Abstract
Since the beginning of the past century, the concept of reliability has attracted an impressive amount of interest by methodologists and substantive researchers across the social and behavioral sciences. The reliability coefficient represents an overall (unconditional) index of ‘precision’ of assessment, the proportion of true individual differences in observed variance. The attention it has received in the literature is appropriate, given the well-known fact that measurement in these disciplines is typically plagued by sizeable measurement error and related problems resulting from imperfect assessment. Over the past few decades, a number of methods have been proposed that aim at estimation of reliability, in particular of sum scores associated with multiple-component measuring instruments such as scales, questionnaires, tests, self-reports or inventories. These instruments are very often employed in social, behavioral and educational research, and a main reason for their popularity is that they provide multiple, converging pieces of information about underlying latent dimensions of major interest in these sciences, such as motivation, attitude, intelligence, social phobia, ability. For many years, Cronbach’s coefficient alpha (α) (Cronbach, 1951) has been a very frequently used index of reliability of multi-component instruments. At the same time, for quite a while its important limitations had not received the attention they deserve by empirical researchers.
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References
Bollen, K. A. (1989). Structural equations with latent variables, New York, Wiley.
Cronbach, L. J. (1951). Coefficient alpha and the internal structure of a test, Psychometrika, 16, 297–334.
Green, S. B., Hershberger, S. L. (2000). Correlated errors in true score models and their effect on coefficient alpha, Structural Equation Modeling, 7, 251–270.
Hogg, R. V., Craig, A. T. (1982). Introduction to mathematical statistics, London, Macmillan.
Jamshidian, M., Bentler, P. M. (2000). Improved standard errors of standardized parameters in covariance structure models: Implications for construct explication. In R. D. Goffin and E. Helmes (Eds.), Problems and solutions in human assessment, (pp. 73–94). Dordrecht, The Netherlands, Kluwer Academic Publishers.
Jöreskog, K. G. (1971). Statistical analysis of sets of congeneric tests, Psychometrika, 36, 109–133.
Komaroff, E. (1997). Effect of simultaneous violations of essential tauequivalence and correlated errors on coefficient alpha, Applied Psychological Measurement, 21, 337–348.
Lord, F. M., Novick, M. (1968). Statistical theories of mental test scores, Readings, MA, Wesley.
McDonald, R. P. (1981). The dimensionality of tests and items. British Journal of Mathematical and Statistical Psychology, 34, 100–117.
McDonald, R. P. (1999). Test theory: A unified treatment, Mahwah, NJ, Lawrence Erlbaum.
Novick, M. R., Lewis, C. (1967). Coefficient alpha and the reliability of composite measurement, Psychometrika, 32, 1–13.
Rao, C. R. (1973). Linear statistical inference and its applications, New York: Wiley.
Raykov, T. (1997a). Estimation of composite reliability for congeneric measures, Applied Psychological Measurement, 22, 173–184.
Raykov, T. (1997b). Scale reliability, Cronbach’s coefficient alpha, and violations of essential tau-equivalence with fixed congeneric components, Multivariate Behavioral Research, 32, 329–353.
Raykov, T. (1998a). Coefficient alpha and composite reliability with interrelated nonhomogeneous items, Applied Psychological Measurement, 22, 375–385.
Raykov, T. (1998b). A method for obtaining standard errors and confidence intervals of composite reliability for congeneric items, Applied Psychological Measurement. 22.369–374.
Raykov, T. (2001a). Bias of Cronbach’s coefficient alpha for fixed congeneric measures with correlated errors, Applied Psychological Measurement, 25, 69–76.
Raykov, T. (2001b). Estimation of congeneric scale reliability using covariance structure models with nonlinear constraints, British Journal of Mathematical and Statistical Psychology, 54, 213–221.
Raykov, T. (2002a). Analytic estimation of standard error and confidence interval for scale reliability, Multivariate Behavioral Research, 37, 89–103.
Raykov, T. (2002b). Examining group differences in reliability of multiplecomponent measuring instruments, British Journal of Mathematical and Statistical Psychology, 55, 145–158.
Raykov, T. (2002c). Automated procedure for interval estimation of scale reliability, Understanding Statistics, 1, 33–42.
Raykov, T. (2003a). Behavioral scale reliability and measurement invariance evaluation via latent variable modeling, Behavior Therapy (in press).
Raykov, T. (2003b). Estimation of maximal reliability: A note on a covariance structure modeling approach, British Journal of Mathematical and Statistical Psychology (in press).
Raykov, T., Grayson, D. A. (2003), A test for change of composite reliability in scale development, Multivariate Behavioral Research, 38, 143–159.
Stewart, J. (1991). Calculus, Pacific Grove, CA: Brooks/Cole.
Yuan, K.-H., Bentler, P. M, (2002). On robustness of the normal-theory based asymptotic distributions of three reliability coefficient estimates, Psychometrika, 67, 251–260.
Zimmerman, D. W. (1972). Test reliability and the Kuder-Richarson formulas: Derivation from probability theory, Educational and Psychological Measurement, 32, 939–954.
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© 2004 Springer Science+Business Media Dordrecht
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Raykov, T., Penev, S. (2004). Improved Analytic Interval Estimation of Scale Reliability. In: van Montfort, K., Oud, J., Satorra, A. (eds) Recent Developments on Structural Equation Models. Mathematical Modelling: Theory and Applications, vol 19. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-1958-6_5
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DOI: https://doi.org/10.1007/978-1-4020-1958-6_5
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