A Preliminary Test for Discriminant Analysis Based on Small Samples

Consider two populations having p~variate normal distributions with a common variancecovariance matrix (N,(l1, 1) and N,(tt2, 1), say) where the parameters are to be estimated from small samples. Letting X denote the vector of observations on an experimental unit, whose origin is uncertain, a test is proposed for the null hypothesis, Ho: [X -Np(tt, 1) or X -Np(V2, 1)] against the alternative that X is distributed according to a third unspecified distribution. It is shown that the critical region can be selected so that its size is known to be between a and a/2, inclusive, for any desired value of a. The test is illustrated by an application to a taxonomy problem.