kruskal_wallis() compares three or more groups when your data isn't
normally distributed or when you have ordinal data (like ratings or rankings).
It's the non-parametric alternative to one-way ANOVA.
Think of it as:
An extension of the Mann-Whitney test for more than two groups
A robust way to compare groups that works with any data shape
Perfect for Likert scales, rankings, or skewed distributions
The test tells you:
Whether at least one group is different from the others
How strong the overall group effect is (effect size)
Which groups tend to have higher or lower values (via mean ranks)
Arguments
- data
Your survey data (a data frame or tibble)
- ...
The variables you want to compare between groups. You can list multiple variables or use helpers like
starts_with("satisfaction")- group
The categorical variable that defines your groups (e.g., education, employment). Must have at least 2 groups (3+ for meaningful use).
- weights
Optional survey weights for population-representative results
- conf.level
Confidence level for intervals (Default: 0.95 = 95%)
Value
Test results showing whether groups differ, including:
H statistic (Kruskal-Wallis chi-square test statistic)
Degrees of freedom (number of groups minus 1)
P-value (are groups different?)
Effect size eta-squared (how big is the group effect?)
Mean rank for each group (which groups are higher/lower?)
Details
Understanding the Results
P-value: If p < 0.05, at least one group is significantly different
p < 0.001: Very strong evidence of group differences
p < 0.01: Strong evidence of group differences
p < 0.05: Moderate evidence of group differences
p > 0.05: No significant group differences found
Effect Size Eta-squared (How much do groups matter?):
< 0.01: Negligible effect
0.01-0.06: Small effect
0.06-0.14: Medium effect
0.14 or higher: Large effect
Mean Ranks:
Higher mean rank = group tends to have higher values
Lower mean rank = group tends to have lower values
Compare mean ranks to see the pattern of group differences
When to Use This
Use Kruskal-Wallis test when:
Your data is not normally distributed (skewed, outliers)
You have ordinal data (rankings, Likert scales)
Sample sizes are small or very unequal across groups
You want a robust alternative to one-way ANOVA
You're comparing satisfaction ratings, income, or other skewed variables
What Comes Next?
If the Kruskal-Wallis test is significant:
Look at mean ranks to see the pattern
Use pairwise Mann-Whitney tests with Bonferroni correction to find which specific groups differ
Consider effect sizes to judge practical importance
Relationship to Other Tests
For 2 groups: Use
mann_whitney()insteadFor normally distributed data: Use
oneway_anova()insteadFor repeated measures (same subjects): Use
friedman_test()instead
References
Kruskal, W. H., & Wallis, W. A. (1952). Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association, 47(260), 583-621.
Tomczak, M., & Tomczak, E. (2014). The need to report effect size estimates revisited. An overview of some recommended measures of effect size. Trends in Sport Sciences, 1(21), 19-25.
See also
kruskal.test for the base R Kruskal-Wallis test.
mann_whitney for comparing exactly two groups.
oneway_anova for parametric one-way ANOVA.
