# Wilcoxon Signed-Rank Calculator Run a paired nonparametric Wilcoxon signed-rank test from paired samples or differences > Canonical page: https://elysiatools.com/en/tools/wilcoxon-signed-rank-calculator - **Category:** Math & Numbers - **Keywords:** wilcoxon signed rank test, paired samples, nonparametric, rank test, p value, calculator ## Overview The Wilcoxon Signed-Rank Calculator is a nonparametric statistical tool used to compare two related samples or repeated measurements on a single sample. It serves as a robust alternative to the paired t-test when data does not follow a normal distribution, analyzing the ranks of the differences between paired observations to determine statistical significance. ## Inputs - **Input Mode** (select) - **Before Values** (textarea): e.g. 72, 75, 78, 74, 76 - **After Values** (textarea): e.g. 76, 79, 80, 77, 81 - **Difference Values** (textarea): e.g. 4, 4, 2, 3, 5 - **Alternative Hypothesis** (select) - **Alpha** (number) - **Decimal Places** (number) ## When to use - When comparing paired data that does not meet the normality assumption required for a parametric t-test. - When analyzing ordinal data or continuous data containing significant outliers that might skew mean-based results. - When evaluating the effectiveness of an intervention by comparing 'before' and 'after' measurements from the same subjects. ## How it works - Calculate the difference between each pair of observations or input pre-calculated differences directly into the tool. - Rank the absolute values of these differences from smallest to largest, excluding any pairs where the difference is zero. - Assign the original signs (positive or negative) to the ranks and calculate the sum of the positive and negative ranks to find the W-statistic. - Compute the p-value based on the rank sums and compare it against your chosen alpha level to decide whether to reject the null hypothesis. ## Use cases - Medical researchers comparing patient heart rates before and after administering a specific treatment. - UX designers evaluating task completion times for the same group of users across two different interface versions. - Environmental scientists measuring pollutant levels at the same locations during two different seasons. ## Frequently asked questions ### What is the main difference between this and a paired t-test? The Wilcoxon signed-rank test is nonparametric and does not require a normal distribution, whereas the paired t-test assumes the differences are normally distributed. ### Can I use this test for independent samples? No, this test is specifically for paired or related samples. For independent samples, use the Mann-Whitney U test. ### How are zero differences handled in the calculation? Pairs with a difference of zero are typically excluded from the ranking process, reducing the effective sample size. ### What does a p-value lower than the alpha level mean? It indicates that the observed difference is statistically significant, providing enough evidence to reject the null hypothesis. ### Which input mode should I choose? 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