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The Maximum Expected Correlation Between Two Multiple-Choice Tests

Published online by Cambridge University Press:  01 January 2025

Paul Horst
Paul Horst*
Affiliation:
University of Washington
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Abstract

A formula is derived which gives the maximum expected correlation between two multiple-choice tests as a function of the distributions of proportions correct for the items in the two tests and the probability of chance success. The formula is similar to one derived by Carroll based on “true” item difficulties. A numerical example is provided.

Type
Original Paper
Information
Psychometrika , Volume 19 , Issue 4 , December 1954 , pp. 291 - 296
Copyright
Copyright © 1954 The Psychometric Society

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References

Carroll, J. B. The effect of difficulty and chance success on correlations between items or between tests. Psychometrika, 1945, 10, 1–19CrossRefGoogle Scholar
Ferguson, G. A. The factorial interpretation of test difficulty. Psychometrika, 1941, 6, 323–329CrossRefGoogle Scholar
Plumlee, L. B. The effect of difficulty and chance success on item-test correlation and on test reliability. Psychometrika, 1952, 17, 69–86CrossRefGoogle Scholar