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Table 1 Comparison of the Bayesian approaches to equivalence testing

From: Bayesian Hodges-Lehmann tests for statistical equivalence in the two-sample setting: Power analysis, type I error rates and equivalence boundary selection in biomedical research

  Pro Con
Interval BFs + Influenced more moderately by varying equivalence regions R, compare the spread in power between different choices of R in Fig. 2 (for example, power ranges between 60% and 80% for small effects) – Less robust to the prior selection (for example, compare the difference in power depending on the selected prior in Fig. 2)
  + Recommended in situations with little uncertainty about the prior selection but limited knowledge how to choose the size of the equivalence region – The OH model may be attractive in some situations but yields very large error rates, making it practically unusable
  + Reliable type I error control for small sample sizes  
ROPEs + Robust to the prior selection (see the horizontal progression in Figs. 3, 4 and 5) – Influenced stronger by varying equivalence regions R, compare the spread in power between different choices of R in Figs. 3 and 4 (for example, power ranges from 50% to 80% for small effects and medium prior)
  + Recommended in situations where the equivalence region is motivated from subject-domain knowledge or pilot studies but there is considerable uncertainty about the prior – Only the full ROPE controls type I errors for small sample sizes
  + The full ROPE yields the best type I error control which is important if the stakes of a false-positive result are high