A Nonparametric Framework for Comparing Trends and Gaps Across Tests

Problems of scale typically arise when comparing test score trends, gaps, and gap trends across different tests. To overcome some of these difficulties, test score distributions on the same score scale can be represented by nonparametric graphs or statistics that are invariant under monotone scale transformations. This article motivates and then develops a framework for the comparison of these nonparametric trend, gap, and gap trend representations across tests. The connections between this framework and other nonparametric tools, including probability–probability (PP) plots, the Mann-Whitney U test, and the statistic known as P( Y > X), are highlighted. The author describes the advantages of this framework over scale-dependent trend and gap statistics and demonstrates applications of these nonparametric methods to frequently asked policy questions.