UniODA vs. Wilcoxon Rank-Sum Test: Invariance over Monotonic Transformations

Paul R. Yarnold

Optimal Data Analysis, LLC

A study compared ordinal scores between two groups (Ns = 9 and 8) using the Wilcoxon rank-sum test (p < 0.03). When the scores were compared using UniODA, p < 0.02, ESS = 66.7 (a relatively strong effect). While the Wilcoxon test is performed on ranks, UniODA is conducted using raw data. However, performing UniODA on the ranks yields identical results because UniODA is invariant over any monotonic transformation of the attribute.

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