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Yuen-Welch trimmed-means t-test

Yuen's t-test compares trimmed means using Winsorised variances, staying robust to outliers and skew, in both independent and paired forms.

What is Yuen-Welch trimmed-means t-test?

Trim the upper and lower γ% (default 20%) of each group; compute the t-statistic on the remaining means with a Welch-style correction using the *Winsorised* variances (where the trimmed values are replaced by the cutoff, not removed). This gives a t-test that's robust to outliers while still gaining power from the structure of the data.

Compared to Mann-Whitney: Yuen tests for *trimmed-mean* differences, which is a more interpretable location parameter than the rank-based 'stochastic shift'. Compared to Welch t on raw data: Yuen is robust to ~γ% outliers per tail; if the data are clean and normal, Welch is slightly more powerful.

Standard trim is 20%, recommended by Wilcox (2017) as a sensible default that balances power against outlier robustness.

When should I use Yuen-Welch trimmed-means t-test?

Heavy-tailed data where Welch's t is over-inflated by outliers.
When you want a mean-difference interpretation but Mann-Whitney's location-shift framing is too restrictive.

What data does it need?

Two numeric columns + paired flag + trim fraction (10/20/25/30 %).

What does it report?

t statistic + Welch-style df + p + trimmed mean difference + SE / CI.

What does it assume?

Independent samples (or paired with the paired option).
Symmetric trimmed distributions.

Formula

t = (trimmed_x₁ − trimmed_x₂) / SE(trimmed),  df via Satterthwaite on Winsorised variances

How do I interpret the result?

The trimmed mean difference is the headline effect — same scale as the data, less outlier-sensitive than the raw mean difference.

References

Yuen (1974). The two-sample trimmed t for unequal population variances. Biometrika 61(1).
Wilcox (2017). Introduction to Robust Estimation and Hypothesis Testing, 4th ed.