| This study proposes three new nonparametric procedures for testing equivalence, including the modified two one-sided Mann-Whitney U-test, the nonparametric analog to the Patel-Gupta test, and the nonparametric analog to the bivariate noncentral t-test. In addition, the performances of the proposed tests, along with Schuirman's (1981, 1987) two one-sided t-test method, the traditional two one-sided Mann-Whitney U-test, Anderson and Hauck's (1983) test, and Patel and Gupta's (1984) test are compared in terms of Type I error rate control and power. To this end, a Monte Carlo simulation is used to estimate the Type I error rates and power under a variety of conditions for a two-sample design.;The results of this study show that none of the equivalence tests that control the Type I error rate is uniformly more powerful than other tests across all the conditions. The proposed nonparametric analog to the Patel-Gupta test is not recommended, as it is erratic in Type I error rate control. The nonparametric analog to the bivariate noncentral t-test based on conservative empirical estimates is shown to be robust and has comparable power. The modified two one-sided Mann-Whitney U-test is slightly liberal for small to medium sample size combinations, while under skewed or bimodal distributions it is more powerful than other tests. |
