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Inequalities among lower bounds to reliability: With applications to test construction and factor analysis

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  • P. Bentler
  • J. Woodward

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  • P. Bentler & J. Woodward, 1980. "Inequalities among lower bounds to reliability: With applications to test construction and factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 45(2), pages 249-267, June.
    • Handle: RePEc:spr:psycho:v:45:y:1980:i:2:p:249-267
    DOI: 10.1007/BF02294079
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    References listed on IDEAS

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    1. Brian Woodhouse & Paul Jackson, 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, Springer;The Psychometric Society, vol. 42(4), pages 579-591, December.
    2. Paul Jackson, 1979. "A note on the relation between coefficient alpha and guttman's “split-half” lower bounds," Psychometrika, Springer;The Psychometric Society, vol. 44(2), pages 251-252, June.
    3. repec:ucp:bkecon:9780226316529 is not listed on IDEAS
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    Citations

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    Cited by:

    1. Klaas Sijtsma & Julius M. Pfadt, 2021. "Part II: On the Use, the Misuse, and the Very Limited Usefulness of Cronbach’s Alpha: Discussing Lower Bounds and Correlated Errors," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 843-860, December.
    2. Massimiliano Pastore & Luigi Lombardi, 2014. "The impact of faking on Cronbach’s alpha for dichotomous and ordered rating scores," Quality & Quantity: International Journal of Methodology, Springer, vol. 48(3), pages 1191-1211, May.
    3. Giacomo Riccia & Alexander Shapiro, 1982. "Minimum rank and minimum trace of covariance matrices," Psychometrika, Springer;The Psychometric Society, vol. 47(4), pages 443-448, December.
    4. Jos Berge & Gregor Sočan, 2004. "The greatest lower bound to the reliability of a test and the hypothesis of unidimensionality," Psychometrika, Springer;The Psychometric Society, vol. 69(4), pages 613-625, December.
    5. Alexander Shapiro & Jos Berge, 2000. "The asymptotic bias of minimum trace factor analysis, with applications to the greatest lower bound to reliability," Psychometrika, Springer;The Psychometric Society, vol. 65(3), pages 413-425, September.
    6. Peter M. Bentler, 2021. "Alpha, FACTT, and Beyond," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 861-868, December.
    7. Ilona Szőcs & Bodo B. Schlegelmilch & Thomas Rusch & Hamed M. Shamma, 2016. "Linking cause assessment, corporate philanthropy, and corporate reputation," Journal of the Academy of Marketing Science, Springer, vol. 44(3), pages 376-396, May.
    8. Jushan Bai & Serena Ng, 2017. "Principal Components and Regularized Estimation of Factor Models," Papers 1708.08137, arXiv.org, revised Nov 2017.
    9. Klaas Sijtsma, 2012. "Future of Psychometrics: Ask What Psychometrics Can Do for Psychology," Psychometrika, Springer;The Psychometric Society, vol. 77(1), pages 4-20, January.
    10. Lee Cronbach, 1988. "Internal consistency of tests: Analyses old and new," Psychometrika, Springer;The Psychometric Society, vol. 53(1), pages 63-70, March.
    11. P. Bentler & J. Woodward, 1985. "On the greatest lower bound to reliability," Psychometrika, Springer;The Psychometric Society, vol. 50(2), pages 245-246, June.
    12. William Revelle & Richard Zinbarg, 2009. "Coefficients Alpha, Beta, Omega, and the glb: Comments on Sijtsma," Psychometrika, Springer;The Psychometric Society, vol. 74(1), pages 145-154, March.
    13. Peter M. Bentler, 2016. "Covariate-free and Covariate-dependent Reliability," Psychometrika, Springer;The Psychometric Society, vol. 81(4), pages 907-920, December.
    14. Alexander Shapiro & Jos Berge, 2002. "Statistical inference of minimum rank factor analysis," Psychometrika, Springer;The Psychometric Society, vol. 67(1), pages 79-94, March.
    15. Peter Bentler, 2009. "Alpha, Dimension-Free, and Model-Based Internal Consistency Reliability," Psychometrika, Springer;The Psychometric Society, vol. 74(1), pages 137-143, March.
    16. Jos Berge & Willem Hofstee, 1999. "Coefficients alpha and reliabilities of unrotated and rotated components," Psychometrika, Springer;The Psychometric Society, vol. 64(1), pages 83-90, March.
    17. Bai, Jushan & Ng, Serena, 2019. "Rank regularized estimation of approximate factor models," Journal of Econometrics, Elsevier, vol. 212(1), pages 78-96.
    18. Klaas Sijtsma, 2009. "On the Use, the Misuse, and the Very Limited Usefulness of Cronbach’s Alpha," Psychometrika, Springer;The Psychometric Society, vol. 74(1), pages 107-120, March.
    19. Jos Berge & Henk Kiers, 1991. "A numerical approach to the approximate and the exact minimum rank of a covariance matrix," Psychometrika, Springer;The Psychometric Society, vol. 56(2), pages 309-315, June.
    20. Tyler Hunt & Peter Bentler, 2015. "Quantile Lower Bounds to Reliability Based on Locally Optimal Splits," Psychometrika, Springer;The Psychometric Society, vol. 80(1), pages 182-195, March.

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