation.com/content/78017/count.gif" alt="The Conversation" width="1" height="1" />
<p class="fine-print"><em><span>The authors do not work for, consult, own shares in or receive funding from any company or organization that would benefit from this article, and have disclosed no relevant affiliations beyond their academic appointment.</span></em></p>Teachers are starting to ditch graphing calculators for math apps. Was the expensive tech ever worth it – or is it just holding students back?Frederick Peck, Assistant Professor of Mathematical Sciences, University of MontanaDavid Erickson, Professor, Teaching and Learning, University of MontanaLicensed as Creative Commons – attribution, no derivatives.