Type I error rates for Huynh's general approximation and improved general approximation tests

For split plot designs exact univariate F tests of the within‐subjects main effect and the between × within interaction are based on the assumption of multi‐sample sphericity. Type I error rates are reported for three tests designed for use when multisample sphericity is violated: the general approximation test, the improved general approximation test and a revised improved general approximation test. The results indicate that when sample sizes are unequal and dispersion matrices are unequal, using the improved general approximation or revised improved general approximation test of the interaction allows better control of the Type I error rate than does the ‐adjusted test.