Statistics can be an effective way to reach a destination or can be dangerous

Professor David Spiegelhalter from Cambridge University. 

Professor David Spiegelhalter from Cambridge University. - Credit: Cambridge University

One of the most famous quotes Benjamin Disraeli never said was: “There are lies, damned lies and statistics.”

It is often used when there is no other way to counter clear statistical evidence. But is it ever true?

Statistics, like driving a car, can be an effective way to reach a destination or can be dangerous. They can be abused and used for propaganda.

As any A-level maths student will tell you, the study of statistics can be complicated but needs to be understood to make any sense.

One of my favourite statisticians is Professor David Spiegelhalter from Cambridge University. 

One of the many fascinating examples he uses to illustrate the pitfalls of dramatic headlines involved a bacon sandwich.

The press covered a genuine story quoting research 'proving' that anyone eating a bacon sandwich every day increases their risk of bowel cancer by 20 per cent.

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This sounds horrific. Should we all avoid bacon? But what does this 20 per cent mean?

If we take 100 healthy people who do not eat bacon, about five will get bowel cancer through shear bad luck.

If all the 100 people eat a bacon sandwich every day, then the risk of bowel cancer increases by 20 per cent. 

But 20 per cent of five is one and so a 20 per cent increased risk means one more person getting bowel cancer. 

So, a daily bacon sandwich increases the risk from five in 100 to six in 100.

And that’s for a daily bacon sandwich. I like bacon sandwiches but do not eat one every day. There is a very small increased risk of cancer from bacon but the risk from the occasional bacon sandwich is so small that I’m willing to take the risk.

This is a personal decision. There are religious reasons for not eating bacon or concerns about saturated fats.

Some people are vegetarian due to concerns about animal welfare or global warming but, before worrying about bowel cancer, it is important to understand the figures. 

Statistics are also an incredibly useful tool for improving healthcare. 

Now that every GP practice is computerised we have access to far more anonymised statistics.

If we were to plot everyone’s height on a graph against number of people we would end up with a bell shape.

Most of us are in the middle, for men about 5ft 9ins, there would be a small number of 'outliers' well over 6ft or under 5 ft.

 If we looked at, for example, how many statins to reduce cholesterol GPs prescribed we would see the same bell-shaped graph.

The outliners are not 'wrong' but interesting. It might be that they have younger or a very fit group of patients with little heart disease, but it might also be that they are not following the guidelines on prescribing statins.

Again we must not see these doctors as 'wrong' but it is an area worth discussing.

Of course, we can be thrown by 'outliers'.

I remember a practice which had half the number of referrals to the Torbay orthopaedic department than similar GP practices.

Did they have a 'cure' for hips and knees so that fewer of their patients needed a replacement?

The answer was simple.

They were halfway between Torbay Hospital and Derriford in Plymouth. We were only looking at the referrals to Torbay and half their referrals went to Derriford.

In one city there were two hospitals, but one had far more deaths. Were they dangerous?

When the statistics were reviewed, it was found that the one with more deaths had an attached hospice.

When these patients were excluded the death rates were similar and lower than the national average.

During the Covid pandemic we have been inundated with statistics.

'Next slide please' has become a catch phrase. There are lies and damned lies on the internet but it is important to understand statistics before suggesting that they are also damned lies. 

As Sir Humphrey Appleby said in Yes Minister: “You can prove anything with statistics. Even the truth.”