THE ROBUSTNESS OF THE ANALYSIS OF VARIANCE AND THE TUKEY WSD TEST UNDER VARIOUS PATTERNS OF HETEROGENEOUS VARIANCES

The WSD and F tests show the same response when the homogeneous variance assumption is violated. Both are robust when the ns are equal, but may be either seriously conservatively biased or seriously permissively biased when heterogeneous variances are combined with unequal ns. The use of equal ns is recommended for either test. There is no virtue in insisting that the F test be significant prior to conducting the WSD when the alternative to the null is μi ≠ μj. However, the conservative bias created by this procedure is small when K = 4; as is the permissive bias created by conducting both tests. For uniformly distributed μ’s, the two tests have very similar powers. This condition would not be expected for different arrangements of the μ’s.