Other hypothesis_tests:
ancova(),
binomial_test(),
chi_square(),
chisq_gof(),
factorial_anova(),
fisher_test(),
friedman_test(),
mann_whitney(),
mcnemar_test(),
oneway_anova(),
t_test(),
wilcoxon_test()
Examples
# Load required packages and data
library(dplyr)
data(survey_data)
# Basic Kruskal-Wallis test (comparing across education levels)
survey_data %>%
kruskal_wallis(life_satisfaction, group = education)
#>
#> Kruskal-Wallis Test Results
#> ---------------------------
#>
#> - Grouping variable: education
#> - Groups: Basic Secondary, Intermediate Secondary, Academic Secondary, University
#>
#> life_satisfaction
#> -----------------
#> Ranks:
#> --------------------------------------
#> Group N Mean Rank
#> Basic Secondary 809 974.29
#> Intermediate Secondary 618 1250.73
#> Academic Secondary 607 1329.56
#> University 387 1456.42
#> Total 2421 NA
#> --------------------------------------
#>
#> Test Statistics:
#> --------------------------------------------
#> Kruskal-Wallis H df p value Eta-squared sig
#> 171.178 3 0 0.071 ***
#> --------------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Effect Size Interpretation (Eta-squared):
#> - Small effect: 0.01 - 0.06
#> - Medium effect: 0.06 - 0.14
#> - Large effect: > 0.14
# Multiple variables
survey_data %>%
kruskal_wallis(life_satisfaction, income, trust_government,
group = education)
#>
#> Kruskal-Wallis Test Results
#> ---------------------------
#>
#> - Grouping variable: education
#> - Groups: Basic Secondary, Intermediate Secondary, Academic Secondary, University
#>
#> life_satisfaction
#> -----------------
#> Ranks:
#> --------------------------------------
#> Group N Mean Rank
#> Basic Secondary 809 974.29
#> Intermediate Secondary 618 1250.73
#> Academic Secondary 607 1329.56
#> University 387 1456.42
#> Total 2421 NA
#> --------------------------------------
#>
#> Test Statistics:
#> --------------------------------------------
#> Kruskal-Wallis H df p value Eta-squared sig
#> 171.178 3 0 0.071 ***
#> --------------------------------------------
#>
#> income
#> ------
#> Ranks:
#> --------------------------------------
#> Group N Mean Rank
#> Basic Secondary 735 623.53
#> Intermediate Secondary 548 1076.65
#> Academic Secondary 548 1359.50
#> University 355 1681.93
#> Total 2186 NA
#> --------------------------------------
#>
#> Test Statistics:
#> --------------------------------------------
#> Kruskal-Wallis H df p value Eta-squared sig
#> 814.174 3 0 0.373 ***
#> --------------------------------------------
#>
#> trust_government
#> ----------------
#> Ranks:
#> --------------------------------------
#> Group N Mean Rank
#> Basic Secondary 791 1191.27
#> Intermediate Secondary 592 1156.01
#> Academic Secondary 595 1170.90
#> University 376 1192.82
#> Total 2354 NA
#> --------------------------------------
#>
#> Test Statistics:
#> --------------------------------------------
#> Kruskal-Wallis H df p value Eta-squared sig
#> 1.235 3 0.745 0.001
#> --------------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Effect Size Interpretation (Eta-squared):
#> - Small effect: 0.01 - 0.06
#> - Medium effect: 0.06 - 0.14
#> - Large effect: > 0.14
# Using tidyselect helpers
survey_data %>%
kruskal_wallis(starts_with("trust_"), group = education)
#>
#> Kruskal-Wallis Test Results
#> ---------------------------
#>
#> - Grouping variable: education
#> - Groups: Basic Secondary, Intermediate Secondary, Academic Secondary, University
#>
#> trust_government
#> ----------------
#> Ranks:
#> --------------------------------------
#> Group N Mean Rank
#> Basic Secondary 791 1191.27
#> Intermediate Secondary 592 1156.01
#> Academic Secondary 595 1170.90
#> University 376 1192.82
#> Total 2354 NA
#> --------------------------------------
#>
#> Test Statistics:
#> --------------------------------------------
#> Kruskal-Wallis H df p value Eta-squared sig
#> 1.235 3 0.745 0.001
#> --------------------------------------------
#>
#> trust_media
#> -----------
#> Ranks:
#> --------------------------------------
#> Group N Mean Rank
#> Basic Secondary 797 1178.24
#> Intermediate Secondary 594 1210.37
#> Academic Secondary 599 1192.69
#> University 377 1140.82
#> Total 2367 NA
#> --------------------------------------
#>
#> Test Statistics:
#> --------------------------------------------
