Estimation of Box's ε for low- and high-dimensional repeated measures designs with unequal covariance matrices.

We present new inference methods for the analysis of low- and high-dimensional repeated measures data from two-sample designs that may be unbalanced, the number of repeated measures per subject may be larger than the number of subjects, covariance matrices are not assumed to be spherical, and they can differ between the two samples. In comparison, we demonstrate how crucial it is for the popular Huynh-Feldt (HF) method to make the restrictive and often unrealistic or unjustifiable assumption of equal covariance matrices. The new method is shown to maintain desired α-levels better than the well-known HF correction, as demonstrated in several simulation studies. The proposed test gains power when the number of repeated measures is increased in a manner that is consistent with the alternative. Thus, even increasing the number of measurements on the same subject may lead to an increase in power. Application of the new method is illustrated in detail, using two different real data sets. In one of them, the number of repeated measures per subject is smaller than the sample size, while in the other one, it is larger.