A canonical form of Anderson's classification statistic

A canonical reduction of Anderson's Classification Statistic in the case of two multivariate normal populations with different means and the same covariance matrix is obtained in this paper. The statistic and a similar statistic that arise in the estimation of relative potency of a new drug, using a composite response, are expressed in terms of χ², non-central χ^2- and normal variables. The moments of Anderson's statistic are derived and used for obtaining an asymptotic normal approximation to the chance of misclassification.