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Internal consistency of tests: Analyses old and new

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Abstract

A coefficient derived from communalities of test parts has been proposed as greatest lower bound to Guttman's “immediate retest reliability.” The communalities have at times been calculated from covariances between itemsets, which tends to underestimate appreciably. When items are experimentally independent, a consistent estimate of the greatest defensible internal-consistency coefficient is obtained by factoring item covariances. In samples of modest size, this analysis capitalizes on chance; an estimate subject to less upward bias is suggested. For estimating alternate-forms reliability, communality-based coefficients are less appropriate than stratified alpha.

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References

  • Bentler, P. M. (1972). A lower bound method for the dimension-free measurement of internal consistency.Social Science Research, 1, 343–357.

    Google Scholar 

  • Bentler, P. M., & Woodward, J. A. (1980). Inequalities among lower bounds to reliability: With applications to test construction and factor analysis.Psychometrika, 45, 249–267.

    Google Scholar 

  • Bentler, P. M., & Woodward, J. A. (1983). The greatest lower bound to reliability. In H. Wainer & S. Messick (Eds.),Principals of modern psychological measurement (pp. 237–253). Hillsdale, NJ: Erlbaum.

    Google Scholar 

  • Comrey, A. L. (1970).EITS manual for the Comrey Personality Scales. San Diego: Educational & Industrial Test Service.

    Google Scholar 

  • Cronbach, L. J. (1947). Test “reliability”: Its meaning and determination.Psychometrika, 12, 1–16.

    Google Scholar 

  • Cronbach, L. J., Gleser, G. C., Nanda, H., & Rajaratnam, N. (1972).The dependability of behavioral measurements: Theory of generalizability for scores and profiles. New York: Wiley.

    Google Scholar 

  • Cronbach, L. J., Ikeda, H., & Avner, R. A. (1964). Intraclass correlation as an approximation to the coefficient of generalizability.Psychological Reports, 15, 727–736.

    Google Scholar 

  • Cronbach, L. J., Schönemann, P., & McKie, D. (1965). Alpha coefficients for stratified-parallel tests.Educational and Psychological Measurement, 25, 291–312.

    Google Scholar 

  • Della Riccia, G., & Shapiro, A. (1980).Minimum rank and minimum trace of covariance matrices. Ben-Gurion University of the Negev, department of Mathematics, Beer-Sheva, Israel.

    Google Scholar 

  • Guttman, L. (1945). A basis for analyzing test-retest reliability.Psychometrika, 10, 255–282.

    Google Scholar 

  • Jackson, P. W., & Agunwamba, C. C. (1977). Lower bounds for the reliability of the total score on a test composed of nonhomogeneous types: I. Algebraic lower bounds.Psychometrika, 42, 567–578.

    Google Scholar 

  • Jackson, R. W. B., & Ferguson, G. A. (1941).Studies on the reliability of tests (Bulletin No. 12). Toronto: University of Toronto, Bureau of Educational Research.

    Google Scholar 

  • Lord, F. M. (1955). Estimating test reliability.Educational and Psychological Measurement, 15, 324–336.

    Google Scholar 

  • Lord, F. M. (1956). Sampling error due to choice of split in split-half reliability coefficients.Journal of Experimental Education, 24, 245–249.

    Google Scholar 

  • Lord, F. M., & Novick, M. R. (1968).Statistical theories of mental test scores. Reading, MA: Addison-Wesley.

    Google Scholar 

  • Rajaratnam, N., Cronbach, L. J., & Gleser, G. C. (1965). Generalizability of stratified-parallel tests.Psychometrika, 30, 39–56.

    Google Scholar 

  • 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.

    Google Scholar 

  • Tryon, R. C. (1957). Reliability and behavior domain validity: Reformulation and historical critique.Psychological Bulletin, 54, 229–249.

    Google Scholar 

  • Woodhouse, B., & Jackson, P. W. (1977). Lower bounds for the reliability of the total score on a test composed of nonhomogeneous types: II. A search procedure to locate the greatest lower bound.Psychometrika, 42, 579–592.

    Google Scholar 

  • Zegers, F. E., & Knol, D. L. (1980, June). Chance capitalization in the greatest lower bound to the reliability of a test. Paper presented at the European meeting of the Psychometric Society, Groningen, The Netherlands.

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I thank Edward Haertel for comments and suggestions, and Andrew Comrey for data.

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Cronbach, L.J. Internal consistency of tests: Analyses old and new. Psychometrika 53, 63–70 (1988). https://doi.org/10.1007/BF02294194

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  • DOI: https://doi.org/10.1007/BF02294194

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