# MASH : Maths and Stats Help

### Mann-Whitney U-Test

#### Introduction

A Mann-Whitney U-Test compares the means between two unrelated groups, such as comparing the difference in heights between Cats and Yorkshire Terriers.

It is considered a non-parametric test and therefore is suitable for non-parametric data. To check if your data is parametric, please check our dedicated guide: Parametric or Not Guide (PDF)

If your data is parametric you should consider using an Independent-Samples t-Test

#### Test Procedure

The Mann-Whitney U test is also known as the Wilcoxon rank sum test and will be displayed as such in the R output. It is different from the Wilcoxon signed rank test, which is a test for paired samples. Both types of tests fall under the wilcox.test() function in R, with a “paired” argument denoting which of the two tests are run (FALSE/TRUE). By default, the argument is FALSE, meaning that the function will run a Mann-Whitney U.

##### Formula method

This is used for when the data is structured using a grouping variable. A grouping variable is a categorical variable indicating which scores belong to different groups.

Data:

The first argument entered in the wilcox.test() function is a formula that takes the following structure:

dependent variable ~ independent variable

The second argument is the data frame.

``wilcox.test(Height ~ Species, pet_height1)``
``````## Warning in wilcox.test.default(x = DATA[[1L]], y = DATA[[2L]], ...): cannot
## compute exact p-value with ties``````
``````##
##  Wilcoxon rank sum test with continuity correction
##
## data:  Height by Species
## W = 35.5, p-value = 0.1012
## alternative hypothesis: true location shift is not equal to 0``````
##### Variables method

This method is used when your data is structured into two separate variables. Both of your variables should be numeric.

Data:

Put both of your variables in the wilcox.test() function in any order. If you have your variables stored in a data frame, use the following structure to indicate the variable: data_frame\$variable_name

``wilcox.test(pet_height2\$cat_height, pet_height2\$york_height)``
``````## Warning in wilcox.test.default(pet_height2\$cat_height,
## pet_height2\$york_height): cannot compute exact p-value with ties``````
``````##
##  Wilcoxon rank sum test with continuity correction
##
## data:  pet_height2\$cat_height and pet_height2\$york_height
## W = 35.5, p-value = 0.1012
## alternative hypothesis: true location shift is not equal to 0``````

R will generate largely the same output for both formula and variables methods.

##### Descriptive Statistics by group

The results of the tests will not include any descriptive statistics. As medians and inter-quartile ranges are commonly reported, please check our guide on descriptive statistics.

##### Test Statistics

The table output shows the Mann-Whitney U statistic (W) and the p-value.

## Reporting the Results in APA Formatting

Heights of Cats and Yorkshire Terriers were compared. On average the Yorkshire Terriers (Mdn = 29.27) were taller than the Cats (Mdn = 28.00) however a Mann-Whitney U test indicated that this difference was not statistically significant, (NCats=11, NTerriers=11) = 35.5, = .101.