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Statistical significance tests are widely used in empirically based quantitative research and have been applied in virtually every field of study to test research hypotheses. Although many applied researchers use statistical methods, the pitfalls and limitations of statistical hypothesis tests due to violations of underlying assumptions are often overlooked (Kesselman, et al., 1998, Snyder & Thompson, 1998). It is known that the most commonly used statistical tests, the ANOVA F and Student’s T-test, have underlying assumptions of independence of observations – that data are obtained from normally distributed populations having equal variances. Furthermore, these commonly used tests suffer potentially severe performance degradation when underlying assumptions of normality and equality of variance are not met (Glass, Peckham & Sanders, 1972). The violation of normality and equality of variance assumptions are often referred to as the generalized BehrensFisher problem.

A Monte Carlo Simulation of the Robust Rank-Order Test Under Various Population Symmetry Conditions