Orthogonal polynomials,repeated measures,and SPSS

We discuss the construction of discrete orthonormal polynomials, using MAPLE procedures. We also study two important applications of these polynomials in statistics: in multiple linear regression and in repeated measures analysis. In particular, it is argued that the tests given by SPSS for linear and other trends in a within-subject factor are inefficient. Examples are given, including two (from psychology and medicine, respectively) which involve repeated measures and SPSS. Extensive tables of discrete orthornormal polynomials are given in the Appendix.