Exact t and F Tests for Analyzing Studies with Multiple Endpoints

SUMMARY The paper describes some methods of forming sum aggregates in multivariate analysis. These methods are useful for the statistical analysis of investigations with multiple endpoints. In particular, the sum statistics can be applied if differences between two or more populations have to be tested and a factorial structure of the means and covariances can be supposed. For this approach the calculation of principal components has great importance. The central mathematical problem is to construct statistics which permit exact t and F tests, i.e., tests keeping the error of first kind at the prescribed level. The paper is based on the theory of spherical matrix distributions treated extensively in the book by Fang and Zhang (1990, Generalized Multivariate Analysis). This paper refers to the problem of the analysis of high-dimensional observations which often occurs in clinical studies. We start from the proposal of O'Brien (1984) to use sum aggregates of the form P E Xi ~~~~~~~~~~~(1.1) i= i