Evaluating clinical significance: incorporating robust statistics with normative comparison tests.

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 α 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.