Sign Test Calculator

The sign test is a simple non-parametric procedure for paired observations. It asks whether positive and negative differences occur equally often, rather than measuring how large those differences are. Typical applications compare measurements before and after treatment, matched subjects, repeated ratings, or observations against a hypothesized median. Because it relies only on direction, the test does not require normally distributed data and is resistant to extreme values. For each pair, the calculator subtracts the first observation from the second. A positive difference receives a plus sign, a negative difference receives a minus sign, and an exact zero is a tie. Ties are removed from the effective sample size. Under the null hypothesis that positive and negative differences are equally likely, the number of positive signs follows a binomial distribution with probability 0.5. The calculator reports the exact two-sided p-value by doubling the probability of the smaller tail, capped at one. A small p-value indicates that the observed imbalance of signs would be unusual if increases and decreases were equally likely. Compare the p-value with the selected significance level before drawing a conclusion. A result below alpha supports rejecting the null hypothesis, while a result at or above alpha does not provide sufficient evidence to reject it. Failure to reject is not proof that the paired distributions are identical; it only means the direction imbalance is not persuasive at that threshold. The sign test is useful when differences are ordinal, strongly skewed, affected by outliers, or too sparse to justify stronger assumptions. Its robustness comes with lower statistical power because it discards the magnitude of every difference. If paired differences are continuous and reasonably symmetric, the Wilcoxon signed-rank test can use both signs and ranks. If normality is defensible, a paired t-test can be more efficient. Choose the method according to the measurement scale and study design rather than according to which produces the smallest p-value. Enter paired values in the same order so each position represents the same subject or matched unit. Unequal sample lengths are invalid, and many ties reduce the information available to the test. Report the positive, negative, and tied counts along with the p-value, significance level, and scientific context. This calculator is suited to teaching, reproducible checks, and exploratory analysis, but important research conclusions should include an effect estimate and appropriate confidence interval.