Sign Test
Also known as: İşaret Testi (Sign Test), one-sample sign test, paired sign test
The sign test is the simplest nonparametric hypothesis test for deciding whether the median of paired differences — or of a single sample — differs significantly from a hypothesised value. Formalised by W. J. Dixon and A. M. Mood in 1946, it imposes virtually no distributional assumptions and can be applied to any data where individual differences can be classified as positive or negative.
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 sign test when you have paired observations or a single sample and want to test whether the median difference departs from zero (or another target), especially when the normality assumption of the paired t-test cannot be met. It requires only that the pairs are independent and that the underlying variable is at least ordinal. It is suitable for both continuous and ordinal outcome variables, and is particularly valuable with very small samples, heavy-tailed distributions, or data containing outliers. When the magnitude of differences is available and trustworthy, the Wilcoxon signed-rank test is more powerful and should be preferred.
Strengths & limitations
- Requires almost no distributional assumptions — valid for any continuous or ordinal variable.
- Extremely robust to outliers because only the sign of each difference is used, not its magnitude.
- Computationally simple: the p-value follows directly from the binomial distribution.
- Appropriate for very small samples (as few as 5 pairs) where other tests break down.
- Less powerful than the Wilcoxon signed-rank test because it discards magnitude information.
- Ignoring the size of differences can mask practically important effects.
- Tied pairs (differences of exactly zero) must be discarded, reducing the effective sample size.
Frequently asked
When should I use the sign test rather than the Wilcoxon signed-rank test?
Use the sign test when you can only determine the direction of differences (not their size), when the distribution is highly irregular or the data contain extreme outliers, or when the sample is very small and ranking differences is unreliable. If numerical differences are available and plausible, the Wilcoxon signed-rank test is more powerful.
What happens to tied pairs (zero differences)?
Observations where the difference is exactly zero carry no sign information and are excluded from the analysis. The effective sample size n used in the binomial calculation is the number of non-zero differences. Discarding many ties substantially reduces power.
Can I use the sign test for a one-sample median problem?
Yes. Subtract the hypothesised median from each observation to form differences, then classify each as positive or negative. The procedure is identical to the paired case.
Is the sign test exact or approximate?
The p-value is exact, derived directly from the binomial distribution with p = 0.5. No large-sample approximation is needed, making it valid even for very small samples.
Sources
- Dixon, W. J. & Mood, A. M. (1946). The statistical sign test. Journal of the American Statistical Association, 41(236), 557–566. DOI: 10.1080/01621459.1946.10501898 ↗
How to cite this page
ScholarGate. (2026, June 1). Sign Test. ScholarGate. https://scholargate.app/en/statistics/sign-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.
- Friedman testStatistics↔ compare
- Mann-Whitney U testStatistics↔ compare
- Paired t-testStatistics↔ compare
- Wilcoxon signed-rank testStatistics↔ compare