What is a p-value, and what does it tell you?

• A. The probability of observing data as extreme as the sample if the null hypothesis is true.
• B. The probability that the null hypothesis is true given the observed data.
• C. The probability that the alternative hypothesis is true.
• D. The p-value is an effect size measure.

Answer: (B)

A p-value tells you how surprising your data would be if there were really no effect. It is the probability, assuming the null hypothesis is true, of obtaining a result as extreme as or more extreme than what you actually observed. A small p-value means the observed data are unlikely under the null, which is why we might question the null hypothesis. A large p-value means the data are quite compatible with the null, offering little evidence against it. It does not give the probability that the null hypothesis is true given the data, nor does it indicate the size of any effect; those require different interpretations or measures.