What does a p-value represent in hypothesis testing?

• A. Probability that the null hypothesis is true given the data.
• B. Probability of observing data as extreme if the null hypothesis is true.
• C. The size of the observed effect.
• D. The probability that the alternative hypothesis is true.

Answer: (B)

A p-value tells you how compatible the observed data are with the assumption that there is no effect (the null hypothesis). It’s the probability, under the null being true, of obtaining a result as extreme as or more extreme than what you actually observed. A small p-value means your data would be unlikely if the null were true, which is why you’d consider rejecting the null at your chosen significance level. It does not tell you the probability that the null hypothesis is true after seeing the data, nor does it indicate the size or importance of the observed effect, nor the probability that the alternative hypothesis is true. Remember, p-values can be influenced by sample size: very large samples can yield small p-values for tiny, possibly unimportant effects, while practical significance depends on the effect size and context.