What does a p-value represent in hypothesis testing?

What does a p-value represent in hypothesis testing?

• A. The probability, under H0, of observing a test statistic as extreme or more extreme than the one observed.
• B. The probability, under H1, of observing the test statistic as extreme as observed.
• C. The probability that H0 is true given the data.
• D. The probability of making a Type I error.

Answer: (A)

The p-value is the probability, under the assumption that the null hypothesis is true, of observing a test statistic as extreme or more extreme than the one actually observed. It assesses how compatible the data are with H0: small values mean the observed result would be rare if H0 were true, while large values mean it would be more plausible. This measure is computed using the sampling distribution of the test statistic under H0, and it corresponds to the tail(s) you consider for your test (two-sided tests look at both tails). A small p-value suggests the data conflict with H0, leading you to reject at your chosen significance level. It’s not the probability that H0 is true given the data, nor the probability of H1 being true, nor the probability of making a Type I error in this single study. The Type I error rate (alpha) is a pre-set long-run frequency that governs how often you’d falsely reject a true H0 across many repetitions, not the p-value itself.

The p-value is the probability, under the assumption that the null hypothesis is true, of observing a test statistic as extreme or more extreme than the one actually observed. It assesses how compatible the data are with H0: small values mean the observed result would be rare if H0 were true, while large values mean it would be more plausible.

This measure is computed using the sampling distribution of the test statistic under H0, and it corresponds to the tail(s) you consider for your test (two-sided tests look at both tails). A small p-value suggests the data conflict with H0, leading you to reject at your chosen significance level.

It’s not the probability that H0 is true given the data, nor the probability of H1 being true, nor the probability of making a Type I error in this single study. The Type I error rate (alpha) is a pre-set long-run frequency that governs how often you’d falsely reject a true H0 across many repetitions, not the p-value itself.