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Randomly Parallel Tests and Lyerly's Basic Assumption for the Kuder-Richardson Formula (21)

Published online by Cambridge University Press:  01 January 2025

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

The K-R (21) formula can be derived without recourse to the undesirable assumption that the test items are all indistinguishable.

Type
Original Paper
Information
Psychometrika , Volume 24 , Issue 2 , June 1959 , pp. 175 - 177
Copyright
Copyright © 1959 The Psychometric Society

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Footnotes

*

While Lyerly's assumptions may seem rather implausible for ordinary mental testing, they are highly appropriate for certain other situations—for example, for rating situations where no two subjects are rated by the same judges. Lyerly's results should be of real value in such situations. The present note deals only with the usual type of objective test, as do the references cited.

References

Lord, F. M. Sampling fluctuations resulting from the sampling of test items. Psychometrika, 1955, 20, 1–22.CrossRefGoogle Scholar
Lord, F. M. Tests of the same length do have the same standard error of measurement. Educ. psychol. Measmt, in press.Google Scholar
Lord, F. M. Statistical inferences about true scores. Psychometrika, 1959, 24, 1–17.CrossRefGoogle Scholar
Lyerly, S. B. The Kuder-Richardson formula (21) as a split-half coefficient, and some remarks on its basic assumption. Psychometrika, 1958, 23, 267–270.CrossRefGoogle Scholar