Evaluating the Impact of Nonparametric Rank Tests on Robustness and Statistical Efficiency in Non-Normal Data

Posted: Sep 07, 2023

• Alexander Bennett
• Amelia Rogers
• Andrew Powell

Abstract

Statistical hypothesis testing represents a cornerstone of empirical research across scientific disciplines, with parametric methods dominating applied work despite their reliance on often-unverifiable distributional assumptions. The widespread application of t-tests, ANOVA, and related parametric procedures persists despite mounting evidence that real-world data frequently violate the normality assumption underlying these methods. This research addresses the critical gap in understanding how nonparametric rank-based tests perform in practical scenarios where data distributions deviate from theoretical ideals. The conventional wisdom in statistical methodology has long maintained a perceived trade-off between robustness and efficiency, positioning nonparametric methods as robust but inefficient alternatives to their parametric counterparts. This perspective, however, fails to adequately account for the performance characteristics of these methods under the conditions most commonly encountered in applied research. Our investigation challenges this traditional dichotomy by systematically evaluating whether the purported efficiency advantages of parametric methods persist when their underlying assumptions are violated. We frame our research around three central questions that have received insufficient attention in the statistical literature. First, to what extent do nonparametric rank tests maintain their robustness properties across diverse forms of distributional violation, including asymmetric distributions, heavy-tailed distributions, and multimodal distributions? Second, how does the statistical efficiency of rank-based methods compare to parametric alternatives when distributional assumptions are not met? Third, can we develop a more nuanced framework for method selection that better reflects the practical realities of applied research? Our contribution extends beyond mere comparative analysis by introducing novel metrics for evaluating statistical performance that incorporate both error control and practical utility. By examining performance across a spectrum of distributional characteristics and sample sizes, we provide actionable guidance for researchers facing the common dilemma of method selection in the presence of uncertain distributional properties.