A note on the operating characteristics of the modified F test

Brownie, Boos, and Hughes-Oliver (1990, Biometrics 46, 259-266) suggested a modification to the fixed-effects analysis of variance (ANOVA) F test for use in situations where treatments are likely to affect mean response while simultaneously increasing between-subject variability. These authors suggest that the modified test (1) is robust against departures from population normality, (2) is more powerful than its classical counterpart when the expected alternative form is encountered, and (3) will suffer only minor power losses relative to the usual test when alternatives are in the form of simple shifts in location. This study shows that the modified test is not generally robust when sampling is from nonnormal distributions and is likely to produce unacceptably high Type I error inflations when sampling is from heavy-tailed or skewed distributions. Some power results are also provided for the multisample situation to supplement those of Brownie et al., who generated results only for the two-sample case.