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ON THE INTERRELATED NATURE OF THE MULTIVARIATE STATISTICS USED IN DISCRIMINATORY ANALYSIS
Author(s) -
Porebski Olgierd R.
Publication year - 1966
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1966.tb00368.x
Subject(s) - mathematics , statistics , statistic , test statistic , multivariate normal distribution , scalar (mathematics) , statistical hypothesis testing , covariance , a priori and a posteriori , notation , multivariate statistics , covariance matrix , discriminant function analysis , econometrics , philosophy , geometry , arithmetic , epistemology
This paper is concerned with discriminatory analysis involving two populations having equal a priori probabilities and a common covariance matrix and normal distribution. It is thus limited to a simple problem of discrimination to which a number of different solutions were proposed during the early period in the development of the subject. These well‐known results are presented here under one heading and in common notation. The paper begins with a discussion of some alternative logical ways of formulating the problem; then it shows the various statistical methods of deriving a discriminant function; finally, it exhibits the interrelated nature of the statistics which may be used in the test of significance. Each statistic is expressed as a scalar product of the same vector of differences between p pairs of means and a vector of discriminatory coefficients which varies only in length.