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
# 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
# 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 (Note: This package has been withdrawn but is still available in the CRAN archives.)

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.