Classical statistical tests are used in many disciplines such as education and psychology. Such tests are based on certain assumptions (e.g., normality and homoscedasticity) that are must to be met in order to produce accurate results. Violation of such assumptions is a common problem researchers encounter, particularly when analyzing real data. When such assumptions are violated, the effectiveness and efficiency of tests to control over the probability of a Type I error and maintain a relatively level of statistical power will be substantially affected. Alternative modern and robust statistical tests such as Yuen test for trimmed means and the Alexander-Govern test can be used to overcome these assumption violations. The purpose of present study, then, is to research and explicate under non-normal and heteroscedastic conditions if the Yuen test or the Alexander-Govern test is more robust with respect to Type I errors while maintaining a power advantage for detecting changes/differences in scale and location shifts. The result of the simulations indicated that under the four distributions, all scales; 1:1,1:4,1:16, alpha levels, and sample sizes, Welch-Aspin, Yuen, and Alexander-Govern tests were similar to be more robust tests to Type I errors and held a power advantage for detecting changes/differences in scale and location shifts. However, the results indicated that the effect size was the main condition that effects the Type I and II rejection for all three competitors statistics. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://bibliotheek.ehb.be:2222/en-US/products/dissertations/individuals.shtml.]