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Some Remarks on Failure to Meet Assumptions in Discriminant Analyses

Published online by Cambridge University Press:  01 January 2025

Richard S. Melton
Richard S. Melton*
Affiliation:
The Psychological Corporation
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Abstract

The linear discriminant function and the generalized distance function, two special cases of discriminant technique, require multivariate normality and homogeneous variance-covariance matrices, and hence utilize only mean differences among groups. The more general methods can also utilize differences in variances and/or covariances. Tables are given showing the discriminatory value of differences in means, variances, and intercorrelations, taken singly. Equations which utilize all such differences are given for the normal multivariate distribution.

Type
Original Paper
Information
Psychometrika , Volume 28 , Issue 1 , March 1963 , pp. 49 - 53
Copyright
Copyright © 1963 The Psychometric Society

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References

Anderson, T. W. Classification by multivariate analysis. Psychometrika, 1951, 16, 31–50.CrossRefGoogle Scholar
Anderson, T. W. Introduction to multivariate statistical analysis, New York: Wiley, 1958.Google Scholar
Lehman, E. L. Theory of hypothesis testing, Berkeley: Univ. Calif. Press, 1949.Google Scholar
Lubin, A. Linear and nonlinear discriminating functions. Brit. J. Psychol., Statist. Sect., 1950, 3, 90–104.CrossRefGoogle Scholar
Neyman, J. and Pearson, E. S. On the use and interpretation of certain test criteria for purposes of statistical inference. Biometrika, 1928, 20A, 175–240.Google Scholar
Rao, C. R. Advanced statistical methods in biometric research, New York: Wiley, 1952.Google Scholar
Rulon, P. J. Distinctions between discriminant analysis and regression analysis and a geometric interpretation of the discriminant function. Harvard Educ. Rev., 1951, 21, 80–90.Google Scholar
Rulon, P. J. et al. The profile problem: a methodological study of the interpretation of multiple test scores, Cambridge, Mass.: Educational Research Corporation, 1954.Google Scholar
Tatsuoka, M. M. and Tiedeman, D. V. Discriminant analysis. Rev. Ed. Res., 1954, 24, 402–420.Google Scholar
Von Mises, R. On the classification of observation data into distinct groups. Ann. math. Statist., 1945, 16, 68–73.CrossRefGoogle Scholar
Welch, B. L. Note on discriminant functions. Biometrika, 1939, 31, 218–220.Google Scholar