Which concept represents the probability of failing to reject a false null hypothesis?

Which concept represents the probability of failing to reject a false null hypothesis?

• A. Type I error
• B. Power
• C. Type II error
• D. P-value

Answer: (C)

The key idea here is the Type II error: it is the probability of failing to reject a false null hypothesis. In other words, when there really is an effect but the test doesn’t show a statistically significant result, that missed detection is a Type II error. The smaller this probability, the better the test is at spotting real effects. This probability is often called beta. Its complement, 1 minus beta, is the test’s power—the chance the test will correctly reject a false null. So when you hear about the ability of a test to detect real differences or effects, you’re hearing about power. It’s helpful to contrast with the other concepts: a Type I error is rejecting a true null hypothesis when there is no real effect; that’s a false positive. The P-value is the probability, under the assumption that the null is true, of observing data as extreme or more extreme than what you obtained; it’s a measure used to decide whether to reject the null, not an error rate itself. Because you want a test that reliably detects real effects, higher power (larger 1 − beta) is desirable, and this is achieved by larger effect sizes, larger samples, or a higher significance level. This is why the correct concept is the Type II error.

The key idea here is the Type II error: it is the probability of failing to reject a false null hypothesis. In other words, when there really is an effect but the test doesn’t show a statistically significant result, that missed detection is a Type II error. The smaller this probability, the better the test is at spotting real effects.

This probability is often called beta. Its complement, 1 minus beta, is the test’s power—the chance the test will correctly reject a false null. So when you hear about the ability of a test to detect real differences or effects, you’re hearing about power.

It’s helpful to contrast with the other concepts: a Type I error is rejecting a true null hypothesis when there is no real effect; that’s a false positive. The P-value is the probability, under the assumption that the null is true, of observing data as extreme or more extreme than what you obtained; it’s a measure used to decide whether to reject the null, not an error rate itself.

Because you want a test that reliably detects real effects, higher power (larger 1 − beta) is desirable, and this is achieved by larger effect sizes, larger samples, or a higher significance level. This is why the correct concept is the Type II error.