Maths, Stats, and Very Bad Graphs

Each day during periods of national lockdown, the government does a briefing in which we are presented with the most recent figures and statistics. Gut instinct says we should believe information when it is presented to us in a graph, so I’ve found some stats and graphs to make you question everything!

Correlation does not equal Causation

We have seen a number of graphs showing us the correlation between number of cases and number of deaths, number of cases compared with dates of lockdowns being lifted, and more. In these cases, it is safe to assume that the correlation is a sign of causation, i.e. the number of cases increased when the ‘stay at home’ guidance was changed to ‘stay alert’ and we were allowed to shop and travel again.

However, these graphs show correlation where actually, there is absolutely no way that the two variables can be related.

Credit: tylervigen.com

And some are just confusing!

There have been some rather bizarre and misleading graphs that have circulated during the pandemic. Take a look at the graph below, for example. The scale is not even, there is no scale along the bottom… and yet this was circulated via an app that thousands of people access every day.

It is definitely important to keep an eye on the axes and the scale. Some institutions have moved to using logarithmic scales rather than linear ones. Where a linear scale would show the figures as 10, 20, 30, etc, a logarithmic scale would increase by a factor of the previous measure, for example, 10,100, 1000, 10000, etc. This is useful in charting some statistics like the number of cases, and has been explained well here in this article by the New York Times.

Trustworthy Sources

There have been a lot of spurious claims during the pandemic, and therefore a lot of false information has been circulated. This is due in part to how quick, easy and accessible social media is. So, who can you trust for accurate statistics?

As far as England and Wales go, the ONS is the one to listen to. The Office of National Statistics collates information on almost everything that happens across:

• Business, Industry and Trade
• The Economy
• Employment and the Labour Market
• People, Population and Community.

You may have heard about them in another context recently, as they are responsible for the administration and collation of the National Census which we all completed last month. If you want accurate statistics, they are an incredibly reliable source.

You can read all the latest COVID-19 statistics here:

Who are the experts advising our government?

When it comes to understanding the statistics and the subsequent measures that need to be taken, this is a joint effort. The Scientific Advisory Group for Emergencies is a committee of people across a broad range of public services, from a variety of backgrounds, who work collaboratively to ensure the government does the right thing with the statistics.

Among the SAGE members are a few names you may have heard:

Sir Patrick Vallance – Government Chief Scientific Advisor

Professor Chris Whitty – Chief Medical Advisor

Professor Jonathan Van Tam – Deputy Chief Medical Advisor

Regularly appearing on the daily briefing has resulted in minor celebrity status for all three of these gentlemen, with Professor Van Tam gaining popularity when he not-so-subtly called out Dominic Cummings for the Barnard Castle Eye Test. Chris Whitty fans have also created a product range for the “Chris Whitty Appreciation Society”.

Aside from the humour though, all three men have been critical in steering the government’s decisions with their years of experience in their respective fields such as epidemiology, infectious diseases, public health medicine and health data. Regardless of their end qualifications and credentials, all of these people will have a strong grasp of mathematics.

It is important to have an analytical eye when we look at statistics, who compiled them, where they came from, whether they had an agenda, and who funds them. By keeping an eye on the aspects I’ve described here, you too can scrutinise the statistics to check that they are reasonable.

For more maths tips and tricks, get my free e-book here!