Access Type

Open Access Dissertation

Date of Award

January 2017

Degree Type

Dissertation

Degree Name

Ph.D.

Department

Education Evaluation and Research

First Advisor

Shlomo Sawilowsky

Abstract

Classical parametric statistic procedures are widely used in the research community. However, for classical tests to produce accurate results, the assumptions underlying them must be sufficiently satisfied. When the assumptions are not met, the results of the analysis may be due to the violation of the assumptions, instead of the true pattern of the data. The assumptions are rarely met when analyzing real data. The use of classic parametric methods with violated assumptions may lead to substantive errors in the interpretation of data. As an alternative to normal theory statistics, nonparametric statistical procedures do not make assumptions about the underlying distribution of the data, nor do they require large sample sizes to produce a normal distribution of errors. Nonparametric statistics also have an advantage of preserving Type I error rates to nominal alpha and having more power under the conditions of concomitant heteroscedasticity and treatment effects under nonnormal distributions.

Haga’s test is a nonparametric method to exam locations of ranks of two independent samples. It is an improved version of Rosenbaum test. This study examines and compares the robustness and power of the nonparametric Haga test with that of the Tukey’s Quick test, Welch-Aspin t test, Yuen’s test and Student’s t test under the condition of concomitant heteroscedasticity and treatment effect via the method of Monte Carlo simulations.

The result of the simulations indicated that under the theoretical nonnormal distributions, Haga’s test and Tukey’s Quick test were more robust than Student’s t test, Welch-Aspin’s t test and Yuen’s test at all alpha levels. When there was no variance effects (scale1:1) or a slight variance increment (scale1:1.1), Haga’s test was the most powerful test for nonnormal theoretical distributions. When there was medium (scale1:4) or large (scale1:16) variance effects, Haga’s test was the most powerful test for equal sample sizes, and Student’s t test was the most powerful test for unequal sample sizes.

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