What is statistical power? What parameters go into it, and how and why is it assessed before a study is conducted?

Question

What will be an ideal response?

Answer 1

Statistical power--that is, the probability of rejecting a null hypothesis when it is, in fact, false. In the context of validation research, the null hypothesis states that there is no relation between a predictor and a criterion in the population. As Cohen (1988) has noted, any statistical test of a null hypothesis may be viewed as a complex relationship among four parameters: (1) the power of the test (1–b, where beta is the probability of making a Type II error); (2) Type I error or ?, the region of rejection of the null hypothesis and whether the test is one tailed or two tailed (power increases as ? increases); (3) sample size, N (power increases as N increases); and (4) the magnitude of the effect in the population or the degree of departure from the null hypothesis (power increases as the effect size increases). The four parameters are so related that when any three of them are fixed, the fourth is completely determined. The importance of power analysis as a research planning tool is considerable, for if power turns out to be insufficient, the research plans can be revised (or dropped if revisions are impossible) so that power may be increased (usually by increasing N and sometimes by increasing ?). Note that a power analysis should be conducted before a study is conducted. Post hoc power analyses, conducted after validation efforts are completed, are of doubtful utility, especially when the observed effect size is used as the effect size one wishes to detect.