# Mann-Whitney independent samples test

## Description

The Mann-Whitney test is used to test the significance of the difference between two independent samples. It is the alternative for the Independent samples t-test, when the distribution of the samples is not Normal.

The Mann-Whitney test combines and ranks the data from sample 1 and sample 2 and calculates a statistic on the difference between the sum of the ranks of sample 1 and sample 2.

If the resulting P-value is small (P<0.05) then a statistically significant difference between the two samples can be accepted.

## Required input

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

## Results

### Summary statistics

The results for the Mann-Whitney test (independent samples) includes summary statistics of the two samples.

The statistics include the Hodges-Lehmann median difference (the Hodges-Lehmann estimate of location shift) and its 95% confidence interval (Conover, 1999).
For two independent samples with sample size *m* and *n*, the Hodges-Lehmann median difference is the median of all *m* × *n* paired differences between the observations in the two samples. Differences are calculated as sample 2 − sample 1. The confidence interval is derived according to Conover (1999, p. 281).

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

### Mann-Whitney test results

The Mann-Whitney test combines and ranks the data from sample 1 and sample 2 and calculates a statistic on the difference between the sum of the ranks of sample 1 and sample 2.

In the presence of ties, SciStat.com calculates the P-value according to the method by Conover, 1999.

When either or both sample sizes are large (>20) then SciStat.com uses the Normal approximation (Lentner, 1982) to calculate the P-value. For small sample sizes, in the absence of ties, SciStat.com calculates the exact probability (Conover, 1999).

If the resulting P-value is small (P<0.05) then a statistically significant difference between the two samples can be accepted.

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