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Wilcoxon Signed-Rank Test Calculator
Determine if there is a statistically significant difference between paired data points without assuming a normal distribution. Enter your pre-test and post-test data below to instantly calculate the W-statistic, Z-score, and p-value.
How to use this calculator
- Enter your paired data: Paste your raw data into the Group 1 and Group 2 text boxes. Because this is a paired test, both groups must have the exact same number of data points. The calculator assumes the first number in Group 1 is paired with the first number in Group 2, and so on.
- Set your parameters: Choose your significance level ($\alpha$) and whether you are running a one-tailed or two-tailed test. (If you aren’t sure, Two-tailed at an $\alpha = 0.05$ level is the standard default).
Wilcoxon Signed-Rank Test
Non-parametric alternative to the paired t-test.
W-Statistic (Min)
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Valid Pairs (N)
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Z-Score
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P-Value
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*Technical note: Zero differences are excluded from the ranking. P-values are calculated using a normal approximation (Z-score) with continuity correction and variance adjustment for tied ranks.
Understanding Your Results
The Wilcoxon Signed-Rank test looks at the differences between your paired data points. It ranks the absolute size of those differences, and then compares the sum of the positive ranks to the sum of the negative ranks.
- W-Statistic ($W$): The test calculates the sum of the ranks for the positive differences ($W+$) and the negative differences ($W-$). The $W$-statistic reported is simply the smaller of those two sums.
- Valid Pairs ($N$): If a pair has a difference of exactly zero (i.e., the pre-test and post-test scores are identical), that pair is excluded from the ranking process. $N$ represents the number of pairs that actually showed a difference.
- Z-Score: For sample sizes larger than a few pairs, the $W$-statistic is converted into an approximate Z-score (a standard normal distribution metric) to find the p-value. This calculator applies a continuity correction and adjusts the variance if there are tied ranks in your data.
- P-Value: The probability of seeing a difference this large by random chance. If the p-value is less than your chosen $\alpha$, the difference between your paired groups is statistically significant.