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Theoretical Distributions of Optima for Univariate Discrimination of Random Data *
Author(s) -
Yarnold Paul R.,
Soltysik Robert C.
Publication year - 1991
Publication title -
decision sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.238
H-Index - 108
eISSN - 1540-5915
pISSN - 0011-7315
DOI - 10.1111/j.1540-5915.1991.tb00362.x
Subject(s) - univariate , linear discriminant analysis , discriminant , statistics , sample size determination , computer science , mathematics , econometrics , sample (material) , multivariate statistics , artificial intelligence , chemistry , chromatography
Optimal linear discriminant models maximize percentage accuracy for dichotomous classifications, but are rarely used because a theoretical framework that allows one to make valid statements about the statistical significance of the outcomes of such analyses does not exist. This paper describes an analytic solution for the theoretical distribution of optimal values for univariate optimal linear discriminant analysis, under the assumption that the data are random and continuous. We also present the theoretical distribution for sample sizes up to N = 30. The discovery of a statistical framework for evaluating the performance of optimal discriminant models should greatly increase their use by scientists in all disciplines.