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Test Scores Examined with the Lexis Ratio

Published online by Cambridge University Press:  01 January 2025

Harold A. Edgerton  and
Kenneth F. Thomson
Harold A. Edgerton
Affiliation:
The Ohio State University
Kenneth F. Thomson
Affiliation:
The Ohio State University
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Abstract

The Lexis Ratio is discussed in its application to distributions of test scores where the items of the test can be assumed to be of equal difficulty. The ratio indicates the extent to which inter-individual variation operates as a source of the variance. The concept is related to the Lexis, Bernoulli, and Poisson distributions and illustrated by urn schemata. The Ratio is applied to the scores of 560 university freshmen on the Robinson Reading Test. The relation of the Lexis Ratio to the Kuder-Richardson estimation of reliability is also discussed and the latter authors' case IV is rewritten explicitly in terms of the Ratio.

Type
Original Paper
Information
Psychometrika , Volume 7 , Issue 4 , December 1942 , pp. 281 - 288
Copyright
Copyright © 1942 The Psychometric Society

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References

* Robinson, F. P. and Hall, P., Studies of higher-level reading abilities, J. Educ. Psychol., 1941, 32, 241-252.

† These data were made available through the courtesy of L. L. Love, Junior Dean of the College of Education.

* Kuder, G. F., and Richardson, M. W. The theory of the estimation of test reliability, Psychometrika, 1937, 2, 151-160.