How to Perform
Kruskal Wallis
test in R

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What is a Kruskal Wallis test?

Use the Kruskal-Wallis test to determine whether the medians of two or more groups differ when you have data that are not symmetric, such as skewed data.

The Kruskal-Wallis test is a non-parametric statistical technique and is an alternative to one-factor ANOVA. This test assumes that we have one continuous dependent variable (e.g. anxiety level, stress level, etc.) and one categorical variable with three or more groups (e.g. marital status, education level, etc.).

When Should a Kruskal Wallis be Used?

The Kruskal-Wallis test is a nonparametric alternative to a one-way ANOVA. Non-parametric means that the test doesn’t assume your data comes from a particular distribution. The test doesn’t require the data to be normal but instead uses the rank of the data values instead of the actual data values for the analysis.

An Example Of the Kruskal Wallis Test

For example, Suppose a researcher wants to examine whether there are differences in test scores based on where a student was born. Therefore, we have one independent categorical variable country with three categories (USA, Australia, Europe) and one continuous dependent variable (exam score).

Therefore, we test the following hypotheses:

Null hypothesis: There is no significant effect of the country where students were born (USA, Australia, Europe) on exam scores.

Alternative hypothesis: There is a significant effect of the country where students were born (USA, Australia, Europe) on exam scores.

R function to Compute Kruskal Wallis Test

The code to run a Kruskal Wallis Test using R is as follows:

kruskal.test(DV~ IV, var.equal=TRUE, data = dataframe)

DV: dependent variable

IV: Independent variable

Running Kruskal Wallis test in Rstudio

In this section, we will show you how to run the Kruskal Wallis H test using the r studio program and how to interpret the test results after we obtain the result of the test. In the first part, we present the r program code and function for the Kruskal Wallis H test. Next, you will see the outputs as a result of running the r codes. In the last section, you can find the interpretation of the Kruskal Wallis H test in APA format.

# LOAD DATA
library(readxl)
Data <- read_excel(“Data.xlsx“)
# VIEW DATA
View(Data)
# NAME VARIABLES
data <- Data
country <- data$country
exams <- data$exams
# SHOW LEVELS OF CATEGORICAL VARIABLE
levels(country)

# SHOW THE MEDIAN OF THE DEPENDENT VARIABLE BY CATEGORICAL VARIABLE
library(dplyr)
group_by(data, country) %>% summarise(count = n(), median = median(exams, na.rm = TRUE))

# PERFORM THE KRUSKAL WALLIS TEST
kruskal.test(exams ~ country, data = data)

> group_by(data, country) %>% summarise(count = n(), median = median(exams, na.rm = TRUE))

## # A tibble: 3 × 3
##   country   count median
##   <chr>     <int>  <dbl>
## 1 Australia    35     52
## 2 Europe       31     58
## 3 USA          33     80


> kruskal.test(exams ~ country, data = data)

## 
##  Kruskal-Wallis rank sum test
## 
## data:  exams by country
## Kruskal-Wallis chi-squared = 3.6755, df = 2, p-value = 0.1592

Reporting Kruskal Wallis in R

The Kruskal-Wallis test was conducted to determine whether the country where students were born (USA, Australia, Europe) has an effect on exam scores. The results indicate a non-significant effect, X-squared (2) = 3.68, p = 0.159. We, therefore, fail to reject the null hypothesis and conclude that there is no effect of the country where students were born (USA, Australia, Europe) on exam scores. The median exam score for students born in Australia is 52, for students born in Europe is 58, and for students born in the USA is 80.

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How to Perform Kruskal Wallis test in R