Implications of statistical power for confidence intervals

The statistical power of a hypothesis test is closely related to the precision of the accompanying confidence interval. In the case of a z ‐test, the width of the confidence interval is a function of statistical power for the planned study. If minimum effect size is used in power analysis, the width of the confidence interval is the minimum effect size times a multiplicative factor φ . The index φ , or the precision‐to‐effect ratio, is a function of the computed statistical power. In the case of a t‐ test, statistical power affects the probability of achieving a certain width of confidence interval, which is equivalent to the probability of obtaining a certain value of φ . To consider estimate precision in conjunction with statistical power, we can choose a sample size to obtain a desired probability of achieving a short width conditional on the rejection of the null hypothesis.