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On the Standard Length of a Test

Published online by Cambridge University Press:  01 January 2025

Max A. Woodbury
Max A. Woodbury*
Affiliation:
Institute for Advanced Study and University of Michigan
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Abstract

(1) A new descriptive parameter for tests, the standard length, is defined and related to reliability, correlation, and validity by means of simplified versions of known formulas. (2) The standard error of measurement is found to be related in simple fashion to the amount of information in a test in the sense of R. A. Fisher. The amount of information is computable as the test length divided by the standard length of the test. (3) The invariant properties of the standard length of a test under changes in length are discussed and proved. Similar results for the correlation coefficient corrected for attenuation and the index of validity are indicated.

Type
Original Paper
Information
Psychometrika , Volume 16 , Issue 1 , March 1951 , pp. 103 - 106
Copyright
Copyright © 1951 The Psychometric Society

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Footnotes

*

The research covered by this note was supported by the Office of Naval Research.

†

Fisher, R. A. Statistical Methods for Research Workers, 10th Edition. London: Oliver and Boyd, 1946, p. 346.

‡

Shannon, C. E. A mathematical theory of communication. Bell System Technical Journal, 1948, 27, 379–423; 623–656.