Simulations of nonparametric analyses of predictor sort (matched specimens) data
2019
Verrill, S. P. | Kretschmann, David E.
A type of blocked experiment has the potential of being poorly designed and analyzed. Several papers by Verrill and co-workers referred to such an experiment as a "predictor sort" experiment. It has also been referred to in other papers and textbooks as "artificial pairing" and "matched pair" or "matched subjects" design. The associated design process is also sometimes described as "forming blocks via a concomitant variable." In a wood research context, the response in such an experiment might be lumber strength after a treatment, and the predictor used to form blocks would be some combination of lumber stiffness, knot size, and slope of grain (all of which can be measured nondestructively prior to specimen allocation). Improperly designed or analyzed, predictor sort experiments can be associated with incorrect power calculations, inappropriate sample sizes, incorrect tests of hypotheses, and incorrect confidence intervals. In a 2017 paper, Verrill and Kretschmann reviewed the main results in the literature, added a section on multiple comparisons, and presented the results from power and confidence interval coverage simulations that emphasized the importance of proper design and analysis of predictor sort experiments; that work was based on the assumption that the predictor and the response have a bivariate normal distribution. This paper, which can be thought of as a companion to the 2017 paper, constitutes a nontheoretical, simulation-based first look at the effect of predictor sort allocation on nonparametric hypothesis tests (Kruskal-Wallis, one-way on ranks, one-way on Van der Waerden ranks, two-way on ranks, and Friedman tests) and nonparametric confidence bounds on quantiles. It also considers situations in which a bivariate normal assumption for the predictor-response pair does not hold.
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