On data-based selection of summary measures from repeated measurements

Abstract

Univariate analysis of variance of a good summary measure, or two, may provide a simple and effective way of analyzing repeated measurements. It is shown here that selection of a linear summary measure on the basis of inspection of the total sample of response curves, leads to valid F-tests in the subsequent analysis of variance. The selection may also be based on residuals from a base model, rather than on the raw data. The treatments should, however, be blinded in this summary measure selection step, that is, the inspection of the sample of curves (or residuals) and the selection of the summary measure may not rely on which responses stem from which treatment groups. It is advocated as a convenient and often effective method to use the first principal component from the total sample of curves as the first summary measure. The main mathematical result of the paper is a simple proof of the validity of the F-tests for linear summary measures selected in this way, provided data are multivariate normally distributed. Alternatively, permutation tests may be used to provide a distribution free reference distribution for the F-statistic. Two examples illustrate the method.