If you’ve ever tried to read a scientific paper, you’ve almost certainly run into a p-value. And if you found it confusing, you’re in good company: plenty of working scientists misunderstand it too.

The p-value is a number measuring the “statistical significance” of an experiment, and it’s often treated as the adjudicator of whether the experiment really found something or not. It decides whether researchers get to say that a drug did something, or that one group differed from another.

Careers, publications and our understanding of the world hinge on p-values. So it’s worth understanding what these numbers actually mean, because it’s not what most people think.

What does a p-value mean?

Suppose we want to know whether adults in one country are taller, on average, than adults in another. We cannot measure everyone, so we sample 50 adults from each country.

The first sample averages 1.80 metres, the second 1.77 metres. That 3cm gap tells us little on its own, because any two samples will differ to some degree simply because of who happened to be picked.

So is the gap good evidence of a real difference in average heights across the whole population? Or is it just the kind of thing that turns up through the luck of the draw?

To find out, a scientist runs a statistical test which returns a p-value. Say it comes back as p = 0.06.

Here is what that means: if there........

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