# Wilcoxon paired samples test

## Description

The Wilcoxon test for paired samples is a non-parametric alternative for the Paired samples t-test, when the distribution of the samples is not Normal.

The statistics include the Hodges-Lehmann median difference (the Hodges-Lehman estimate of location shift) and its 95% confidence interval.

## Required input

- For both Sample 1 and Sample 2 select the variable of interest.
- Optionally select a filter to include a subset of cases.

## Results

### Summary statistics

The results section for the Wilcoxon test first displays summary statistics of the two samples. Note that only cases are included with data available for the two variables, therefore the sample size will always be equal.

The statistics include the Hodges-Lehmann median difference (the Hodges-Lehmann estimate of location shift) and its 95% confidence interval (Conover, 1999).
The Hodges-Lehmann median difference between two paired samples with sample size *n* is calculated as follows: first the *n* paired differences are calculated. For each possible set of 2 differences, the average is calculated. The Hodges-Lehmann median difference is the median of all *n* × *(n+1) / 2* averages. The confidence interval is derived according to Conover (1999, p. 360).

Note that the Hodges-Lehmann median difference is not necessarily the same as the difference between the medians.

### Wilcoxon test results

The Wilcoxon test (for paired samples) ranks the absolute values of the differences between the paired observations in sample 1 and sample 2 and calculates a statistic on the number of negative and positive differences (differences are calculated as sample 2 − sample 1).

If the resulting P-value is small (P<0.05) then it can be accepted that the median of the differences between the paired observations is statistically significantly different from 0.

Note that on SciStat.com P-values are always two-sided.

## See also

## Link

Go to Wilcoxon paired samples test.