mann_whitney() compares two groups when your data isn't normally
distributed or when you have ordinal data (like ratings or rankings). It's the
go-to alternative when t-tests aren't appropriate.
Think of it as:
A robust way to compare groups that works with any data shape
Perfect for Likert scales, ratings, or skewed distributions
A test that compares the typical values between groups
The test tells you:
Whether one group tends to have higher values than the other
How strong the difference is (effect size)
Which group has higher average ranks
Usage
mann_whitney(
data,
...,
group,
weights = NULL,
mu = 0,
alternative = c("two.sided", "less", "greater"),
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 two groups (e.g., gender, treatment/control). Must have exactly two groups.
- weights
Optional survey weights for population-representative results
- mu
The hypothesized difference (Default: 0, meaning no difference)
- alternative
Direction of the test:
"two.sided"(default): Test if groups are different"greater": Test if group 1 > group 2"less": Test if group 1 < group 2
- conf.level
Confidence level for intervals (Default: 0.95 = 95%)
Value
Test results showing whether groups differ, including:
U and W statistics (test statistics)
Z-score and p-value (are groups different?)
Effect size r (how big is the difference?)
Rank means for each group (which group is higher?) Use
summary()for the full SPSS-style output with toggleable sections.
Details
Understanding the Results
P-value: If p < 0.05, the groups are significantly different
p < 0.001: Very strong evidence of difference
p < 0.01: Strong evidence of difference
p < 0.05: Moderate evidence of difference
p ≥ 0.05: No significant difference found
Effect Size r (How big is the difference?):
|r| < 0.1: Negligible difference
|r| ~ 0.1: Small difference
|r| ~ 0.3: Medium difference
|r| ~ 0.5: Large difference
|r| > 0.5: Very large difference
Rank Mean Difference:
Positive: Group 1 tends to have higher values
Negative: Group 2 tends to have higher values
Zero: Groups have similar distributions
When to Use This
Use Mann-Whitney test when:
Your data is not normally distributed (skewed, outliers)
You have ordinal data (rankings, Likert scales)
Sample sizes are small (< 30 per group)
You want a robust alternative to the t-test
You're comparing satisfaction ratings, income, or other skewed variables
References
Mann, H. B., & Whitney, D. R. (1947). On a test of whether one of two random variables is stochastically larger than the other. The Annals of Mathematical Statistics, 18(1), 50-60.
Wilcoxon, F. (1945). Individual comparisons by ranking methods. Biometrics Bulletin, 1(6), 80-83.
Lumley, T., & Scott, A. (2013). Two-sample rank tests under complex sampling. Biometrika, 100(4), 831-842.
See also
wilcox.test for the base R Wilcoxon test function.
svyranktest for survey-weighted rank tests.
t_test for parametric t-tests.
summary.mann_whitney for detailed output with toggleable sections.
Other hypothesis_tests:
ancova(),
binomial_test(),
chi_square(),
chisq_gof(),
factorial_anova(),
fisher_test(),
friedman_test(),
kruskal_wallis(),
mcnemar_test(),
oneway_anova(),
t_test(),
wilcoxon_test()
Examples
# Load required packages and data
library(dplyr)
data(survey_data)
# Basic Mann-Whitney test (non-parametric comparison)
survey_data %>%
mann_whitney(age, group = gender)
#> Mann-Whitney U Test: age by gender
#> U = 776,732, Z = -0.164, p = 0.870 , r = 0.003 (negligible), N = 2500
# Multiple variables
survey_data %>%
mann_whitney(age, income, life_satisfaction, group = region)
#> Mann-Whitney U Test: age by region
#> U = 462,234, Z = -1.850, p = 0.064 , r = 0.037 (negligible), N = 2500
