Perform a sign test on paired data using only the direction of differences.
The sign test is the simplest paired test, requiring only the direction of each difference. Tied pairs are discarded, which reduces the effective sample size. Discarding magnitude makes the sign test less powerful than Wilcoxon, but it requires almost no assumptions and works on purely ordinal data.
Sign Test
Under the no-effect hypothesis positives follow a binomial with p = 0.5; z = (positives − n/2) ÷ √(n/4)
Under the no-effect hypothesis positives follow a binomial with p = 0.5; z = (positives − n/2) ÷ √(n/4) The sign test is the simplest paired test, requiring only the direction of each difference. Tied pairs are discarded, which reduces the effective sample size.
Discarding magnitude makes the sign test less powerful than Wilcoxon, but it requires almost no assumptions and works on purely ordinal data.
This calculator takes 3 inputs: Positive differences, Negative differences, Significance level. The pre-filled defaults are a realistic starting point — replace them with figures from your own environment for a result you can act on.