Robust normative comparison tests for evaluating clinical significance

The purpose of this study was to evaluate a modified test of equivalence for conducting normative comparisons when distribution shapes are non-normal and variances are unequal. A Monte Carlo study was used to compare the empirical Type I error rates and power of the proposed Schuirmann–Yuen test of equivalence, which utilizes trimmed means, with that of the previously recommended Schuirmann and Schuirmann–Welch tests of equivalence when the assumptions of normality and variance homogeneity are satisfied, as well as when they are not satisfied. The empirical Type I error rates of the Schuirmann–Yuen were much closer to the nominal a level than those of the Schuirmann or Schuirmann–Welch tests, and the power of the Schuirmann–Yuen was substantially greater than that of the Schuirmann or Schuirmann–Welch tests when distributions were skewed or outliers were present. The Schuirmann–Yuen test is recommended for assessing clinical significance with normative comparisons.