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The Prediction of Averages

Published online by Cambridge University Press:  01 January 2025

William Meredith
William Meredith*
Affiliation:
University of California, Berkeley
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Abstract

Criterion measures are frequently obtained by averaging ratings, but the number and kind of ratings available may differ from individual to individual. This raises issues as to the appropriateness of any single regression equation, about the relation of variance about regression to number and kind of criterion observations, and about the preferred estimate of regression parameters. It is shown that if criterion ratings all have the same true score the regression equation for predicting the average is independent of the number and kind of criterion scores averaged.

Two cases are distinguished, one where criterion measures are assumed to have the same true score, and the other where criterion measures have the same magnitude of error of measurement as well. It is further shown that the variance about regression is a function of the number and kind of criterion ratings averaged, generally decreasing as the number of measures averaged increases. Maximum likelihood estimates for the regression parameters are derived for the two cases, assuming a joint normal distribution for predictors and criterion average within each subpopulation of persons for whom the same type of criterion average is available.

Type
Original Paper
Information
Psychometrika , Volume 28 , Issue 3 , September 1963 , pp. 239 - 258
Copyright
Copyright © 1963 The Psychometric Society

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