Master of Science / Department of Statistics / Leigh W. Murray / 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.

In this thesis, we hope to dispel some confusion regarding the so-called post hoc power, i.e. power computed making the assumption that the estimated sample effect is equal to the population effect size. In previous research, it has been shown that post hoc power is a function of the p-value, making it redundant as a tool of analysis. We go further, arguing for it to never be reported, since it is a source of confusion and potentially harmful incentives. We also conduct a Monte Carlo simulation to illustrate our points of view. Previous research is confirmed by the results of this study.