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Predicted Differences and Differences between Predictions

Published online by Cambridge University Press:  01 January 2025

William G. Mollenkopf
William G. Mollenkopf*
Affiliation:
Educational Testing Service
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Abstract

When K tests are given to N individuals, and for each individual there are two criterion measures, then (1) the multiple regression weight to be applied to the standard score for each test to predict the criterion-difference score equals the difference of the weights for predicting each criterion separately; (2) the difference between the predicted scores equals the predicted difference (each test being assigned the appropriate multiple regression weight); (3) the square of the multiple correlation between predicted and actual criterion-difference scores equals the sum of squares of the multiple correlations of the battery with each criterion less the product of these correlations and the correlation between predicted scores all divided by twice the quantity one minus the criterion intercorrelation; and (4) the variance of errors of estimating the criterion-difference score equals the sum of the variances of errors of estimating each criterion score minus twice the criterion intercorrelation, plus twice the correlation between predicted scores multiplied by the product of the square root of one minus the variance of errors of estimating one criterion and the corresponding square root for the second criterion.

Type
Original Paper
Information
Psychometrika , Volume 15 , Issue 4 , December 1950 , pp. 409 - 417
Copyright
Copyright © 1950 The Psychometric Society

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Footnotes

*

The author wishes to express his appreciation for the suggestions and guidance given by Dr. Harold Gulliksen in the preparation of this article. He also wishes to acknowledge the helpful comments of Dr. Paul Horst and Dr. Ledyard Tucker on certain phases of the development.

References

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