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A K-Sample Significance Test for Independent Alpha Coefficients

Published online by Cambridge University Press:  01 January 2025

A. Ralph Hakstian  and
Thomas E. Whalen
A. Ralph Hakstian*
Affiliation:
University of British Columbia
Thomas E. Whalen
Affiliation:
University of British Columbia
*
Requests for reprints should be sent to A. Ralph Hakstian, Department of Psychology, University of British Columbia, Vancouver, British Columbia, Canada.
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Abstract

The earlier two-sample procedure of Feldt [1969] for comparing independent alpha reliability coefficients is extended to the case of K ≥ 2 independent samples. Details of a normalization of the statistic under consideration are presented, leading to computational procedures for the overall K-group significance test and accompanying multiple comparisons. Results based on computer simulation methods are presented, demonstrating that the procedures control Type I error adequately. The results of a power comparison of the case of K = 2 with Feldt’s [1969] F test are also presented. The differences in power were negligible. Some final observations, along with suggestions for further research, are noted.

Keywords

reliabilityinternal consistencycomparison of reliability coefficients
Type
Original Paper
Information
Psychometrika , Volume 41 , Issue 2 , June 1976 , pp. 219 - 231
Copyright
Copyright © 1976 The Psychometric Society

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Footnotes

The authors gratefully acknowledge the assistance of Michael E. Masson, in the computations performed, and of Leonard S. Feldt, in suggesting the data generation procedures used in the study. In addition, the authors thank James Zidek and the Institute of Applied Mathematics and Statistics, University of British Columbia, for advice concerning some of the theoretical development.

References

Reference Note

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Wilson, E. B., and Hilferty, M. M. The distribution of chi-square. Proceedings of the National Academy of Science, 1931, 17, 684–688.CrossRefGoogle ScholarPubMed
Cronbach, L. J. Coefficient alpha and the internal structure of tests. Psychometrika, 1951, 16, 297–334.CrossRefGoogle 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
Hays, W. L. Statistics for psychologists, 1963, New York: Holt, Rinehart & Winston.Google Scholar
Koehler, R. A. A comparison of the validities of conventional choice testing and various confidence marking procedures. Journal of Educational Measurement, 1971, 8, 297–303.CrossRefGoogle 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
Li, C. C. Introduction to experimental statistics, 1964, New York: McGraw-Hill.Google Scholar
Lord, F. M. Sampling fluctuations resulting from the sampling of test items. Psychometrika, 1955, 20, 1–22.CrossRefGoogle Scholar
Lord, F. M., and Novick, M. Statistical theories of mental test scores, 1968, Reading, Mass.: Addison-Wesley.Google Scholar
Marascuilo, L. A. Large-sample multiple comparisons. Psychological Bulletin, 1966, 65, 280–290.CrossRefGoogle ScholarPubMed
Paulson, E. An approximate normalization of the analysis of variance distribution. Annals of Mathematical Statistics, 1942, 13, 233–235.CrossRefGoogle Scholar
Rao, C. R. Linear statistical inference and its applications, 1965, New York: Wiley.Google Scholar
Scheffé, H. The analysis of variance, 1959, New York: Wiley.Google Scholar
Wilson, E. B., and Hilferty, M. M. The distribution of chi-square. Proceedings of the National Academy of Science, 1931, 17, 684–688.CrossRefGoogle ScholarPubMed