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The Factorial Interpretation of Test Difficulty

Published online by Cambridge University Press:  01 January 2025

George A. Ferguson
George A. Ferguson*
Affiliation:
Department of Educational Research, University of Toronto
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Abstract

This paper discusses the influence of test difficulty on the correlation between test items and between tests. The greater the difference in difficulty between two test items or between two tests the smaller the maximum correlation between them. In general, the greater the number of degrees of difficulty among the items in a test or among the tests in a battery, the higher the rank of the matrix of intercorrelations; that is, differences in difficulty are represented in the factorial configuration as additional factors. The suggestion is made that if all tests included in a battery are roughly homogeneous with respect to difficulty existing hierarchies will be more clearly defined and meaningful psychological interpretation of factors more readily attained.

Type
Original Paper
Information
Psychometrika , Volume 6 , Issue 5 , October 1941 , pp. 323 - 329
Copyright
Copyright © 1941 The Psychometric Society

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References

* The correlation coefficient used to indicate the relation between two dichotomously scored test items is arbitrary. The formula given here is identical with the coefficient ø commonly used in dealing with fourfold point surfaces.

* Cyril Burt. The factors of the mind. London: University of London Press, 1940.