## 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.

## What is a p value?

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 the p value is a confounded index, it is never a good idea to interpret results on the basis of p values.

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### 2 thoughts on “What does a p value represent?”

1. Henk September 22, 2011 / 12:31 am

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 September 22, 2011 / 4:14 pm

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.