ABSTRACT
This chapter outlines the development of the mixed-model approach. It reviews analysis of within-subjects designs with two levels. The chapter then considers designs with three levels. It reviews designs with more than three levels. The logic behind the multivariate approach for three levels is based on the formation of variables as in the two-level case. However, a single difference score cannot be used to explain all the possible patterns of mean differences that could occur among the three levels, as was possible in the two-level case. The determinant of a matrix is an ordinary number, which distills the multivariate information in a matrix into a single piece of information. Determinants play an important role in multivariate statistics because the determinant can reflect the "generalized variance" of more than one variable. Measures of effect are frequently of interest in within-subjects designs, just as they are in between-subjects designs.
