A Rank-Order Alternative for Non-Parametric Analysis with the General Linear Model

Violations of normality and homogeneity are common in educational data. When this occurs, the use of parametric statistics may be inappropriate. A generalized form of nonparametric analyses based on the Puri and Sen L statistic provides an alternative approach. Using a chi-square distribution, this technique is easy to apply and has significant power. Another advantage of the L statistic is its utility to link nonparametric tests with their parametric counterparts. After rank-ordering and analyzing the data, an adjustment is made by calculating L instead of relying on the parametric test statistic. This permits the researcher to choose between parallel strategies based on the distribution characteristics of the data. In this paper, I present case illustrations to demonstrate the approach and offer guidance to faculty, students, and staff researchers interested in nonparametric options when working with educational data that possess asymmetrical and/or heteroscedastic qualities.