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On the Theory of Test Discrimination

Published online by Cambridge University Press:  01 January 2025

George A. Ferguson
George A. Ferguson*
Affiliation:
McGill University
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Abstract

This paper discusses the properties of distributions of test scores and advances the view that the properties of the distribution should depend on the function which the test is intended to perform. A theory of test discrimination is developed which defines discriminatory capacity in terms of the number of relations of difference established by the operation of administering a test of k items to a sample of n individuals. A simple proof is presented which indicates that maximum discrimination between individuals is achieved when tests are constructed to yield distributions of the rectangular form. A coefficient of test discrimination is developed. The problem of obtaining in practice distributions approximating to the rectangular form is briefly discussed.

Type
Original Paper
Information
Psychometrika , Volume 14 , Issue 1 , March 1949 , pp. 61 - 68
Copyright
Copyright © 1949 The Psychometric Society

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Footnotes

*

This paper was prepared under the auspices of the Defence Research Board, Ottawa, Canada.

References

Campbell, Norman Rober. An account of the principles of measurement and calculation (pp. 293–293). London: Longman's, Green and Co. Ltd., 1928.Google Scholar
Ferguson, George A. The reliability of mental tests (pp. 150–150). London: University of London Press, Ltd., 1941.Google Scholar
Gulliksen, Harol. The relation of item difficulty and inter-item correlation to test variance and reliability. Psychometrika, 1945, 10, 79–91.CrossRefGoogle Scholar
Jackson, R. W. B. and Ferguson, George A. A functional approach in test construction. Educational and Psychological Measurement, 1943, 3, 23–28.CrossRefGoogle Scholar