Define p-value.

• A. The probability that the null hypothesis is true.
• B. The probability that the observed result occurred by chance alone.
• C. The magnitude of the observed difference.
• D. The probability of observing the data, or more extreme, assuming the null hypothesis is true.

Answer: (D)

The p-value measures how surprising the observed data would be if there were really no effect (the null hypothesis is true). It is defined as the probability, under the null model, of obtaining a statistic as extreme as or more extreme than what was actually observed. In a two-sided test, “as extreme” means as far from the null expectation in either direction; in a one-sided test it means in the specified direction. It is not the probability that the null hypothesis is true, nor the probability that the observed result happened by chance alone in the real world, and it does not convey how large or important the effect is. A small p-value suggests the data are unlikely under the null, providing evidence against the null at a chosen significance level.