Which statement about power is true?

Which statement about power is true?

• A. Power is the probability of finding a difference if none exists
• B. Power is the probability of detecting a difference if one exists
• C. Power increases with smaller sample size
• D. Power is unaffected by variability

Answer: (B)

Power is the probability of detecting a true difference if one actually exists. It reflects how likely a study is to reject the null hypothesis when the alternative is true, i.e., 1 minus the probability of a Type II error. Power depends on several factors: how big the real difference is (effect size), how many observations you have (sample size), how variable the data are, and the chosen significance level. The statement identified as correct matches this idea: power measures the chance of finding a difference when there is one. The other ideas don’t fit because they mix up concepts or ignore key influences. Power is not the probability of finding a difference when no difference exists—that describes the false positive rate (alpha). Power does not increase with smaller sample sizes; in fact, larger samples raise power. And power is affected by variability: more variability makes it harder to detect a true difference, reducing power.

Power is the probability of detecting a true difference if one actually exists. It reflects how likely a study is to reject the null hypothesis when the alternative is true, i.e., 1 minus the probability of a Type II error. Power depends on several factors: how big the real difference is (effect size), how many observations you have (sample size), how variable the data are, and the chosen significance level. The statement identified as correct matches this idea: power measures the chance of finding a difference when there is one.

The other ideas don’t fit because they mix up concepts or ignore key influences. Power is not the probability of finding a difference when no difference exists—that describes the false positive rate (alpha). Power does not increase with smaller sample sizes; in fact, larger samples raise power. And power is affected by variability: more variability makes it harder to detect a true difference, reducing power.