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A Test Can Have Multiple Reliabilities

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  • Jules L. Ellis

    (Radboud University Nijmegen)

Abstract

It is argued that the generalizability theory interpretation of coefficient alpha is important. In this interpretation, alpha is a slightly biased but consistent estimate for the coefficient of generalizability in a subjects x items design where both subjects and items are randomly sampled. This interpretation is based on the “domain sampling” true scores. It is argued that these true scores have a more solid empirical basis than the true scores of Lord and Novick (1968), which are based on “stochastic subjects” (Holland, 1990), while only a single observation is available for each within-subject distribution. Therefore, the generalizability interpretation of coefficient alpha is to be preferred, unless the true scores can be defined by a latent variable model that has undisputed empirical validity for the test and that is sufficiently restrictive to entail a consistent estimate of the reliability—as, for example, McDonald’s omega. If this model implies that the items are essentially tau-equivalent, both the generalizability and the reliability interpretation of alpha can be defensible.

Suggested Citation

  • Jules L. Ellis, 2021. "A Test Can Have Multiple Reliabilities," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 869-876, December.
    • Handle: RePEc:spr:psycho:v:86:y:2021:i:4:d:10.1007_s11336-021-09800-2
    DOI: 10.1007/s11336-021-09800-2
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    References listed on IDEAS

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    1. Louis Guttman, 1945. "A basis for analyzing test-retest reliability," Psychometrika, Springer;The Psychometric Society, vol. 10(4), pages 255-282, December.
    2. Lee Cronbach, 1951. "Coefficient alpha and the internal structure of tests," Psychometrika, Springer;The Psychometric Society, vol. 16(3), pages 297-334, September.
    3. 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.
    4. Paul Holland, 1990. "On the sampling theory roundations of item response theory models," Psychometrika, Springer;The Psychometric Society, vol. 55(4), pages 577-601, December.
    5. Peter Bentler, 2009. "Alpha, Dimension-Free, and Model-Based Internal Consistency Reliability," Psychometrika, Springer;The Psychometric Society, vol. 74(1), pages 137-143, March.
    6. Jules Ellis & Brian Junker, 1997. "Tail-measurability in monotone latent variable models," Psychometrika, Springer;The Psychometric Society, vol. 62(4), pages 495-523, December.
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    Cited by:

    1. Alexander Robitzsch, 2022. "Comparing the Robustness of the Structural after Measurement (SAM) Approach to Structural Equation Modeling (SEM) against Local Model Misspecifications with Alternative Estimation Approaches," Stats, MDPI, vol. 5(3), pages 1-42, July.
    2. Klaas Sijtsma & Julius M. Pfadt, 2021. "Rejoinder: The Future of Reliability," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 887-892, December.
    3. Jules L. Ellis & Klaas Sijtsma, 2024. "Proof of Reliability Convergence to 1 at Rate of Spearman–Brown Formula for Random Test Forms and Irrespective of Item Pool Dimensionality," Psychometrika, Springer;The Psychometric Society, vol. 89(3), pages 774-795, September.

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