For split plot designs exact univariate F tests of the within-subjects main effect are based on the assumption of multisample sphericity. Type I error rates and power are reported for the F test and two tests designed for use when multisample sphericity is violated: the $widetilde{xi}$-adjusted test and the Corrected Improved General Approximation(CIGA) test.The results indicate that even though the F test and the $widetilde{xi}$-adjusted test have better power than the CIGA test in some conditions, the F test and the $widetilde{xi}$-adjusted test do not control Type I error rates when the design is unbalanced and the F test dose not have a good control of Type I error rates when sphericity assumption is severely violated.