What is a p-value?

• A. Probability the null hypothesis is true.
• B. Probability, under the null hypothesis, of observing results as extreme.
• C. Probability of obtaining a significant result.
• D. Probability that the alternative hypothesis is true.

Answer: (B)

A p-value expresses how compatible your data are with the assumption that the null hypothesis is true. Specifically, it is the probability of obtaining results as extreme as the ones observed (or more extreme, depending on the test) under the null. For a two-sided test, that means looking in both directions of the test statistic and usually doubling the tail probability.

This measures consistency with the null, not the truth of the null itself. A small p-value suggests the observed data are unlikely if the null is true, so you might reject the null at your chosen significance level. A large p-value means the data aren’t unusual under the null, so you don’t have enough evidence to reject it.

It’s important to avoid thinking a p-value is the probability that the null is true or that a significant result will occur in the future. For example, if you obtain a p-value of 0.03 in a two-sided test, and your alpha is 0.05, you would reject the null here, because the data are unlikely under the null, but this does not say the null is true or false with any probability.