Hostname: page-component-599cfd5f84-56l7z Total loading time: 0 Render date: 2025-01-07T06:13:05.531Z Has data issue: false hasContentIssue false
  • English
  • Français

A Test of the Hypothesis that Cronbach's Alpha Reliability Coefficient is the Same for Two Tests Administered to the Same Sample

Published online by Cambridge University Press:  01 January 2025

Leonard S. Feldt
Leonard S. Feldt*
Affiliation:
University of Iowa
*
Requests for reprints should be sent to Leonard S. Feldt, College of Education, Division of Educational Psychology, Measurement & Statistics, The University of Iowa, Iowa City, Iowa 52242.
Get access Rights & Permissions [Opens in a new window]

Abstract

In measurement studies the researcher may wish to test the hypothesis that Cronbach’s alpha reliability coefficient is the same for two measurement procedures. A statistical test exists for independent samples of subjects. In this paper three procedures are developed for the situation in which the coefficients are determined from the same sample. All three procedures are computationally simple and give tight control of Type I error when the sample size is 50 or greater.

Keywords

coefficient alphareliability coefficientstests of significance
Type
Original Paper
Information
Psychometrika , Volume 45 , Issue 1 , March 1980 , pp. 99 - 105
Copyright
Copyright © 1980 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

The author is indebted to Jerry S. Gilmer for development of the computer programs used in this study.

References

Bose, S. The distribution of the ratio of variances of two samples drawn from a given normal bivariate correlated population. Sankhyā: The Indian Journal of Statistics, 1935, 1, 65–72.Google Scholar
Feldt, L. S. The approximate sampling distribution of Kuder-Richardson reliability coefficient twenty. Psychometrika, 1965, 30, 357–370.CrossRefGoogle ScholarPubMed
Feldt, L. S. A test of the hypothesis that Cronbach’s alpha or Kuder-Richardson coefficient twenty is the same for two tests. Psychometrika, 1969, 34, 363–373.CrossRefGoogle Scholar
Finney, D. J. The distribution of the ratio estimates of the two variances in a sample from a normal bivariate population. Biometrika, 1938, 30, 190–192.Google Scholar
Hakstian, A. R. & Whalen, T. E. A k-sample significance test for independent alpha coefficients. Psychometrika, 1976, 41, 219–231.CrossRefGoogle Scholar
Hogg, R. V. & Craig, A. T. Introduction to mathematical statistics, 3rd ed., (pp. 187–188). New York: Macmillan, 1970.Google Scholar
Kendall, M. G. & Stuart, A. The advanced theory of statistics, 3rd ed., London: Charles Griffin, 1969.Google Scholar
Kristof, W. The statistical theory of stepped-up reliability coefficients when a test has been divided into several equivalent parts. Psychometrika, 1963, 28, 221–238.CrossRefGoogle Scholar
Odell, P. L. & Feiveson, A. H. A. A numerical procedure to generate a sample covariance matrix. Journal of the American Statistical Association, 1966, 61, 199–203.CrossRefGoogle Scholar
Pitman, E. J. G. A note on normal correlation. Biometrika, 1939, 31, 9–12.CrossRefGoogle Scholar