On determining the power of a test after data collection

Abstract

The term retrospective power describes methods for estimating the true power of a test after data have been collected. These methods have been recommended by some authors when null hypothesis of a test cannot be rejected. This report uses simulations to study power as a construct of an observed effect, variance, sample size, and set level of significance under the balanced one-way analysis of variance model for normally distributed populations with constant variance. Retrospective power, as a construct of sample data, is not recommended when the null hypothesis of a test cannot be rejected. When the p-value of the test is large, estimates for true power tend to fall below the 0.80 level and width-minimized confidence limits for true power tend to be wide.