# Nonparametric Tests of Group Differences

**R** provides functions for carrying out Mann-Whitney U, Wilcoxon Signed Rank, Kruskal Wallis, and Friedman tests.

`# independent 2-group Mann-Whitney U Test `

wilcox.test(y~A)

# where y is numeric and A is A binary factor

`# independent 2-group Mann-Whitney U Test`

wilcox.test(y,x) # where y and x are numeric

`# dependent 2-group Wilcoxon Signed Rank Test `

wilcox.test(y1,y2,paired=TRUE) # where y1 and y2 are numeric

`# Kruskal Wallis Test One Way Anova by Ranks `

kruskal.test(y~A) # where y1 is numeric and A is a factor

`# Randomized Block Design - Friedman Test `

friedman.test(y~A|B)

# where y are the data values, A is a grouping factor

# and B is a blocking factor

For the wilcox.test you can use the **alternative="less"** or **alternative="greater"** option to specify a one tailed test.

Parametric and resampling alternatives are available.

The package **pgirmess** provides nonparametric multiple comparisons. (Note: This package has been
withdrawn but is still available in the CRAN archives.)

`library(npmc)`

npmc(x)

#
where x is a data frame containing variable 'var'

#
(response variable) and 'class' (grouping variable)

## Visualizing Results

Use box plots or density plots to visual group differences.

## To Practice

This interactive example allows you to practice the Wilcoxon Signed Rank test with R.