Trimmed Mean Test (Yuen's Test)
Two-Sample Trimmed Mean Test (Yuen's Test) · Also known as: Yuen's test, Yuen-Welch test, robust mean comparison, kırpılmış ortalama testi
The trimmed mean test compares two groups using trimmed means, which discard a fixed proportion of the most extreme observations in each tail before averaging. Introduced by Karen K. Yuen in 1974, it is a robust alternative to the classical t-test when the data are non-normal or contain outliers and the population variances are unequal.
Read the full method
Sign in with a free account to read this section.
Method map
The neighbourhood of related methods — select a node to explore.
When to use it
Use the trimmed mean test to compare two independent groups on a continuous outcome when normality is doubtful or outliers are present, especially if the group variances differ. It needs independent observations and a reasonable sample (at least about 20 per group), and it assumes the trimmed data still represent the phenomenon of interest. It is a strong default when a plain t-test would be distorted by heavy tails but you still want to reason about a mean-like centre.
Strengths & limitations
- Resistant to outliers and heavy tails because the most extreme observations are removed before comparison.
- Handles unequal population variances through Yuen-Welch degrees of freedom, unlike the pooled t-test.
- Keeps a familiar mean-difference interpretation while gaining robustness, and is simple to compute and report.
- Discarding tail observations sacrifices some information and statistical efficiency when the data really are normal.
- The result depends on the chosen trimming proportion, which must be fixed in advance rather than tuned to the data.
- Unreliable in very small samples (below about 10 per group) and when the outlier share is so high that even trimming cannot stabilise the centre.
Frequently asked
How much should I trim?
Trimming 10-20% from each tail is the common default and works well across many distributions. The key rule is to fix the proportion before looking at the test result, since choosing it to get a significant outcome invalidates the test.
How is this different from the Mann-Whitney U test?
Both are robust to outliers, but the trimmed mean test compares trimmed means and keeps a mean-like, interpretable difference, whereas Mann-Whitney compares stochastic dominance through ranks. Use the trimmed mean test when you want to reason about a central tendency on the original scale.
What happens if there are too many outliers?
When the outlier share climbs above roughly 25%, even trimming cannot fully stabilise the centre. You should either raise the trimming proportion or switch to a median-based or MAD-based comparison.
Can I use it on small samples?
It needs a reasonable sample, about 20 per group, to be reliable. Below roughly 10 observations per group the trimmed mean test becomes untrustworthy and a permutation test is the better choice.
Sources
- Yuen, K. K. (1974). The Two-Sample Trimmed t for Unequal Population Variances. Biometrika, 61(1), 165-170. DOI: 10.1093/biomet/61.1.165 ↗
- Wilcox, R. R. (2012). Introduction to Robust Estimation and Hypothesis Testing (3rd ed.). Academic Press. ISBN: 978-0123869838
How to cite this page
ScholarGate. (2026, June 1). Two-Sample Trimmed Mean Test (Yuen's Test). ScholarGate. https://scholargate.app/en/statistics/trimmed-mean-test
Which method?
Set this method beside its closest kin and read them side by side — the library lays the books on the table; the choice is yours.
- MAD EstimationStatistics↔ compare
- Mann-Whitney U testStatistics↔ compare
- Permutation TestStatistics↔ compare
- Welch t-testStatistics↔ compare