Circularity and multiple comparisons in repeated measure designs

In an RS × T design, MS T /MS RST is distributed as F with the usual df only if the population variance‐covariance matrix has ε = 1.0. This same condition is needed for the usual multiple comparison procedures to be accurate. When testing K — 1 orthogonal contrasts the conventional estimate of the variance of the contrasts is the mean of the K — 1 different true variance estimates. This condition also is observed when testing all pairwise contrasts. A Monte Carlo study demonstrates that with reasonable ns , little power is lost using a robust general matrix solution. The conventional solution will often be inaccurate when ε < 1.0.