Robust Friedman Test

The standard Friedman test ranks raw scores within each block and tests whether rank sums differ across conditions. The robust version applies trimming or Winsorization to reduce the influence of extreme values before or during ranking, making the test statistic less sensitive to outliers and heavy tails.

Rand Wilcox recommends 20% trimming as a general-purpose default, which balances robustness against the loss of efficiency. A 10% trim is sometimes used when distributions are only mildly non-normal. The choice should be fixed before data analysis to avoid data-driven inflation of false positives.

Kendall's W remains a commonly reported effect size for Friedman-type tests, but with robust variants some researchers prefer to report the robust rank-based correlation or the explained variance analog derived from the trimmed-mean framework. Always clarify which effect-size metric you are reporting.

Yes. Because the test is rank-based at its core, it is appropriate for ordinal data such as Likert scales with five or more points. Trimming is less meaningful for truly ordinal data with few categories, so verify that the robust modification adds value given your measurement scale.

Pairwise robust Wilcoxon signed-rank tests with a false discovery rate (Benjamini-Hochberg) or Bonferroni-Holm correction are commonly used. Wilcox's WRS2 package provides dedicated robust post-hoc procedures that match the trimming logic of the omnibus test.