On the Use, the Misuse, and the Very Limited Usefulness of Cronbach’s Alpha

Psychometrika - Tập 74 - Trang 107-120 - 2008
Klaas Sijtsma1
1Department of Methodology and Statistics, Faculty of Social Sciences, Tilburg University, Tilburg, The Netherlands

Tóm tắt

This discussion paper argues that both the use of Cronbach’s alpha as a reliability estimate and as a measure of internal consistency suffer from major problems. First, alpha always has a value, which cannot be equal to the test score’s reliability given the interitem covariance matrix and the usual assumptions about measurement error. Second, in practice, alpha is used more often as a measure of the test’s internal consistency than as an estimate of reliability. However, it can be shown easily that alpha is unrelated to the internal structure of the test. It is further discussed that statistics based on a single test administration do not convey much information about the accuracy of individuals’ test performance. The paper ends with a list of conclusions about the usefulness of alpha.

Tài liệu tham khảo

Bentler, P. A., & Woodward, J. A. (1980). Inequalities among lower bounds to reliability: With applications to test construction and factor analysis. Psychometrika, 45, 249–267. Borsboom, D. (2005). Measuring the mind. Conceptual issues in contemporary psychometrics. Cambridge: Cambridge University Press. Borsboom, D. (2006). The attack of the psychometricians. Psychometrika, 71, 425–440. Campbell, D. T. (1960). Recommendations for APA tests regarding construct, trait or discriminant validity. American Psychologist, 15, 546–553. Cavalini, P. M. (1992). It’s an ill wind that brings no good. Studies on odour annoyance and the dispersion of odorant concentrations from industries. Ph.D. thesis, University of Groningen, The Netherlands. Cronbach, L. J. (1951). Coefficient alpha and the internal structure of tests. Psychometrika, 16, 297–334. Cronbach, L. J. (1988). Internal consistency of tests: Analyses old and new. Psychometrika, 53, 63–70. Cortina, J. M. (1993). What is coefficient alpha? An examination of theory and applications. Journal of Applied Psychology, 78, 98–104. De Hooge, I. E., Zeelenberg, M., & Breugelmans, S. M. (2007). Moral sentiments and cooperation: Differential influences of shame and guilt. Cognition and Emotion, 21, 1025–1042. Ellis, J. L., & Van den Wollenberg, A. L. (1993). Local homogeneity in latent trait models. A characterization of the homogeneous monotone IRT model. Psychometrica, 58, 417–429. Emons, W. H. M., Sijtsma, K., & Meijer, R. R. (2007). On the consistency of individual classification using short scales. Psychological Methods, 12, 105–120. Feldt, L. S., Woodruff, D. J., & Salih, F. A. (1987). Statistical inference for coefficient alpha. Applied Psychological Measurement, 11, 93–103. Green, S. B., Lissitz, R. W., & Mulaik, S. A. (1977). Limitations of coefficient alpha as an index of test unidimensionality. Educational and Psychological Measurement, 37, 827–838. Guttman, L. (1945). A basis for analyzing test-retest reliability. Psychometrika, 10, 255–282. Hayashi, K., & Kamata, A. (2005). A note on the estimator of the alpha coefficient for standardized variables under normality. Psychometrika, 70, 579–586. Holland, P. W. (1990). On the sampling theory foundations of item response theory models. Psychometrika, 55, 577–601. Hoyt, C. (1941). Test reliability estimated by analysis of variance. Psychometrika, 6, 153–160. Jackson, P. H., & Agunwamba, C. C. (1977). Lower bounds for the reliability of the total score on a test composed of non-homogeneous items: I: Algebraic lower bounds. Psychometrika, 42, 567–578. Kistner, E. O., & Muller, K. E. (2004). Exact distributions of intraclass correlation and Cronbach’s alpha