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Optimal Sample Size Determinations for the Heteroscedastic Two One-Sided Tests of Mean Equivalence

Author

Listed:
  • Show-Li Jan

    (Chung Yuan Christian University)

  • Gwowen Shieh

    (National Chiao Tung University)

Abstract

Equivalence assessment is becoming an increasingly important topic in many application areas including behavioral and social sciences research. Although there exist more powerful tests, the two one-sided tests (TOST) procedure is a technically transparent and widely accepted method for establishing statistical equivalence. Alternatively, a direct extension of Welch’s solution for the Behrens–Fisher problem is preferred in equivalence testing of means when the homogeneity of variance assumption is violated. For advance planning of equivalence studies, this article describes both exact and nearly exact power functions of the heteroscedastic TOST procedure and develops useful approaches to optimal sample size determinations under various allocation and cost considerations. Detailed numerical illustrations and simulation studies are presented to demonstrate the distinct features of the suggested techniques and the potential deficiency of existing method. Moreover, computer programs are provided to facilitate the implementation of the described sample size procedures. The proposed formulas and algorithms are recommended over the current results for their technical transparency, overall performance, and diverse utility.

Suggested Citation

  • Show-Li Jan & Gwowen Shieh, 2017. "Optimal Sample Size Determinations for the Heteroscedastic Two One-Sided Tests of Mean Equivalence," Journal of Educational and Behavioral Statistics, , vol. 42(2), pages 145-165, April.
    • Handle: RePEc:sae:jedbes:v:42:y:2017:i:2:p:145-165
    DOI: 10.3102/1076998616671974
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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. Heilbrun, Lance K. & McGee, Daniel L., 1985. "Sample size determination for the comparison of normal means when one sample size is fixed," Computational Statistics & Data Analysis, Elsevier, vol. 3(1), pages 99-102, May.
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