Which statement about p-values is correct?

Which statement about p-values is correct?

• A. A p-value is the probability that the null hypothesis is true.
• B. A p-value is the probability that the alternative hypothesis is true.
• C. A p-value is the probability of observing the data, or more extreme, assuming the null hypothesis is true.
• D. A p-value is the probability of making a correct decision about the null hypothesis.

Answer: (C)

Think of the p-value as a measure of how compatible the observed data are with the null hypothesis being true. It answers: if the null hypothesis really were true, what is the probability of obtaining data as extreme as the observed data, or more extreme? This is exactly what the p-value represents. It does not tell us the probability that the null hypothesis is true, nor the probability that the alternative hypothesis is true, and it is not the probability of making a correct decision about the null. A small p-value means the observed result is unlikely under the null, giving evidence against it; a large p-value means the data are consistent with the null. The idea of “more extreme” depends on the test: two-sided tests consider extremes in both directions, while one-sided tests focus on extremes only in the direction of the alternative.

Think of the p-value as a measure of how compatible the observed data are with the null hypothesis being true. It answers: if the null hypothesis really were true, what is the probability of obtaining data as extreme as the observed data, or more extreme? This is exactly what the p-value represents. It does not tell us the probability that the null hypothesis is true, nor the probability that the alternative hypothesis is true, and it is not the probability of making a correct decision about the null. A small p-value means the observed result is unlikely under the null, giving evidence against it; a large p-value means the data are consistent with the null. The idea of “more extreme” depends on the test: two-sided tests consider extremes in both directions, while one-sided tests focus on extremes only in the direction of the alternative.