Necessary and Sufficient Conditions for F Ratios in the L × J × K Factorial Design with Two Repeated Factors

Abstract

Assuming multivariate normality, a necessary and sufficient condition is derived for the validity of each F ratio in an L × J × K factorial design with repeated measurements on the last two factors. The condition is: C'Σ₁C = C'Σ₂C =…= C'Σ _L C = σ²I, where C is the contrast matrix representing the comparison of interest, and Σ _i , i = 1, 2, …, L, is a (JK) × (JK) population dispersion matrix.