A Power Comparison of the Welch-James and Improved General Approximation Tests in the Split-Plot Design

Power for the improved general approximation (IGA) and Welch-James (WJ) tests of the within-subjects (trials) main effect and the within-subjects × between-subjects (groups × trial) interaction was estimated for a design with one between- and one within-subjects factor. The distribution of the data had two levels: multivariate normal and multivariate lognormal Power estimates for conditions in which there were between-groups differences in dispersion matrices showed that, for both effects, there were conditions in which the IGA test was more powerful and conditions in which the WJ test was more powerful. The power advantage for the IGA test tended to be fairly small, whereas the power advantage for the WJ test was quite large in many conditions. Furthermore, the number of conditions favoring the WJ test was much larger than the number of conditions favoring the IGA test. Power for IGA, WJ, ε̃-adjusted, and MANOVA tests was compared for conditions in which dispersion matrices were equal across groups. Results indicate that little if any power was sacrificed by using WJ or IGA tests in place of MANOVA or ε̃-adjusted tests.