with Gaussian data and general covariance. Psychometrika, 69, 459–474. Kuder, G. F., & Richardson, M. W. (1937). The theory of estimation of test reliability. Psychometrika, 2, 151–160. Lord, F. M. (1960). An empirical study of the normality and independence of errors of measurement in test scores. Psychometrika, 25, 91–104. Lord, F. M., & Novick, M. R. (1968). Statistical theories of mental test scores. Reading: Addison-Wesley. Molenaar, P. C. M. (2004). A manifesto on psychology as idiographic science: Bringing the person back into scientific psychology—This time forever. Measurement, 2, 201–218. Novick, M. R. (1966). The axioms and principal results of classical test theory. Journal of Mathematical Psychology, 3, 1–18. Novick, M. R., & Lewis, C. (1967). Coefficient alpha and the reliability of composite measurements. Psychometrika, 32, 1–13. Nunnally, J. C. (1978). Psychometric theory. New York: McGraw-Hill. Raykov, T. (2001). Bias of coefficient alpha for fixed congeneric measures with correlated errors. Applied Psychological Measurement, 25, 69–76. Reise, S. P., & Waller, N. G. (1993). Traitedness and the assessment of response pattern scalability. Journal of Personality and Social Psychology, 65, 143–151. Rodriguez, M. C., & Maeda, Y. (2006). Meta-Analysis of coefficient alpha. Psychological Methods, 11, 306–322. Schmitt, N. (1996). Uses and abuses of coefficient alpha. Psychological Assessment, 8, 350–353. Shapiro, A., & Ten Berge, J. M. F. (2000). The asymptotic bias of minimum trace factor analysis, with applications to the greatest lower bound to reliability. Psychometrika, 65, 413–425. SPSS Inc. (2006). SPSS 14.0 for Windows (computer software). Chicago: Author. Takane, Y., & De Leeuw, J. (1987). On the relationship between item response theory and factor analysis of discretized variables. Psychometrika, 52, 393–408. Tellegen, A. (1988). The analysis of consistency in personality assessment. Journal of Personality, 56, 621–663. Ten Berge, J. M. F., & Kiers, H. A. L. (1991). A numerical approach to the exact and the approximate minimum rank of a covariance matrix. Psychometrika, 56, 309–315. Ten Berge, J. M. F., & Kiers, H. A. L. (2003). The minimum rank factor analysis program MRFA (Internal report). Department of Psychology, University of Groningen, The Netherlands. Ten Berge, J. M. F., & Sočan, G. (2004). The greatest lower bound to the reliability of a test and the hypothesis of unidimensionality. Psychometrika, 69, 613–625. Ten Berge, J. M. F., & Zegers, F. E. (1978). A series of lower bounds to the reliability of a test. Psychometrika, 43, 575–579. Ten Berge, J.M.F., Snijders, T.A.B., & Zegers, F.E. (1981). Computational aspects of the greatest lower bound to the reliability and constrained minimum trace factor analysis. Psychometrika, 46, 201–213. Van Zyl, J. M., Neudecker, H., & Nel, D. G. (2000). On the distribution of the maximum likelihood estimator of Cronbach’s alpha. Psychometrika, 65, 271–280. Verhelst, N. D. (1998). Estimating the reliability of a test from a single test administration (Measurement and Research Department Report 98-2). Arnhem, The Netherlands, CITO National Institute for Educational Measurement. Watson, J. D., & Crick, F. H. C. (1953). Molecular structure of nuclied acids—a structure for deoxyribose nucleid acid. Nature, 171, 737–738. Woodhouse, B., & Jackson, P. H. (1977). Lower bounds for the reliability of the total score on a test composed of non-homogeneous items: II: A search procedure to locate the greatest lower bound. Psychometrika, 42, 579–591. Zinbarg, R. E., Revelle, W., Yovel, I., & Li, W. (2005). Cronbach’s α, Revelle’s β, and McDonald’s ω H : their relations with each other and two alternative conceptualizations of reliability. Psychometrika, 70, 123–133.