Robust analysis of within-unit variances in repeated measurement experiments

The objective of some experiments is to compare the within-unit variances of two or more treatments, products, or techniques. In this situation, a repeated measurement design involving a random effects model, with possibly heterogeneous variances, is appropriate. Under the assumption that the random errors have a normal or a multivariate t-distribution, this design was analyzed in Chinchilli, Esinhart, and Miller (1995, Biometrics 51, 215-216). However, the resulting methodology is quite vulnerable to skewness and outliers. We propose two distribution-free procedures that are quite robust for balanced designs when the number of repeated measurements is the same for all units and for all treatments. We then show how these procedures are modified to handle unbalanced situations. We illustrate the methodology with an example from a trial comparing serum cholesterol measurements from a routine laboratory analyzer with those of a standardized method.