Fool me once, shame on you; fool me twice, shame on me: COVID-19 data and the log scale

By Alessandro Romano, Chiara Sotis, Goran Dominioni and Sebastian Guidi

After some months of relative calm, countries like France, Spain, and Italy seem to be  facing a second wave of COVID-19. In countries that experienced a drop in the number of cases, people seem to have relaxed their precautions, which helps foster a new spread of the virus. For the public to engage in protective behavior it is vital that people understand the situation. It is essential, therefore, that the media conveys information to the public in a way they understand and allows them to make informed choices on their behavior. But is this happening?

Imagine being in Spain and seeing this graph on the total number of COVID-19 cases in the country:

Alternatively, imagine seeing this one:

The two graphs look and feel very different, despite displaying the same data. The last graph plots the information on an old good linear scale, of the type many people learn to read in elementary school. The first one, instead, deploys a logarithmic scale. This scale, some media and experts explain, is better to show exponential growth: a straight line shows a constant growth rate, which in turn makes it easier to spot deviations from the exponential trend.

Although the logarithmic scale may have this theoretical advantage, it does a poor job at showing the second wave of cases in Spain: it is only when we look closely that we see a bump in the line of total cases in August, despite the fact that the amount of daily new cases in the country is similar to that of April. The key issue is that the information these graphs are allegedly good at conveying is no longer the relevant one. What matters is not how much the cases are growing with respect to the total amount of cases, as this includes cases that took place months ago. What matters to understand if a second wave is on the way is whether the speed at which the virus spreads is increasing at a significant rate. But a graph that uses a logarithmic scale to plot total cases hides this information, and hence it may induce people to underestimate the gravity of the situation in their area. This could lead them to make choices that they would have not made otherwise; choices that can be consequential for the spread of the virus, the economy, and politics. This problem exists also for countries where the second wave has been much more severe than the first one, such as Japan:

In fact, logarithmic scale graphs plotting total cases will become increasingly inadequate to show future waves. As the number of total cases grows and reaches higher intervals on the Y axis, an increase of, say 3000 cases (which would have been extremely salient at the beginning of the pandemic) becomes increasingly less visible. Sticking to this way of reporting cases, as done for example by the Financial Times and the CNN, might be confusing to the public.

Admittedly, the problem is more serious because many newspapers only show the number of total cases. Using these graphs even large and significant increases in the number of cases become very hard to notice, once the overall number of cases becomes sufficiently high.  To address this issue, some media show a rolling 7 day average of daily new confirmed cases per million population.

This seems a better way to use the log scale at this point of the pandemic, as it shows clearly when the number of cases is growing. However, the logarithmic scale has also another significant downside. Research shows that even experts do not fully grasp logarithmic scales, and our recent article confirms this finding when it comes to the general public and COVID-19 information. In a survey with 2,000 Americans, participants showed much better understanding of linear scale than logarithmic ones – despite the fact that both groups stated similar levels of confidence in their answers. More importantly, people who were shown different graphs with the same data state different attitudes and policy preferences. Therefore, the scale in which the data is represented has important real world consequences.

Research suggests caution in using logarithmic scale charts to communicate with the public. The use of this scale combined with a focus on total cases hides the beginning of a second wave. Focusing only on recent data partially addresses this issue, but research shows that people still cannot understand the logarithmic scale, and hence information conveyed in this way does a poor job in helping the public make informed choices. As we move to a phase likely to experience peaks and valleys of cases, carefully thinking about something as seemingly innocuous as the graphs we use to inform people of the epidemiological situation is and will remain very important.

Alessandro Romano is Assistant Professor at Bocconi Law School. He has published in leading journals in the areas of law, business, environmental science, political science, economics and multidisciplinary.

Chiara Sotis is a PhD Candidate in Environmental Economics in the Geography and Environment Department (LSE) and the EC201 Course Manager in the Economics Department at LSE.

Goran Dominioni is Assistant Professor at Dublin City University. He holds a PhD from Erasmus University Rotterdam.

Sebastián Guidi is a doctoral student and graduate tutor at Yale Law School.

Photo by United Nations COVID-19 Response


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