Which Wilcoxon should we use? An interactive rank test and other alternatives
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Classical nonparametric tests to compare multiple samples, such as the Wilcoxon test, are often based on the ranks of observations. We design an interactive rank test called i-Wilcoxon—an analyst is allowed to adaptively guide the algorithm using observed outcomes, covariates, working models and prior knowledge—that guarantees type-I error control using martingales. Numerical experiments demonstrate the advantage of (an automated version of) our algorithm under heterogeneous treatment effects. The i-Wilcoxon test is first proposed for two-sample comparison with unpaired data, and then extended to paired data, multi-sample comparison, and sequential settings, thus also extending the Kruskal-Wallis and Friedman tests. As alternatives, we numerically investigate (non-interactive) covariance-adjusted variants of the Wilcoxon test, and provide practical recommendations based on the anticipated population properties of the treatment effects.
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