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Eta, Disco, Odisco, and F

Published online by Cambridge University Press:  01 January 2025

Louis Guttman
Louis Guttman*
Affiliation:
The Hebrew University of Jerusalem The Israel Institute of Applied Social Research
*
Requests for reprints should be sent to James C. Lingoes, 2664 Lowell Road, Ann Arbor, MI 48103.
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Abstract

Two coefficients are proposed for measuring the extent of overlap in distributions as a direct function of the variance between the arithmetic means (“disco” and “odisco”). They are designed to answer such questions as: “Given the value of a numerical variable x, to which population should an individual be assigned so that minimum error would be incurred?” This is just the reverse of the question addressed by ANOVA. These coefficients are shown to be analytic in x and they are related to Pearson's eta and Fisher's F. Extensions of these coefficients (designed for univariate, one-way discrimination) to k-way and multivariate discriminant analysis and measurement of “interaction” are suggested.

Keywords

discriminant analysisdiscriminant coefficientsFetamonotonicity coefficientsconsistent statisticscumulative scienceANOVAsize of effectinteraction
Type
Original Paper
Information
Psychometrika , Volume 53 , Issue 3 , September 1988 , pp. 393 - 405
Copyright
Copyright © 1988 The Psychometric Society

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