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The Theory of the Estimation of Test Reliability

Published online by Cambridge University Press:  01 January 2025

G. F. Kuder  and
M. W. Richardson
G. F. Kuder
Affiliation:
The University of Chicago
M. W. Richardson
Affiliation:
The University of Chicago
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Abstract

The theoretically best estimate of the reliability coefficient is stated in terms of a precise definition of the equivalence of two forms of a test. Various approximations to this theoretical formula are derived, with reference to several degrees of completeness of information about the test and to special assumptions. The familiar Spearman-Brown Formula is shown to be a special case of the general formulation of the problem of reliability. Reliability coefficients computed in various ways are presented for comparative purposes.

Type
Original Paper
Information
Psychometrika , Volume 2 , Issue 3 , September 1937 , pp. 151 - 160
Copyright
Copyright © 1937 The Psychometric Society

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Footnotes

*

The critical reader will reflect that, in addition, the investigator must report the range, or better, the variance of the group tested. The present study is not concerned with that matter.

References

* With certain assumptions as to the distribution of inter-itam correlations it would be possible to estimate, theoretically, the expected distribution of reliability coefficients thus to be computed. The most representative value (perhaps the mean) could then be taken as the best estimate and the problem thus solved. It is likely, however, that the solution would be enormously complicated by the possibilit. v that the matrix of inter-item coefficients would have a rank greater than one. See Mosier, Charles I., “A Note on Item Analysis and the Criterion of Internal Consistency,” Psychometrika, 1936, 1, pp. 275-282.

† Brownell Wm. A., “On the Accuracy with which Reliability May Be Measured by Correlating Test Halves,” J. Exper. Educ., 1933, 1, pp. 204-215.

‡ It should be mentioned that the main outlines of the simple argument in this article were derived independently by the two authors. In a chance conversation it developed that the two had reached similar conclusions by methods similar in principle.

* It should be noted that this definition of equivalence is more rigid than the one usually stated.

* Dunlap, J. W. and Kurtz, A. K., Handbook of Statistical Nomographs, Tables and Formulas, World Book Company, New York. Formula No. 46.