Sign Test Calculator
Perform the sign test, a non-parametric hypothesis test that evaluates whether the median of paired differences is significantly different from a hypothesized value. No normality assumption is required.
The sign test is one of the simplest non-parametric tests for matched-pair data. For each observation, you compute the difference from a hypothesized median and record whether it is positive or negative. Ties (differences of zero) are excluded. Under the null hypothesis that the true median equals the hypothesized value, the number of positive signs follows a Binomial(n, 0.5) distribution.
The test statistic S is the smaller of the positive and negative sign counts. A very small S indicates that the data is overwhelmingly on one side of the hypothesized median, providing evidence against the null hypothesis. The two-tailed p-value is computed as twice the cumulative binomial probability of observing S or fewer successes.
The sign test trades statistical power for robustness. It makes no assumptions about the shape of the distribution and works well even with ordinal data or small samples. However, it is less powerful than the Wilcoxon signed-rank test (which also uses the magnitudes of differences) and much less powerful than the paired t-test when the normality assumption holds.