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Maximizing Predictive Efficiency for a Fixed Total Testing Time

Published online by Cambridge University Press:  01 January 2025

Calvin W. Taylor
Calvin W. Taylor*
Affiliation:
University of Utah
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Abstract

For any fixed total time of testing it is possible, through proper item-and-time allotment, to combine tests into a battery so that the multiple correlation with a pre-assigned criterion will be maximized. By holding constant the ratio of the length in number of items to the time length for each test, a set of general equations has been derived which will yield this maximum value of the multiple R and will enable one to determine, in any given case, the optimal fraction of total testing time that should be devoted to each type of test under consideration. The set of general equations is applied to a two-test-battery problem to obtain the optimal length of each type of test for one hour total testing time. If two other tests had been selected for the two-test sample problem, different subdivisions of the total time would generally occur. The manner in which the results would change when using other tests with different initial reliability, validity, and intercorrelation values is briefly presented. Some general implications of this method of battery development are also discussed.

Type
Original Paper
Information
Psychometrika , Volume 15 , Issue 4 , December 1950 , pp. 391 - 406
Copyright
Copyright © 1950 The Psychometric Society

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Footnotes

*

The writer is indebted to Max Woodbury for his assistance and especially to Dr. N. J. F. Van Steenberg and Dr. Anna S. Henriques, who provided valuable guidance and aid in the development of the solution to this problem. This paper is a revision of a thesis submitted in 1939 at the University of Utah in partial fulfillment of the requirements for the master's degree.

†

Horst, Paul. Determination of optimal test length to maximize the multiple correlation. Psychomstrika, 1949, 14, 79–88.