Relative Efficiencies in the Multivariate Analysis of Repeated Measurements.

Abstract

Frequently in the life sciences, the scope of an experimental study is such that the application of several treatments to a single experimental unit will not alter the nature of that unit. When this occurs, the experimenter has a choice between applying some or all of the treatments to a given unit or selecting independent units to receive each treatment combination. The former choice leads to what is commonly referred to as a repeated measures design (RMD) while the latter choice results in a completely crossed r and omized design (CCRD). While much is known regarding the theory and analysis of a RMD, little attention has been given to a priori considerations for choosing a RMD over the corresponding CCRD. This is particularly true with respect to a multivariate analysis of repeated measurements. It is the objective of this research to provide the experimenter with a means for choosing between a RMD and CCRD. The specific goals of this research are to determine conditions under which a RMD, when analyzed multivariately, is more or less efficient than the corresponding CCRD and to formulate a means by which sample sizes for a RMD can be determined. Following the work of Cole and Grizzle (1966) and Timm (1975), a multivariate general linear model is developed for a K-factor RMD in which the factors are grouped into "within unit" and "between unit" factors. A corresponding CCRD general linear model is provided and the two models are formulated so as to better compare the relative efficiency of the two designs. The efficiency of the two designs is compared by means of the ratio of expected squared half lengths of Scheffe'-type confidence intervals. By comparing relative efficiency with respect to pairwise comparisons, an algorithm is presented for determining sample sizes in the multivariate analysis of a single-factor RMD. Numerical and analytical results suggest that a RMD will often be more efficient than its CCRD counterpart for comparisons involving "within unit" treatment combinations. However, for comparisons restricted to "between unit" factors, the RMD will, in almost all cases, be less efficient than the corresponding CCRD.