The Wilcoxon signed-rank test is robust to outliers in the data if the population is at least somewhat symmetric.

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The Wilcoxon signed-rank test is based on the ranks of the absolute differences between pairs of observations. It does not depend on the actual values of the observations, but only on their relative order. Therefore, it is less sensitive to outliers than parametric tests that rely on specific assumptions about the distribution of the data. However, if the population is highly skewed or has extreme outliers, the Wilcoxon signed-rank test may not be suitable, and alternative non-parametric tests or transformations may be necessary.

The Wilcoxon Signed-Rank Test Is Robust to Outliers in the Data