The operating characteristics of the nonparametric Levene test for equal variances with assessment and evaluation data

Many assessment and evaluation studies use statistical hypothesis tests, such as the independent samples t test or analysis of variance, to test the equality of two or more means for gender, age groups, cultures or language group comparisons. In addition, some, but far fewer, studies compare variability across these same groups or research conditions. Tests of the equality of variances can therefore be used on their own for this purpose but they are most often used alongside other methods to support assumptions made about variances. This is often done so that variances can be pooled across groups to yield an estimate of variance that is used in the standard error of the statistic in question. The purposes of this paper are twofold. The first purpose is to describe a new nonparametric Levene test for equal variances that can be used with widely available statistical software such as SPSS or SAS, and the second purpose is to investigate this test‟s operating characteristics, Type I error and statistical power, with real assessment and evaluation data. To date, the operating characteristics of the nonparametric Levene test have been studied with mathematical distributions in computer experiments and, although that information is valuable, this study will be an important next step in documenting both the level of non-normality (skewness and kurtosis) of real assessment and evaluation data, and how this new statistical test operates in these conditions.

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