A method for obtaining standard errors and confidence intervals of composite reliability co-efficients based on the bootstrap method is proposed. Using a structural equation modeling framework for estimating composite reliability of congeneric measures (Raykov, 1997), the approach takes repeated samples from a given sample and then estimates reliability. This approach extends earlier research on the distribution of scale reliability that is primarily concerned with Cronbach's coefficient alpha, and represents a general method based on fewer assumptions. It also permits testing hypotheses about composite reliability. Its use is demonstrated on simulated data.
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References
1.
Bay, K. S. (1973). The effect of non-normality on the sampling distribution and standard error of reliability coefficient estimates under an analysis of variance model. British Journal of Mathematical and Statistical Psychology, 26, 45-57.
2.
Bentler, P. M. (1995). EQS structural equations manual [Computer program]. New York: Harcourt Brace.
3.
Crocker, L. , & Algina, J. (1986). Introduction to classical and modern test theory. New York: Holt, Rinehart, & Winston.
4.
Cronbach, L. J. (1951). Coefficient alpha and the internal structure of a test. Psychometrika, 16, 297-334.
5.
Efron, B. , & Tibshiriani, R. J. (1993). An introduction to the bootstrap. New York: Chapman and Hall.
6.
Feldt, L. S. (1965). The approximate sampling distribution of Kuder-Richardson reliability coefficient twenty. Psychometrika, 30, 357-370.
7.
Feldt, L. S. (1969). A test of the hypothesis that Cronbach's alpha or Kuder-Richardson coefficient twenty is the same for two tests. Psychometrika, 34, 363-373.
8.
Feldt, L. S. (1980). A test of the hypothesis that Cronbach's alpha reliability coefficient is the same for two tests administered to the same sample. Psychometrika, 45, 99-105.
9.
Feldt, L. S. , & Brennan, R. L. (1989). Reliability. In R. L. Linn (Ed.), Educational measurement (pp. 105-146). New York: Macmillan.
10.
Hakstian, A. R. , & Whalen, T. E. (1976). A k- sample significance test for independent alpha co-efficients. Psychometrika, 41, 219-231.
11.
Hays, W. L. (1994). Statistics. Fort Worth TX: Harcourt Brace.
12.
Hjorth, J. S. U. (1994). Computer intensive statistical methods: Validation, model selection, and bootstrap. London: Chapman and Hall.
13.
Hoyt, C. J. (1941). Test reliability estimated by analysis of variance. Psychometrika, 6, 153-160.
14.
Jackson, R. W., & Ferguson, G. A. (1941). Studies on the reliability of tests. Department of Education Research Bulletin, 12, Toronto.
15.
Joreskog, K. G. (1971). Statistical analysis of sets of congeneric tests. Psychometrika, 36, 109-133.
16.
Joreskog, K. G. , & Sorbom, D. (1993). LISREL 8: User's guide [Computer program]. Chicago: Scientific Software International.
17.
Kristof, W. (1963). The statistical theory of stepped-up reliability co-efficients when a test has been divided into several equivalent parts. Psychometrika, 28, 221-238.
18.
Kristof, W. (1964). Testing differences between reliability co-efficients. British Journal of Mathematical and Statistical Psychology, 17, 105-111.
19.
Kristof, W. (1970). On the sampling theory of reliability estimation. Journal of Mathematical Psychology, 7, 371-377.
20.
Lord, F. M. , & Novick, R. (1968). Statistical theories of mental test scores. Reading MA: Addison-Wesley.
21.
Mooney, C. Z. , & Duval, R. D. (1993). Bootstrapping: A nonparametric approach to statistical inference. Newbury Park CA: Sage.
22.
Pandey, T. N. , & Hubert, L. (1975). An empirical comparison of several interval estimation procedures for coefficient alpha. Psychometrika, 40, 169-181.
23.
Raykov, T. (1997). Estimation of composite reliability for congeneric measures. Applied Psychological Measurement, 21, 173-184.
24.
SAS Institute (1991). SAS procedures guide (Release 6.03) [Computer software manual]. Cary NC: Author.
25.
SPSS (1990). SPSS base system user's guide [Computer software manual]. Chicago: Author.
26.
Woodruff, D. J. , & Feldt, L. S. (1986). Tests for equality of several alpha co-efficients when their sample estimates are dependent. Psychometrika, 51, 393-413.
27.
Zimmerman, D. W. (1975). Probability spaces, Hilbert spaces, and the axioms of test theory. Psychometrika, 40, 395-412.
