Sage Journals: Discover world-class research

Abstract

Internal-consistency reliability coefficients that are Spearman-Brown extrapolations of the original observed coefficients must occasionally be compared. This might occur in a comparison of measurement procedures that need to be differentially shortened or lengthened in order to equalize their administration time. The effect on rating scale reliability of a training program for raters might also require such a comparison. A statistical test was developed for the hypothesis of the equality of extrapolated coefficients when the original values (Cronbach’s α) are based on the same sample of persons and, therefore, are statistically dependent. Monte carlo studies showed that the test precisely controlled Type I error, even with very small numbers of parttest units or raters.

Get full access to this article

View all access options for this article.

References

Alsawalmeh, Y. M. , & Feldt, L. S. (1994a). A modifi-cation of Feldt’s test of the equality of two dependent alpha coefficients. Psychometrika, 59, 49–57.

Alsawalmeh, Y. M. , & Feldt, L. S. (1994b). Testing the equality of two related intraclass reliability coefficients. Applied Psychological Measurement, 18, 183–190.

Alsawalmeh, Y. M. , & Feldt, L. S. (1999). Testing the equality of two independent α coefficients adjusted by the Spearman-Brown formula. Applied Psychological Measurement, 23, 363–370.

Bose, S. (1935). The distribution of the ratio of variances of two samples drawn from a given bivariate correlated population. Sankhya, 1, 65–72.

Brennan, R. L. (1992). Elements of generalizability theory. Iowa City IA: American College Testing Program.

Bross, I. D. J. (1959). Note on an application of the Schumann-Bradley table. Annals of Mathematical Statistics, 30, 220–238.

Feldt, L. S. (1969). A test of the hypothesis that Cronbach’s alpha orKuder-Richardson coefficient twenty is the same for two tests. Psychometrika, 34, 363–373.

Feldt, L. S. (1980). Atest of the hypothesis that Cronbach’s alpha reliability coefficient is the same for two tests administered to the same sample. Psychometrika, 49, 99–105.

Forsyth, R. A. , & Feldt, L. S. (1969). An investigation of empirical sampling distributions of correlation coefficients corrected for attenuation. Educational and Psychological Measurement, 29, 61–71.

10.

Gulliksen, H. (1950). Theory of mental tests. New York: Wiley.

11.

Hogg, R. V. , & Craig, A. T. (1978). Introduction to mathematical statistics(4th ed.). New York: Macmillan.

12.

Kelley, T. L. (1947). Fundamentals of statistics. Cambridge MA: Harvard University Press.

13.

Kendall, M. G. , Stuart, A. , and Ord, J. K. (1987).Kendall’s advanced theory of statistics(5th ed., Volume 1). London: Charles Griffin.

14.

Lord, F. M. (1957). A significance test for the hypothesis that two variables measure the same trait except for errors of measurement. Psychometrika, 22, 207–220.

15.

McNemar, Q. (1958). Attenuation and interaction. Psychometrika, 23, 259–266.

16.

Novick, M. R. , & Lewis, C. (1967). Coefficient alpha and the reliability of composite measurements. Psychometrika, 32, 1–13.

17.

Odell, P. L. , & Feiveson, A. N. (1966). A numerical procedure to generate a sample covariance matrix. Journal of the American Statistical Association, 61, 199–203.

18.

Satterthwaite, F. E. (1941). Synthesis of variance. Psychometrika, 6, 309–316.

19.

Satterthwaite, F. E. (1946). An approximate distribution of estimates of variance components. Biometrics Bulletin, 2, 110–114.

A Test of the Equality of Two Related α Coefficients Adjusted by the Spearman-Brown Formula

Abstract

Get full access to this article

References