Sign Test Calculator
The simplest paired test there is — count how many pairs went up and how many went down, and ask whether the split is fair.
Discard the ties, count the positives and negatives, and test the count against a fair coin: under the null hypothesis of no shift, each pair is equally likely to go either way, so the count follows a binomial distribution with p = 0.
How the sign test calculator works
Discard the ties, count the positives and negatives, and test the count against a fair coin: under the null hypothesis of no shift, each pair is equally likely to go either way, so the count follows a binomial distribution with p = 0.5.
It makes almost no assumptions — not even that the differences are on a meaningful scale — which makes it very robust and, correspondingly, not very powerful. Use it when you can only say which of a pair was larger.
Formula: P = binomial(k; n, 0.5), two-tailed
Worked examples
| Inputs | p-value (two-tailed, exact) | Note |
|---|---|---|
| 14 up, 4 down | 0.03088379 | p = 0.031 |
| An even split | 1 | p = 1 |
| All in one direction | 0.0078125 | p = 0.0078 |
FAQFrequently asked questions
What does the sign test assume?
Almost nothing — only that the pairs are independent and that under the null each is equally likely to go either way.
Why discard the ties?
Because a tie is evidence for neither direction. Dropping them is the standard treatment, though it does reduce the effective sample.
How does it compare to the Wilcoxon signed-rank test?
Wilcoxon also uses the *size* of each difference, so it is more powerful — but it needs the differences to be on a real scale. The sign test only needs the direction.
When is it the right choice?
When all you can say is "this one is bigger" — taste tests, subjective preferences, ordinal ratings.
Why is it weak?
Because it throws away magnitude. A dozen tiny increases count the same as a dozen huge ones.
Where these figures come from
- NIST Digital Library of Mathematical Functions — reference definitions for elementary and special functions
- Wolfram MathWorld — definitions and formulas for every topic on this page
- NIST/SEMATECH e-Handbook of Statistical Methods — the statistical formulas (mean, variance, z, confidence intervals, sample size)
- Australian Curriculum (ACARA) — Mathematics — the terms and methods taught in Australian schools
Last checked: September 2026. Formulas are fixed by mathematics and do not change with tax years or regulations.