On the distribution of quadratic forms and applications in the analysis of repeated measurements

Abstract

In this paper a unified approach is given to the distribution of scalar quadratic forms for dependent variables. Necessary and sufficient conditions are found for the sums of squares of the various hierarchical layers in ANOVA to be distributed as multiples of chi-square variables. Results concerning the usual univariate F-tests in ANOVA of repeated measurements are derived as a special case.

Keywords:

• Analysis of variance compound symmetry Spherety
• Split-plot design