Robust Paired Samples t-test
Also known as: trimmed-mean paired t-test, Yuen paired t-test, robust dependent-samples t-test, trimmed paired comparison
The robust paired samples t-test replaces arithmetic means with trimmed means and Winsorized variance to compare two related measurements while resisting the distorting influence of outliers and non-normal distributions, producing reliable inference where the classic paired t-test breaks down.
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When to use it
Use the robust paired samples t-test whenever you have matched pairs or repeated measures on the same subjects and the difference scores show notable outliers, skewness, or heavy tails that make the classic paired t-test unreliable. It is particularly valuable with small to moderate samples where violations of normality cannot be ignored. Do not use it when the untrimmed mean is the quantity of theoretical interest, or when your sample is so small (n < 10) that trimming removes too many observations. For pure ordinal data, the Wilcoxon signed-rank test remains a more principled nonparametric choice.
Strengths & limitations
- Substantially more powerful than the Wilcoxon signed-rank test when the distribution is symmetric but heavy-tailed.
- Controls Type I error rate well under non-normality, unlike the classic paired t-test with small samples.
- Still yields an interpretable location estimate — the trimmed mean difference — rather than a rank-based statistic.
- Can be augmented with bootstrapping to obtain robust confidence intervals without distributional assumptions.
- Widely implemented in R (WRS2 package) and specialized robust-statistics software.
- The trimmed mean is not the same as the arithmetic mean, so results may not be directly comparable to studies using the classic test.
- Optimal trim proportion depends on the unknown degree of contamination; 20% is a common default but may not be ideal in all situations.
- Power is lower than the classic paired t-test when data truly are normally distributed without outliers.
- Less familiar to reviewers in applied fields, which may require additional explanation in manuscripts.
Frequently asked
How is this different from the Wilcoxon signed-rank test?
The Wilcoxon signed-rank test ranks the absolute differences and sums the ranks, discarding magnitude information. The robust paired t-test retains the actual difference values but down-weights extremes through trimming. It tends to be more powerful when the distribution is symmetric and heavy-tailed, while Wilcoxon is preferable for strongly skewed or ordinal data.
What trim proportion should I use?
20% trimming from each tail (g = 0.20) is the standard recommendation in Wilcox's framework, as it provides good protection across a wide range of contamination levels. Smaller trim proportions (10%) preserve more data but offer less protection; larger proportions waste information unnecessarily when outliers are rare.
Can I add bootstrapping to this test?
Yes. Bootstrapping the trimmed mean difference provides confidence intervals that do not rely on the approximate t-distribution for the Winsorized variance. This combination — trimming plus bootstrap — is often recommended for small samples or when the distribution is asymmetric.
Does this test still require independence of pairs?
Yes. Within each pair, the two measurements must be related (that is what makes them paired), but pairs must be independent of each other. The design assumption is unchanged from the classic paired t-test.
How do I report results?
Report the trim proportion used, the trimmed mean difference, its standard error, the t statistic, degrees of freedom (h − 1), p-value, and, ideally, a bootstrap confidence interval for the trimmed mean difference. State explicitly that a 20% trimmed mean was used so readers can interpret the location estimate correctly.
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 3). Robust Paired Samples t-test. ScholarGate. https://scholargate.app/en/statistics/robust-paired-samples-t-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.
- Paired samples t-testStatistics↔ compare
- Robust independent samples t-testStatistics↔ compare
- Robust one-sample t-testStatistics↔ compare