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A Test of the Hypothesis that Cronbach's Alpha or Kuder-Richardson Coefficent Twenty is the Same for Two Tests

Published online by Cambridge University Press:  01 January 2025

Leonard S. Feldt*
Affiliation:
University of Iowa

Abstract

An approximate statistical test is derived for the hypothesis that the reliability coefficients (Cronbach's α) associated with two measurement procedures are equal. Control of Type I error is investigated by comparing empirical sampling distributions of the test statistic with the theoretical model derived for it. The effect of platykurtosis in the test-score distribution on the test statistic is also considered.

Type
Original Paper
Copyright
Copyright © 1969 The Psychometric Society

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References

Cook, D. L. A replication of Lord's study of skewness and kurtosis of observed test-score distributions. Educational and Psychological Measurement, 1959, 19, 8187.CrossRefGoogle Scholar
Cronbach, L. J. Coefficient alpha and the internal structure of tests. Psychometrika, 1951, 16, 297334.CrossRefGoogle Scholar
Feldt, L. S. The approximate sampling distribution of Kuder-Richardson reliability coefficient twenty. Psychometrika, 1965, 30, 357370.CrossRefGoogle ScholarPubMed
Hogg, R. V., & Craig, A. T. Introduction to mathematical statistics, 2nd ed., New York: Macmillan, 1965.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, 221238.CrossRefGoogle Scholar
Kristof, W. Testing differences between reliability coefficients. The British Journal of Mathematical and Statistical Psychology, 1964, 17, 105111.CrossRefGoogle Scholar
Kuder, G. F., & Richardson, M. W. The theory of the estimation of test reliability. Psychometrika, 1937, 2, 151160.CrossRefGoogle Scholar
Lord, F. M. A survey of observed test-score distributions with respect to skewness and kurtosis. Educational and Psychogical Measurement, 1955, 15, 383389.CrossRefGoogle Scholar
Paulson, E. An approximate normalization of the analysis of variance distribution. Annals of Mathematical Statistics, 1942, 13, 233235.CrossRefGoogle Scholar
Schumann, D. E. W., & Bradley, R. A. The comparison of the sensitivities of similar experiments: Theory. Annals of Mathematical Statistics, 1957, 28, 902920.CrossRefGoogle Scholar