New multivariate tests for data with an inherent structure

In this paper a new class of exact parametric tests for multivariate normal data based on the theory of spherical distributions (FANG and ZHANG, 1990) is proposed. These tests maintain the α level in each case. They are advantageous with respect to power when special restrictions such as factorial structures are given in the data. The scope of the new theory is very broad so that it can be adapted to many different situations. Especially, it allows an inclusion of data-preprocessing in the analysis without influencing the error of the first kind. Thus the approach presented in the paper provides a link between exploratory and confirmatory techniques. The method can be used successfully with high-dimensional samples of small sample size or with highly correlated variables. In such cases classical multivariate analysis would lead to very unstable results.