What Does the p-Value Mean?

Summary:  The p-value tells you how likely it is to get the sample you got (or a more extreme sample) if the null hypothesis is true.

Many people are confused about the p-value and try to read too much into it. In your experiment, you got a certain set of results, like a sample mean. The hypothesis test asks whether random chance can account for those results if the null hypothesis is true.

The p-value is the likelihood, if H₀ is actually true, that random chance could give you the results you got. It is a conditional probability:

p-value = P(this sample | H₀ is true)

When you write it in symbols like that, you can see right away that the p-value is not the probability that either hypothesis is true or false:

• The p-value is not the probability that H₀ is true.
• The p-value is not the probability that H₀ is false.
• The p-value is not the probability that H₁ is true.
• The p-value is not the probability that H₁ is false.
• The p-value is not the probability that your results are due to random chance.
• The p-value is not the probability that your results are not due to random chance.

The p-value is not any of the above because they are all plain probabilities. Once again, the p-value is just a measure of how likely your results would be if  H₀ is true and random chance is the only factor in selecting the sample.

Another way of looking at the p-value is that it’s your chance of being wrong (Type I error) if you reject H₀.

See also:  P-value for Kids, a brief article by David Moore (link verified 2009-12-28)

There’s one other thing: the p-value is not a measure of the size or importance of an effect. A small p-value means you can be pretty confident in rejecting H₀ and accepting H₁. But it doesn’t tell you by how much you’re rejecting H₀ (the effect size), or whether that rejection has any practical consequences.