# Mann-Whitney test (independent samples)

Command: | Statistics Rank sum tests Mann-Whitney test (independent samples) |

## Description

The **Mann-Whitney test** is the non-parametric equivalent of the independent samples t-test (it is sometimes - wrongly - called a 'non-parametric t-test').

This test should be used when the sample data are not Normally distributed, and they cannot be transformed to a Normal distribution by means of a logarithmic transformation.

## Required input

Select the variables for sample 1 and sample 2. You can use the button to select variables and filters in the variables list.

Caveat: the two filters must define distinct groups so that the same case is not included in the two samples.

## Results

### Summary statistics

The results windows for the Mann-Whitney test (independent samples) displays 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 two medians.

### Mann-Whitney test results

The Mann-Whitney test (independent samples) 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.

When either or both sample sizes are large (>20) then MedCalc uses the Normal approximation (Lentner, 1982) to calculate the P-value. For small sample sizes, in the absence of ties, MedCalc 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 in MedCalc P-values are always two-sided.

## Literature

- Conover WJ (1999) Practical nonparametric statistics, 3
^{rd}edition. New York: John Wiley & Sons. - Lentner C (ed) (1982) Geigy Scientific Tables, 8
^{th}edition, Volume 2. Basle: Ciba-Geigy Limited.