scribed in the Appendix, we find that when the versions differ by less than ∼ 30 − 40% in magnitude and have the same sign our method has better power to reject Fisher’s sharp null than the F-test. Being an omnibus test, the F-test power is much less sensitive to the specific pattern of alternative hypothesis. In Figure 2, we compare the intervals returned by our version method to the three intervals returned by a Bonferroni correction (BC) to the comparison of the football players against all controls and each version of control. In the top panel, the BC interval using all controls is 22% longer than I $_{c}$. In the bottom panel, I v is only 3% longer than the BC interval using only “no sport” controls and 15% shorter than the BC interval using “other sport” controls. In this particular case, where versions appear to be relatively innocuous, the cost of lengthening the primary interval is significant for what apears to be little if any gain from investigating each version separately. Bonferroni correction may be more appropriate when the investigator suspects the versions are important, and he may even replace the primary comparison with a comparison of the two versions of control themselves. However, if the versions are only modestly different, for which our method is designed, it is unlikely that Bonferroni would have sufficient power to detect such modest differences in the versions of control. In the study of the effects of playing high school football on cognitive decline, the two versions of control and the football players have significant overlap in observed covariates. An anonymous reviewer suggested the following situation. Suppose that athletes who did not play football and non-athletes who did not play football differ noticeably on observed 7 Versions, effect modification, and insufficient overlap Bonferroni corrected intervals 19