What does a p-value indicate in hypothesis testing?

• A. The probability of observing the data (or more extreme) if the null hypothesis is true.
• B. The probability that the null hypothesis is true.
• C. The probability that the alternative hypothesis is true.
• D. The probability of repeating the study.

Answer: (A)

In hypothesis testing, the p-value shows how compatible your observed data are with the assumption that the null hypothesis is true. It is the probability, under the null, of obtaining a test statistic as extreme as the one you observed (or more extreme, depending on whether the test is one- or two-tailed). A small p-value means the data look unlikely under the null and may lead you to consider rejecting it; a large p-value means the data are reasonably consistent with the null.

This value does not tell you the probability that the null hypothesis is true, nor the probability that the alternative is true. It also isn’t the chance of repeating the study. Those probabilities refer to hypotheses themselves or future experiments, whereas the p-value describes the likelihood of the observed data given the null assumption. Keep in mind that p-values can be influenced by sample size and don’t by themselves measure practical significance.