On determining the power of a test after data collection - Chernoff, William Avram (Kansas State University, 2009)
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.
Keywords: Retrospective power; Power; Post hoc power; Non-rejected null hypothesis; Statistical significance; Estimate power; Statistics (0463)