## It’s been a long time since I studied statistics. Remind me, what does a p value represent?

A common misperception is that p = .05 means there is a 5% probability of obtaining the observed result by chance. The correct interpretation is that there is a 5% probability of getting a result this large (or larger) if the effect size equals zero.

A p value is the answer to the question: if the null hypothesis were true, how likely is this result? A low p says “highly unlikely”, making the null improbable and therefore rejectable.

In substantive terms, a p value really tells us very little. As it is a confounded index, it is not a good idea to interpret results on the basis of p values.

For better ways of interpreting results, see this.

### 2 Responses to It’s been a long time since I studied statistics. Remind me, what does a p value represent?

1. Henk says:

In ‘The Essential Guide to Effect Sizes’ on page 4 you write that “[a] statistically significant result is one that is unlikely to be the result of chance.” This seems to contradict what you say here.

• Paul Ellis says:

You are very sharp-eyed to pick this up. Well done! The line in the book was flagged by one of my reviewers as being potentially misleading and in one sense it is. As I indicate above and elsewhere in the book a statistically significant result is one that generates a conditional probability value that is lower that certain conventions given a bunch of assumptions pertaining to the null and other things. But it gets a little tiresome to have to say all this every time you discuss the meaning of statistical significance. The point I was trying to make on p.4 is that statistical significance is not the same as practical significance.