DEVELOPING AND EVALUATING NONPARAMETRIC TESTS FOR MIXED DESIGNS COMBINING BLOCK AND COMPLETELY RANDOMIZED DESIGNS

Abstract

This study develops and evaluates nonparametric tests for mixed experimental designs that integrate block and completely randomized designs. Traditional rank-based tests such as the Friedman, Modified Friedman, and Quade tests are widely used for randomized complete block designs (RCBDs), while the Kruskal–Wallis test is appropriate for completely randomized designs (CRDs). However, statistical tools that effectively address experiments combining both within- and between-subject factors remain limited. This research consisted of two major parts. Part I focuses on comparing the Friedman-type tests (Friedman, Modified Friedman, and Quade) under various distributions and design conditions to evaluate their power and Type I error performance. Part II extends the framework to mixed designs by combining each block-based test with the Kruskal–Wallis test, forming three new statistics evaluated through extensive Monte Carlo simulations. Results were analyzed under four probability distributions — Normal, Exponential, Chi-Square, and t-distribution — spanning symmetric, skewed, and heavy-tailed data-generating mechanisms. For each distribution, the between-subject (CRD) component is evaluated under multiple variance-ratio conditions relative to the within-subject (RCBD) component, with the Normal distribution examined under four conditions (2×, 4×, and 8× at two scale levels) and the remaining distributions under two conditions each, providing a comprehensive assessment of robustness under heterogeneous variance structures across multiple combinations of treatment numbers, block sizes, and sample sizes. Because rank-based procedures operate in the order of the observations rather than their magnitudes, they retain validity under conditions of skewness, outliers, or heavy tails where parametric mixed-model ANOVA can be fragile. This robustness motivates their use in mixed iv designs combining within- and between-subject factors (Hollander, Wolfe, & Chicken, 2014; Conover, 1999). The findings identified the most powerful and robust nonparametric procedures for mixed designs, contributing to more flexible and distribution-free analytical frameworks in experimental research.