Wilcoxon Signed Rank Calculator
wilcoxon signed-rank calculator. Get instant, accurate results. Enter values for instant results with step-by-step formulas.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator
Wilcoxon Signed Rank Calculator
Calculator
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Formula: W = min(W⁺, W⁻)
Worked example — W statistic
Formula
W = min(W⁺, W⁻)
Non-parametric alternative to paired t-test. Ranks absolute differences, sums positive and negative ranks.
Worked Examples
Example 1: Paired comparison
Problem:Before:[125,130,140,132,128] After:[110,125,135,128,120]
Solution:Rank differences, sum positive/negative ranks
Result:W statistic
Frequently Asked Questions
What does the Wilcoxon signed-rank test measure?
The Wilcoxon signed-rank test assesses whether the median difference between paired observations is significantly different from zero. Unlike the paired t-test it considers both the direction and magnitude of differences by ranking absolute differences and summing the ranks for positive and negative differences separately.
When should I use Wilcoxon signed-rank instead of a paired t-test?
Use the Wilcoxon signed-rank test when paired differences are clearly non-normal — especially with small samples (n < 30), skewed distributions, or significant outliers. The paired t-test is preferred when normality holds because it is more statistically powerful. For very small samples (n < 10), consult exact critical value tables rather than relying on normal approximations.
What are the assumptions of the Wilcoxon signed-rank test?
Observations must be paired and each pair must be independent of other pairs; the differences must come from a continuous symmetric distribution (symmetry around the median, not necessarily normal); and the measurement scale must be at least interval (so that differences are meaningful and rankable). Zero differences are excluded from the analysis, and tied ranks are averaged using the standard mid-rank method.
Reviewed for accuracy by Manoj Kumar, Mathematics Educator · Editorial policy
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