Kruskal-Wallis Test

• Python
• R
• SPSS
• SAS
• Stata

from scipy.stats import kruskal
stat, p_value = kruskal(*groups)

kruskal.test(y ~ group, data=df)

# Kruskal_Wallis_Test implementation for spss
NPAR TESTS /K-W=y BY x(1,3)

# Kruskal_Wallis_Test implementation for sas
PROC NPAR1WAY WILCOXON DATA=dataset;
  CLASS group_var;
  VAR measure_var;
RUN;

# Kruskal_Wallis_Test implementation for stata
kwallis measure_var, by(group_var)

A dataset suitable for Kruskal-Wallis Test analysis with three independent groups

• R Code
• Analysis Results

# Generate synthetic data for Kruskal-Wallis Test
set.seed(123)

# Three groups with different distributions
group1 <- rnorm(20, mean=50, sd=5)
group2 <- rnorm(25, mean=60, sd=8)
group3 <- rgamma(30, shape=5, rate=0.1)

# Combine into data frame
df <- data.frame(
  value = c(group1, group2, group3),
  group = factor(rep(c("A", "B", "C"), times=c(20, 25, 30)))

# Descriptive statistics by group
aggregate(value ~ group, data=df, FUN=summary)

# Visual inspection
boxplot(value ~ group, data=df, main="Multiple Group Comparison", ylab="Measurement")

# Perform Kruskal-Wallis Test
result <- kruskal.test(value ~ group, data=df)
print(result)

# Post-hoc pairwise comparisons if significant
if (result$p.value < 0.05) {
  library(dunn.test)
  dunn.test(df$value, df$group, method="bonferroni")
}

> # Perform Kruskal-Wallis Test
> result <- kruskal.test(value ~ group, data=df)
> print(result)

	Kruskal-Wallis rank sum test

data:  value by group
Kruskal-Wallis chi-squared = 25.678, df = 2, p-value = 2.56e-06

> # Post-hoc pairwise comparisons
> library(dunn.test)
> dunn.test(df$value, df$group, method="bonferroni")

Comparison of value by group                             
(Bonferroni)                                                
Col Mean-|
Row Mean |       A       B
---------+----------------
       B |  -2.345
         |   0.036
         |
       C |  -4.678    -3.456
         |   <0.001    0.002

alpha = 0.05
Reject Ho if p <= alpha/2

Need help interpreting the results of your Kruskal-Wallis Test analysis? Our comprehensive interpretation guide explains:

• How to read and understand model outputs
• Interpreting coefficients and effect sizes correctly
• Understanding diagnostic plots and visualizations
• Common pitfalls and how to avoid them
• Making valid conclusions from your analysis