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Maximizing the validity of a unit-weight composite as a function of relative component lengths with a fixed total testing time

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Abstract

An explicit solution is given to the problem of assigning relative lengths to the subtests of a test so as to maximize the correlation of the unit weight composite with a specified criterion when the total testing time is fixed. This solution is valid and unique whenever it specifies nonnegative times for all variables. A step-down procedure is suggested for cases in which some of the testing times are zero. This procedure does not necessarily provide an optimal allocation. However in examples studied it is found to provide near optimum results. Algorithms are also developed for the determination of the least total testing time required to attain specified multiple and composite correlations. A numerical example is given illustrating the use of the unit weight procedure in combination with the regression weight algorithm.

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Authors and Affiliations

  1. University College of Wales, UK

    Paul H. Jackson

  2. Educational Testing Service, UK

    Melvin R. Novick

Authors
  1. Paul H. Jackson
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  2. Melvin R. Novick
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Additional information

Supported in part by the Personnel and Training Branch of the Office of Naval Research under Contrast Number 000-14-69C-0119, Melvin R. Novick, Principal Investigator. Reproduction, translation, publication, use and disposal in whole or in part by or for the United States Government is permitted.

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Jackson, P.H., Novick, M.R. Maximizing the validity of a unit-weight composite as a function of relative component lengths with a fixed total testing time. Psychometrika 35, 333–347 (1970). https://doi.org/10.1007/BF02310793

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  • DOI: https://doi.org/10.1007/BF02310793

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