A Comparative Study of TOST and UMPT Procedures for Evaluating Dispersion Equivalence

Show-Li Jan, Gwowen Shieh*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


The two one-sided tests (TOST) procedure is widely applied for assessing bioequivalence between two different drugs in clinical studies. The same notion can be applied to construct TOST method for establishing dispersion equivalence. In addition to the TOST extension, a uniformly most power test (UMPT) for equivalence in variability has been described in the literature. This article presents analytic and numerical comparisons to clarify the limitation and strength of the two procedures. The UMPT approach has comparatively superior control of Type I errors and demands more involved computations than the TOST method. To enhance the utility of the recommended UMPT procedure, a full set of computer algorithms are constructed to implement the described hypothesis testing and power calculation. Optimal sample size determinations are also developed for planning equivalence designs under different allocation and cost concerns. The suggested procedures are demonstrated with the data regarding the dispersion comparability between two measuring devices of breaking strengths in dental medicine.

Original languageAmerican English
Number of pages6
JournalStatistics in Biopharmaceutical Research
StateE-pub ahead of print - 1 Jan 2022


  • Dispersion
  • Equivalence
  • Power
  • Sample size
  • Type I error
  • Variability


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