#> Kruskal-Wallis H df p value Eta-squared sig
#> 2.709 3 0.439 0.001
#> --------------------------------------------
#>
#> trust_science
#> -------------
#> Ranks:
#> --------------------------------------
#> Group N Mean Rank
#> Basic Secondary 807 1200.79
#> Intermediate Secondary 610 1172.31
#> Academic Secondary 597 1235.52
#> University 384 1183.98
#> Total 2398 NA
#> --------------------------------------
#>
#> Test Statistics:
#> --------------------------------------------
#> Kruskal-Wallis H df p value Eta-squared sig
#> 3.047 3 0.384 0.001
#> --------------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Effect Size Interpretation (Eta-squared):
#> - Small effect: 0.01 - 0.06
#> - Medium effect: 0.06 - 0.14
#> - Large effect: > 0.14
# Weighted analysis
survey_data %>%
kruskal_wallis(life_satisfaction, group = education,
weights = sampling_weight)
#>
#> Weighted Kruskal-Wallis Test Results
#> ------------------------------------
#>
#> - Grouping variable: education
#> - Groups: Basic Secondary, Intermediate Secondary, Academic Secondary, University
#> - Weights variable: sampling_weight
#>
#> life_satisfaction
#> -----------------
#> Ranks:
#> ----------------------------------------
#> Group N Mean Rank
#> Basic Secondary 815.7 984.25
#> Intermediate Secondary 629.6 1258.61
#> Academic Secondary 618.2 1338.55
#> University 373.2 1464.69
#> Total 2436.7 NA
#> ----------------------------------------
#>
#> Weighted Test Statistics:
#> --------------------------------------------
#> Kruskal-Wallis H df p value Eta-squared sig
#> 167.149 3 0 0.069 ***
#> --------------------------------------------
#>
#> Note: Weighted analysis uses frequency-weighted ranks.
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Effect Size Interpretation (Eta-squared):
#> - Small effect: 0.01 - 0.06
#> - Medium effect: 0.06 - 0.14
#> - Large effect: > 0.14
# Grouped analysis (separate test for each region)
survey_data %>%
group_by(region) %>%
kruskal_wallis(life_satisfaction, group = education)
#>
#> Kruskal-Wallis Test Results
#> ---------------------------
#>
#> - Grouping variable: education
#> - Groups: Basic Secondary, Intermediate Secondary, Academic Secondary, University
#>
#>
#> Group: region = East
#> --------------------
#>
#> life_satisfaction
#> -----------------
#> Ranks:
#> -------------------------------------
#> Group N Mean Rank
#> Basic Secondary 161 202.35
#> Intermediate Secondary 119 232.99
#> Academic Secondary 110 254.85
#> University 75 266.77
#> Total 465 NA
#> -------------------------------------
#>
#> Test Statistics:
#> --------------------------------------------
#> Kruskal-Wallis H df p value Eta-squared sig
#> 17.105 3 0.001 0.037 ***
#> --------------------------------------------
#>
#>
#> Group: region = West
#> --------------------
#>
#> life_satisfaction
#> -----------------
#> Ranks:
#> --------------------------------------
#> Group N Mean Rank
#> Basic Secondary 648 771.38
#> Intermediate Secondary 499 1018.44
#> Academic Secondary 497 1075.24
#> University 312 1190.70
#> Total 1956 NA
#> --------------------------------------
#>
#> Test Statistics:
#> --------------------------------------------
#> Kruskal-Wallis H df p value Eta-squared sig
#> 158.807 3 0 0.081 ***
#> --------------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Effect Size Interpretation (Eta-squared):
#> - Small effect: 0.01 - 0.06
#> - Medium effect: 0.06 - 0.14
#> - Large effect: > 0.14
# Compare across employment status (5 groups)
survey_data %>%
kruskal_wallis(income, group = employment)
#>
#> Kruskal-Wallis Test Results
#> ---------------------------
#>
#> - Grouping variable: employment
#> - Groups: Student, Employed, Unemployed, Retired, Other
#>
#> income
#> ------
#> Ranks:
#> --------------------------
#> Group N Mean Rank
#> Student 65 1495.58
#> Employed 1390 1075.60
#> Unemployed 159 1073.29
#> Retired 471 1089.83
#> Other 101 1129.95
#> Total 2186 NA
#> --------------------------
#>
#> Test Statistics:
#> --------------------------------------------
#> Kruskal-Wallis H df p value Eta-squared sig
#> 28.026 4 0 0.013 ***
#> --------------------------------------------
#>
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Effect Size Interpretation (Eta-squared):
#> - Small effect: 0.01 - 0.06
#> - Medium effect: 0.06 - 0.14
#> - Large effect: > 0.14