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An Application of Confidence Intervals and of Maximum Likelihood to the Estimation of an Examinee's Ability

Published online by Cambridge University Press:  01 January 2025

Frederic M. Lord
Frederic M. Lord*
Affiliation:
Educational Testing Service
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Abstract

A mathematical definition of the theoretical relation between the examinee's actual responses to the test items and his “true ability” is selected. A maximum-likelihood solution is obtained for estimating the examinee's “true ability” from his responses to the items. The standard error of the maximum-likelihood estimate is obtained, its relation to the discriminating power of the test is pointed out, and some generalizations are drawn as to the optimum level of item difficulty. The Neyman-Pearson power function is applied to determine which of two psychological tests is the most powerful for the selection of “successful” examinees.

Type
Original Paper
Information
Psychometrika , Volume 18 , Issue 1 , March 1953 , pp. 57 - 76
Copyright
Copyright © 1953 The Psychometric Society

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Footnotes

*

The author is indebteded to Dr. John W. Tukey for helpful comments on a draft of the present manuscript.

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