Wilcoxon Signed-Rank Test
Computes the Wilcoxon signed-rank test, the non-parametric alternative to the paired t-test. When you measure the same subjects twice — before and after a treatment — and the data don't follow a normal distribution, this is the test to use. It works with the differences between pairs: it ranks the magnitudes of those differences, assigns ranks and separately sums the ranks of the positive and negative differences. The tool computes W+, W− and the normal approximation z, with a tie correction. Enter the two paired series.
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Wilcoxon Signed-Rank Test
Computes the Wilcoxon signed-rank test, the non-parametric alternative to the paired t-test. When you measure the same subjects twice — before and after a treatment — and the data don't follow a normal distribution, this is the test to use. It works with the differences between pairs: it ranks the magnitudes of those differences, assigns ranks and separately sums the ranks of the positive and negative differences. The tool computes W+, W− and the normal approximation z, with a tie correction. Enter the two paired series.
The paired t-test for when the data aren't normal
Whenever you measure the same person, the same machine or the same patient twice — before and after an intervention — the question arises: was the change real? The paired t-test answers that, but it requires the differences to be roughly normal. When that condition fails, the Wilcoxon signed-rank test steps in without demanding normality.
The idea is to swap the values for positional information. You compute each pair's difference, drop the zeros, then rank the magnitudes of the remaining differences. Next you separately sum the ranks of the positive and negative differences. If the treatment had no effect, those two sums would be similar; a large imbalance is what the test detects, capturing both the sign and the relative size of the changes.
Enter the two paired series. The tool returns W+, W− and the normal approximation z, already with the tie correction in the variance, which matters when several difference magnitudes are equal. With the z you obtain the p-value and decide whether the difference between the two measurements is statistically significant.
Related Tools
Mann-Whitney U Test
Computes the Mann-Whitney U test, the non-parametric alternative to the t-test for comparing two independent groups. Instead of comparing means, it compares the ranks of the combined data, which makes it valid even when the data don't follow a normal distribution or are ordinal. The tool computes the U statistic and the normal approximation z, with a tie correction. Enter the two groups of observations, separated by commas.
Friedman Test
Computes the Friedman test, the non-parametric version of repeated-measures ANOVA. It's used when the same subjects (or blocks) go through three or more conditions and you want to know whether the conditions differ, without assuming normality. Within each block, the treatments are ranked; if one treatment is consistently better, it accumulates low ranks across all blocks, and the Friedman chi-square statistic grows. Enter the blocks: treatments separated by commas, blocks by semicolons.
Sign Test (Paired)
Computes the sign test, the simplest and most robust paired test of all. It completely ignores the magnitude of the differences between pairs and looks only at the sign: how many times the value went up and how many it went down. Under the hypothesis of no effect, ups and downs should balance out, like heads and tails, and the p-value comes straight from a binomial distribution. Because it uses so little information, it's less powerful than Wilcoxon, but it makes almost no assumptions. Enter the two paired series.
The results provided by this tool are for general informational and educational purposes only and do not constitute professional, financial, medical, legal, tax or accounting advice. Always confirm important decisions with a qualified professional and official sources.