Compare Multiple Groups Without Assuming Normal Data

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)

Usage

kruskal_wallis(data, ..., group, weights = NULL, conf.level = 0.95)

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 epsilon-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 Epsilon-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() instead
For normally distributed data: Use oneway_anova() instead

Weighted variants

SPSS NPAR TESTS ignores WEIGHT BY, so weighted results have no SPSS reference. The weighted variant is an R-only frequency-weight extension that reduces exactly to the unweighted test when all weights equal 1 (enforced by an internal invariance suite); see vignette("spss-compatibility") for validation status.

For 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.

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: life_satisfaction by education
#>   H(3) = 171.178, p < 0.001 ***, eps2 = 0.071, N = 2421
#> Use summary() for detailed output.

# Multiple variables
survey_data %>%
  kruskal_wallis(life_satisfaction, income, trust_government,
                 group = education)
#> Kruskal-Wallis Test: life_satisfaction by education
#>   H(3) = 171.178, p < 0.001 ***, eps2 = 0.071, N = 2421
#> Kruskal-Wallis Test: income by education
#>   H(3) = 814.174, p < 0.001 ***, eps2 = 0.373, N = 2186
#> Kruskal-Wallis Test: trust_government by education
#>   H(3) = 1.235, p = 0.745 , eps2 = 0.001, N = 2354
#> Use summary() for detailed output.

# Using tidyselect helpers
survey_data %>%
  kruskal_wallis(starts_with("trust_"), group = education)
#> Kruskal-Wallis Test: trust_government by education
#>   H(3) = 1.235, p = 0.745 , eps2 = 0.001, N = 2354
#> Kruskal-Wallis Test: trust_media by education
#>   H(3) = 2.709, p = 0.439 , eps2 = 0.001, N = 2367
#> Kruskal-Wallis Test: trust_science by education
#>   H(3) = 3.047, p = 0.384 , eps2 = 0.001, N = 2398
#> Use summary() for detailed output.

# Weighted analysis
survey_data %>%
  kruskal_wallis(life_satisfaction, group = education,
                 weights = sampling_weight)
#> Kruskal-Wallis Test: life_satisfaction by education [Weighted]
#>   H(3) = 167.075, p < 0.001 ***, eps2 = 0.069, N = 2437
#> Use summary() for detailed output.

# Grouped analysis (separate test for each region)
survey_data %>%
  group_by(region) %>%
  kruskal_wallis(life_satisfaction, group = education)
#> [region = 1]
#> Kruskal-Wallis Test: life_satisfaction by education
#>   H(3) = 17.105, p < 0.001 ***, eps2 = 0.037, N = 465
#> [region = 2]
#> Kruskal-Wallis Test: life_satisfaction by education
#>   H(3) = 158.807, p < 0.001 ***, eps2 = 0.081, N = 1956
#> Use summary() for detailed output.

# Compare across employment status (5 groups)
survey_data %>%
  kruskal_wallis(income, group = employment)
#> Kruskal-Wallis Test: income by employment
#>   H(4) = 28.026, p < 0.001 ***, eps2 = 0.013, N = 2186
#> Use summary() for detailed output.