Wilcoxon signed-rank test and Wilcoxon rank-sum test

Wilcoxon Effect Size

• Compute Wilcoxon effect size (r) for:
  • one-sample test (Wilcoxon one-sample signed-rank test);
  • paired two-samples test (Wilcoxon two-sample paired signed-rank test) and
  • independent two-samples test ( Mann-Whitney, two-sample rank-sum test).

The effect size r is calculated as Z statistic divided by square root of the sample size (N)\frac{Z}{\sqrt{N}}

The Z value is extracted from either coin::wilcoxsign_test() (case of one- or paired-samples test) or coin::wilcox_test() (case of independent two-samples test).

Note that N corresponds to total sample size for independent samples test and to total number of pairs for paired samples test.

The r value varies from 0 to close to 1. The interpretation values for r commonly in published litterature and on the internet are: 0.10 - < 0.3 (small effect), 0.30 - < 0.5 (moderate effect) and >= 0.5 (large effect).

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