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On the theory of test discrimination

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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 ofk items to a sample ofn 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.

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

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Ferguson, G.A. On the theory of test discrimination. Psychometrika 14, 61–68 (1949).

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