Some Aspects of the Statistical Analysis of the 'Mixed Model'

This paper deals with the statistical analysis (both parametric and non-parametric) of 'mixed model' experiments. The general structure of such experiments involves n randomly chosen subjects who respond once to each of p distinct treatments. Thus the subject or block effects are random and treatment effects are fixed. The hypothesis of no treatment effects is considered under several different combinations of assumptions concerning the joint distribution of the observations corresponding to each of the particular subjects. For each situation, an appropriate test procedure is discussed and its properties studied. The different methods considered in the paper are illustrated in detail in two numerical examples. These examples have been chosen to illustrate the relative performances of the different test criteria for a situation in which the null hypothesis is essentially true (Example 1) and for a situation in which the null hypothesis is essentially false (Example 2). The reader may wish to begin by studying these examples for a better understanding of the theory. Finally, the section on examples contains algorithms for the efficient computation of the various test criteria. A computer program based on these algorithms has been written and can be made available to any interested persons.