T²Tests, the Linear Two-Group Discriminant Function, and Their Computation by Linear Regression

Tests for redundancy of variables in linear two-group discriminant analysis are well known and frequently used. We give a survey of similar tests, including the one-sample T 2 as a special case, in the situation in which only the mean vector (but no covariance matrix) is available in one sample. Then we show that a relation between linear regression and discriminant functions found by Fisher (1936) can be generalized to this situation. Relating regression and discriminant analysis to a multivariate linear model sheds more light on the relationship between them. Practical and didactical advantages of the regression approach to T 2 tests and discriminant analysis are outlined.