ABSTRACT
Example 8.7.1. Consider Example 5.3.1. Assume that the data pertaining to 1971, 1972 constitute two independent samples from two six-variate normal populations with mean vectors, µ1, µ2 and positive definite covariance matrices S1, S2, respectively. We are interested in testing H0: S1=S2 when µ1, µ2 are unknown. Here N1=N2=27. From (8.190),
since asymptotically
for
Hence we reject the null hypothesis H0. Since the hypothesis is rejected our method of solution of Example 7.2.1 is not appropriate. It is necessary to test the equality of mean vectors when the covariance matrices are unequal, using the Behrens-Fisher approach.
