ABSTRACT
Most of univariate results in connection with design of experiments can be extended to the multivariate case. We consider here one-way and two-way classifications as examples.
One-Way Classification
Suppose we have r p-variate normal populations with the same positive definite covariance matrix S but with different mean vectors µi, i=1,…, r. We are interested here in testing the null hypothesis
Let xij=(xij1,…, xijp)', j=1,…, Ni(Ni>p), i=1,…, r, be a sample of size Ni from the ith p-variate normal population with mean µi and covariance matrix S. Define
A straightforward calculation shows that the likelihood ratio test of H0 rejects H0 whenever
where c depends on the level of significance of the test. Since
