mariposa (version 0.7.3)

kruskal_wallis: Compare Multiple Groups Without Assuming Normal Data

Description

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)

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?)

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%)

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:

1. Look at mean ranks to see the pattern

2. Use pairwise Mann-Whitney tests with Bonferroni correction to find which specific groups differ

3. 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.

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)

# Multiple variables
survey_data %>%
  kruskal_wallis(life_satisfaction, income, trust_government,
                 group = education)

# Using tidyselect helpers
survey_data %>%
  kruskal_wallis(starts_with("trust_"), group = education)

# Weighted analysis
survey_data %>%
  kruskal_wallis(life_satisfaction, group = education,
                 weights = sampling_weight)

# Grouped analysis (separate test for each region)
survey_data %>%
  group_by(region) %>%
  kruskal_wallis(life_satisfaction, group = education)

# Compare across employment status (5 groups)
survey_data %>%
  kruskal_wallis(income, group = employment)