What is a p-value?

• A. The probability of obtaining data as extreme as observed (or more) assuming the null hypothesis is true.
• B. The probability that the null hypothesis is true.
• C. The observed effect size.
• D. The probability of observing data under the alternative hypothesis.

Answer: (A)

The p-value measures how surprising your data would be if the null hypothesis were true. It is the probability of obtaining data as extreme as the observed data (or more extreme) under that assumption. In other words, it tells you how compatible your data are with the notion that there is no real effect.

This is not the probability that the null hypothesis is true itself, which is a common misinterpretation. The p-value is a statement about the data given the null, not about the truth of the null. It also does not reflect the size of the effect—that’s the role of the observed (or estimated) effect size. And it isn’t the probability of the data under the alternative hypothesis.

So, a small p-value means the observed result would be unlikely if the null were true, which is why researchers often consider it evidence against the null at a chosen significance level.