Discrimination in the case of zero mean differences

and p2(x) the same proportion of the probability for the second group. In the case of multivariate normal populations with the same variance-covariance matrix, this criterion is equivalent to the linear discriminant function, but the discriminating function becomes of the second degree if the dispersion matrices differ (Smith, 1946-47). If the mean differences between two groups are all zero, no discrimination is of course possible in the normal case with equal dispersion, but it is worth examining this special situation in the case of unequal dispersions, as it may sometimes arise in practice, as will be shown below by an example.