Computer Contribution 39: FORTRAN IV Program for Generalized Statistical Distance and Analysis of Covariance Matrices for the CDC 3600 Computer

Heterogeneity in sample covariance matrices, deriving from differences in the orientation of major axes of the ellipsoids of scatter, may be of common occurrence. The generalized test of equality of covariance matrices will give a significant result in instances where the scatter ellipsoids are (1) unequally inflated, although identically oriented, (2) identically inflated but differently oriented and (3) a combination of these conditions. Equations to the major axes of a scatter ellipsoid of morphologic variables represent growth patterns in the variables. An approximate application of the asymptotic test developed by T. A. Anderson is used here to identify structure of the heterogeneity between two covariance matrices where such exists. The foregoing procedures are preliminary to a treatment of generalized distances in which the path taken by the computer program is decided by structure of the covariance matrices of the samples. Depending on the nature of the covariance matrices either the Mahanolobis' generalized distance is computed or the Anderson-Bahadur distance for heterogeneous covariance matrices. Tests of significance of the results are provided and the linear discriminant function coefficients produced as a by-product.