Variable error: variance-covariance heterogeneity, block size and type L error rates

The degree to which blocked (VE) data satisfies the assumptions of compound symmetry required for a repeated measures ANOVA was studied. Monte Carlo procedures were used to study the effect of violation of this assumption, under varying block sizes, on the Type l error rate. Populations of 10,000 subjects for each of two groups, the underlying variance-covariance matrices reflecting a specific condition of violation of the homogeneity of covariance assumptions, was generated based on each of three actual experimental data sets. The data were blocked in various ways, VE calculated, and subsequently analyzed by a repeated measures ANOVA. The complete process was replicated for four covariance homogeneity conditions for each of the three data sets, resulting in a total of 22,000 simulated experiments. Results indicated that the Type l error rate increases as the degree of heterogeneity within the variance-covariance matrices increases when raw (unblocked) data are analyzed. With VE, the effects of within-matrix heterogeneity on the Type l error rate are inconclusive. However, block size does seem to affect the probability of obtaining a significant interaction, but the nature of this relationship is not clear as there does not appear to be any consistent relationship between the size of the block and the probability of obtaining significance. For both raw and VE data there was no inflation in the number of Type l errors when the covariances within a given matrix were homogeneous, regardless of the differences between the group variance-covariance matrices.