Results from classical power analysis (Brewer, 1972) suggest that a researcher should not set a=p (when p is less than a) in a posteriori fashion when a study yields statistically significant results because of a resulting decrease in power. The purpose of the present report is to use Bayesian theory in examining the validity of this generalization. Using the t-test and Bayes' theorem we show that while the substitution of p for a (when p is less than a) reduces unconditional or simple power, it actually increases the conditional power of the test--i.e., the probability that the alternative hypothesis is true given a statistically significant result. Because of this, the substitution of p for a a posteriori (when p is less than a), i.e., acting as though the value of a is equal to the obtained p value, seems to be a harmless practice at worst, and on the positive side, provides important information to the research consumer interested in the validity of the alternative hypothesis given the data of the study. (Author/RC)