📊

Sign Test Calculator

The simplest paired test — count improvements versus declines and get the exact binomial one- and two-sided p-values, with the normal approximation.

Before (or sample A)

After (or sample B)

Loading calculator…

How it works

Under H₀ each non-tied pair is + or − with probability ½; one-sided p = P(Binomial(n, ½) ≤ min(+, −)); two-sided p = 2 × that

The sign test uses only the direction of each paired change, so it makes no assumption about the size or distribution of differences — it is valid for ordinal data and robust to anything. The price is power: it ignores how big the changes are, so the Wilcoxon signed-rank test usually detects effects the sign test misses. It is ideal as a quick sanity check or when only “better/worse” is recorded.

Worked example

Twelve blood-pressure pairs: 10 fell, 1 rose, 1 unchanged → exact two-sided p = 0.012.

Frequently asked questions

What happens to ties?

They are dropped and n is reduced — a tie says nothing about direction.

Sign test or Wilcoxon?

Wilcoxon when differences can be meaningfully ranked; the sign test when only direction is trustworthy.

Related calculators

Wilcoxon Signed-Rank Test Calculator

Paired non-parametric test — W statistic, z with tie correction and two-sided p-value for before/after or matched data.

Binomial Probability Calculator

Find the probability of exactly, at most, or at least k successes in n independent trials, each with the same success probability p.

Paired t-Test Calculator

Paste before-and-after (paired) data or summary statistics and get the paired t-test: mean difference, t statistic, degrees of freedom, one- or two-tailed p-value, confidence interval, effect size, a Shapiro–Wilk normality check and every step worked out.

For education — check assumptions (sample size, distribution, independence) before using a test result in a real decision.