Increasing scientific power with statistical power.

A survey of basic ideas in statistical power analysis demonstrates the advantages and ease of using power analysis throughout the design, analysis, and interpretation of research. The power of a statistical test is the probability of rejecting the null hypothesis of the test. The traditional approach to power involves computation of only a single power value. The more general power curve allows examining the range of power determinants, which are sample size, population difference, and error variance, in traditional ANOVA. Power analysis can be useful not only in study planning, but also in the evaluation of existing research. An important application is in concluding that no scientifically important treatment difference exists. Choosing an appropriate power depends on: a) opportunity costs, b) ethical trade-offs, c) the size of effect considered important, d) the uncertainty of parameter estimates, and e) the analyst's preferences. Although precise rules seem inappropriate, several guidelines are defensible. First, the sensitivity of the power curve to particular characteristics of the study, such as the error variance, should be examined in any power analysis. Second, just as a small type I error rate should be demonstrated in order to declare a difference nonzero, a small type II error should be demonstrated in order to declare a difference zero. Third, when ethical and opportunity costs do not preclude it, power should be at least .84, and preferably greater than .90.