Hostname: page-component-745bb68f8f-d8cs5 Total loading time: 0 Render date: 2025-01-07T18:32:24.864Z Has data issue: false hasContentIssue false
  • English
  • Français

Test Skewness and Kurtosis as Functions of Item Parameters

Published online by Cambridge University Press:  01 January 2025

William S. Ray ,
John D. Hundleby  and
Donald A. Goldstein
William S. Ray
Affiliation:
The Woman's College of the University of North Carolina
John D. Hundleby
Affiliation:
University of Illinois
Donald A. Goldstein
Affiliation:
General Dynamics Corporation
Get access Rights & Permissions [Opens in a new window]

Abstract

Indexes of skewness and kurtosis for a test-score distribution are expressed in terms of item parameters. Both are shown to depend, in part, on item means, variances, and covariances. The index of skewness depends also on trivariances. A trivariance is a product moment involving first powers of deviation scores for three items. The index of kurtosis depends on quadrivariances, as well as trivariances. A quadrivariance is a product moment involving first powers of deviation scores for four items. Empirical data are presented for responses of groups of subjects to 25 triads and 25 tetrads of items from five tests.

Type
Original Paper
Information
Psychometrika , Volume 27 , Issue 1 , March 1962 , pp. 39 - 47
Copyright
Copyright © 1962 The Psychometric Society

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

*

Certain parts of this article represent the results of doctoral research conducted by Hundleby and Goldstein under the direction of Ray in the Department of Psychology at Pennsylvania State University. The authors are indebted to Professor Lester Guest and Professor William Lepley for their supervisory assistance in the final stages of the two dissertations during the absence of the senior author.

References

Bahadur, R. R. Probability and statistics on item analysis and classification problems; a representation of the joint distribution of responses ton dichotomous items, Texas: Air University School of Aviation Medicine, USAF, Randolph AFB, 1959.Google Scholar
Guilford, J. P. Psychometric methods (2nd ed.), New York: McGraw-Hill, 1954.Google Scholar
Gulliksen, H. The theory of mental tests, New York: Wiley, 1950.CrossRefGoogle Scholar
Lazarsfeld, P. F. The algebra of dichotomous systems. (Multilithed report) June, 1960.Google Scholar