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Variation in Test Validity with Variation in the Distribution of Item Difficulties, Number of Items, and Degree of their Intercorrelation

Published online by Cambridge University Press:  01 January 2025

Hubert E. Brogden
Hubert E. Brogden*
Affiliation:
Personnel Research Section The Adjutant General's Office
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Abstract

The relation between item difficulty distributions and the “validity” and reliability of tests is computed through use of normal correlation surfaces for varying numbers of items and varying degrees of item intercorrelations. Optimal or near optimal item difficulty distributions are thus identified for various possible item difficulty distributions. The results indicate that, if a test is of conventional length, is homogeneous as to content, and has a symmetrical distribution of item difficulties, correlation with a normally distributed perfect measure of the attribute common to the items does not vary appreciably with variation in the item difficulty distribution. Greater variation was evident in correlation with a second duplicate test (reliability). The general implications of these findings and their particular significance for evaluating techniques aimed at increasing reliability are considered.

Type
Original Paper
Information
Psychometrika , Volume 11 , Issue 4 , December 1946 , pp. 197 - 214
Copyright
Copyright © 1946 The Psychometric Society

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Footnotes

*

When expressed in terms of standard score scale values—not percentage correct

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