One reason why we might calculate retrospective power is to help in the design of
future research. Suppose that we have just completed an experiment and want to replicate
it, perhaps with a different sample size and a demographically different pool of partici-
pants. We can take the results that we just obtained, treat them as an accurate reflection of
the population means and standard deviations, and use those values to calculate the esti-
mated effect size. We can then use that effect size to make power estimates. This use of ret-
rospective power, which is, in effect, the a priori power of our next experiment, is relatively
non-controversial. Many statistical packages, including SAS and SPSS, will make these
calculations for you, and that is what I asked G*Power to do.
What is more controversial, however, is to use retrospective power calculations as an
explanation of the obtained results. A common suggestion in the literature claims that if
the study was not significant, but had high retrospective power, that result speaks to the
acceptance of the null hypothesis. This view hinges on the argument that if you had high
power, you would have been very likely to reject a false null, and thus nonsignificance
indicates that the null is either true or nearly so. That sounds pretty convincing, but as
Hoenig and Heisey (2001) point out, there is a false premise here. It is not possible to fail
to reject the null and yet have high retrospective power. In fact, a result with pexactly equal
to .05 will have a retrospective power of essentially .50, and that retrospective power will
decrease for p..05. It is impossible to even create an example of a study that just barely
failed to reject the null hypothesis at a5.05 which has power of .80. It can’t happen!
The argument is sometimes made that retrospective power tells you more than you
can learn from the obtained pvalue. This argument is a derivative of the one in the previ-
ous paragraph. However, it is easy to show that for a given effect size and sample size,240 Chapter 8 Power
Figure 8.5 Power as a function of sample size and alpha