Robust One-Sample t-test (Trimmed Mean)
Also known as: one-sample trimmed mean test, Yuen one-sample test, robust one-sample location test, trimmed mean t-test
The robust one-sample t-test replaces the ordinary mean with a trimmed mean and the sample variance with a Winsorized variance to compare a population location against a hypothesized value. It retains the t-test decision framework while sharply reducing sensitivity to outliers and heavy-tailed distributions, making it reliable in real-world continuous data that deviate from normality.
Key highlights
- Substantially more resistant to outliers and heavy-tailed distributions than the classical one-sample t-test.
- Retains an approximate t-distribution framework, so it is familiar and straightforward to interpret.
- Performs well across a wide range of non-normal distributions with minimal power loss under normality.
- Can be paired with bootstrap confidence intervals for even greater robustness.
- The trimming proportion is a transparent, pre-specified tuning parameter rather than a black-box adjustment.
Intuition
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How it works
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When to use it
Use the robust one-sample t-test when you want to test a location hypothesis about a single continuous variable but the data contain outliers, are skewed, or come from a heavy-tailed distribution that makes the classical t-test unreliable. It is especially valuable with small-to-moderate samples (n < 100) where the central limit theorem has not yet tamed the mean. Do not use it when data are genuinely normally distributed with no outliers — the classical t-test is slightly more powerful there. Also avoid it when the trimming proportion is chosen post-hoc after inspecting the data, which inflates the Type I error rate.
Strengths & limitations
- Substantially more resistant to outliers and heavy-tailed distributions than the classical one-sample t-test.
- Retains an approximate t-distribution framework, so it is familiar and straightforward to interpret.
- Performs well across a wide range of non-normal distributions with minimal power loss under normality.
- Can be paired with bootstrap confidence intervals for even greater robustness.
- The trimming proportion is a transparent, pre-specified tuning parameter rather than a black-box adjustment.
- The trimmed mean estimates a truncated population mean, not the full-population mean, which changes the inferential target.
- Choosing the trimming proportion requires a priori justification; the default 20% may not suit every context.
- Loses efficiency relative to the classical t-test when data are truly normal and outlier-free.
- Less widely known than the classical t-test, so reviewers may request justification for its use.
Common pitfalls
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Applications
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Frequently asked
How is this different from the Wilcoxon signed-rank test?
The Wilcoxon signed-rank test is fully nonparametric and tests the population median (under symmetry). The robust one-sample t-test is semi-parametric, tests the trimmed mean, and provides a direct t-distribution approximation. For symmetric distributions they target similar quantities; for skewed data the trimmed mean may be a more interpretable location summary than the median.
What trimming proportion should I choose?
A common default is 20% from each tail (gamma = 0.20). Wilcox (2012) shows this balances robustness and efficiency across many real distributions. If prior knowledge suggests only mild outlier contamination, 10% may suffice. The trimming proportion must be decided before analyzing the data.
Does the test work for small samples?
Yes — simulation studies show the robust t-test achieves better Type I error control than the classical t-test in small samples from non-normal distributions. However, very small samples (n < 15) leave few untrimmed observations after 20% trimming, which can reduce power substantially.
Can I combine trimming with bootstrapping?
Yes, and this is often recommended. Bootstrap confidence intervals for the trimmed mean require no distributional assumption beyond a sufficient sample size and tend to be more accurate than the t-approximation when the distribution is strongly skewed.
When should I stick to the classical one-sample t-test?
When you have strong evidence (e.g., from previous studies or a Shapiro-Wilk test on an adequate sample) that the data are approximately normal with no serious outliers, the classical t-test is slightly more powerful and its inferential target — the full-population mean — is easier to communicate.
Sources
- 1.Wilcox, R. R. (2012). Introduction to Robust Estimation and Hypothesis Testing (3rd ed.). Academic Press.ISBN 978-0123869838
- 2.Yuen, K. K. (1974). The two-sample trimmed t for unequal population variances. Biometrika, 61(1), 165–170.
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Cite this page
ScholarGate. (2026, June 3). Robust one-sample t-test. ScholarGate. https://scholargate.app/statistics/robust-one-sample-t-test