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Equivalence Test and Sample Size Procedures for Standardized Mean Differences in ANCOVA Studies

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  • Gwowen Shieh

Abstract

This article presents exact equivalence tests of standardized mean differences in ANCOVA studies. As an alternative to the traditional hypothesis testing for confirming the existence of substantial differences, the proposed equivalence procedure helps appraise whether the target effect is practically identical to a meaningful magnitude or a trivial value. The general formulation of standardized mean differences permits a wide range of research hypotheses to be examined, including the contrast effect for treatment comparisons and the interaction effect in factorial designs. The associated power and sample size formulas are also described to accommodate the stochastic features of response and covariate variables. The usefulness and applicability of the suggested techniques are illustrated with two examples for the comparison of intervention effects and the assessment of training interactions. Extensive empirical investigations demonstrate the importance of random features and disparity of covariate variables in power and sample size calculations.

Suggested Citation

  • Gwowen Shieh, 2025. "Equivalence Test and Sample Size Procedures for Standardized Mean Differences in ANCOVA Studies," Journal of Probability and Statistics, John Wiley & Sons, vol. 2025(1).
    • Handle: RePEc:wly:jnljps:v:2025:y:2025:i:1:n:5557130
    DOI: 10.1155/jpas/5557130
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    References listed on IDEAS

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    1. Stegner, Bruce L. & Bostrom, Alan G. & Greenfield, Thomas K., 1996. "Equivalence testing for use in psychosocial and services research: An introduction with examples," Evaluation and Program Planning, Elsevier, vol. 19(3), pages 193-198, August.
    2. Gwowen Shieh, 2023. "Assessing standardized contrast effects in ANCOVA: Confidence intervals, precision evaluations, and sample size requirements," PLOS ONE, Public Library of Science, vol. 18(2), pages 1-18, February.
    3. Gwowen Shieh, 2006. "Exact Interval Estimation, Power Calculation, and Sample Size Determination in Normal Correlation Analysis," Psychometrika, Springer;The Psychometric Society, vol. 71(3), pages 529-540, September.
    4. Gwowen Shieh, 2007. "A Unified Approach to Power Calculation and Sample Size Determination for Random Regression Models," Psychometrika, Springer;The Psychometric Society, vol. 72(3), pages 347-360, September.
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