#> Mann-Whitney U Test: income by region
#> U = 374,226, Z = -0.226, p = 0.821 , r = 0.005 (negligible), N = 2186
#> Mann-Whitney U Test: life_satisfaction by region
#> U = 452,568, Z = -0.168, p = 0.867 , r = 0.003 (negligible), N = 2421
# Using tidyselect helpers
survey_data %>%
mann_whitney(starts_with("trust_"), group = gender)
#> Mann-Whitney U Test: trust_government by gender
#> U = 678,806, Z = -0.775, p = 0.438 , r = 0.016 (negligible), N = 2354
#> Mann-Whitney U Test: trust_media by gender
#> U = 661,523, Z = -2.320, p = 0.020 *, r = 0.048 (negligible), N = 2367
#> Mann-Whitney U Test: trust_science by gender
#> U = 697,309, Z = -1.234, p = 0.217 , r = 0.025 (negligible), N = 2398
# Weighted analysis
survey_data %>%
mann_whitney(income, group = region, weights = sampling_weight)
#> Mann-Whitney U Test: income by region [Weighted]
#> U = 386,321, Z = -0.536, p = 0.592 , r = 0.011 (negligible), N = 2201
# Grouped analysis (separate tests for each education level)
survey_data %>%
group_by(education) %>%
mann_whitney(life_satisfaction, group = gender)
#> [education = 1]
#> Mann-Whitney U Test: life_satisfaction by gender
#> U = 81,439, Z = -0.036, p = 0.971 , r = 0.001 (negligible), N = 809
#> [education = 2]
#> Mann-Whitney U Test: life_satisfaction by gender
#> U = 45,218, Z = -1.001, p = 0.317 , r = 0.040 (negligible), N = 618
#> [education = 3]
#> Mann-Whitney U Test: life_satisfaction by gender
#> U = 45,788, Z = -0.130, p = 0.897 , r = 0.005 (negligible), N = 607
#> [education = 4]
#> Mann-Whitney U Test: life_satisfaction by gender
#> U = 17,319, Z = -1.281, p = 0.200 , r = 0.065 (negligible), N = 387
# One-sided test
survey_data %>%
mann_whitney(life_satisfaction, group = region, alternative = "greater")
#> Mann-Whitney U Test: life_satisfaction by region
#> U = 452,568, Z = -0.168, p = 0.433 , r = 0.003 (negligible), N = 2421
# --- Three-layer output ---
result <- survey_data %>%
mann_whitney(income, group = gender, weights = sampling_weight)
result # compact one-line overview
#> Mann-Whitney U Test: income by gender [Weighted]
#> U = 592,273, Z = -0.755, p = 0.450 , r = 0.016 (negligible), N = 2201
summary(result) # full detailed output with all sections
#> Weighted Mann-Whitney U Test Results
#> ------------------------------------
#>
#> - Grouping variable: gender
#> - Groups compared: Male vs. Female
#> - Weights variable: sampling_weight
#> - Confidence level: 95.0%
#> - Alternative hypothesis: two.sided
#> - Null hypothesis (mu): 0.000
#>
#>
#> --- income ---
#>
#> Male: rank mean = 1111.3, n = 1047.9
#> Female: rank mean = 1090.7, n = 1153.1
#>
#>
#> Weighted Mann-Whitney U Test Results:
#> ------------------------------------------------------------
#> Test U W Z p_value effect_r sig
#> Mann-Whitney U 592,273 1,257,619 -0.755 0.45 0.016
#> ------------------------------------------------------------
#>
#>
#> Note: Weighted analysis uses design-based rank test (Lumley & Scott, 2013).
#> U and W are descriptive statistics derived from weighted ranks.
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05
#>
#> Effect Size Interpretation (r):
#> - Negligible effect: |r| < 0.1
#> - Small effect: |r| ~ 0.1
#> - Medium effect: |r| ~ 0.3
#> - Large effect: |r| ~ 0.5
summary(result, effect_sizes = FALSE) # hide effect sizes
#> Weighted Mann-Whitney U Test Results
#> ------------------------------------
#>
#> - Grouping variable: gender
#> - Groups compared: Male vs. Female
#> - Weights variable: sampling_weight
#> - Confidence level: 95.0%
#> - Alternative hypothesis: two.sided
#> - Null hypothesis (mu): 0.000
#>
#>
#> --- income ---
#>
#> Male: rank mean = 1111.3, n = 1047.9
#> Female: rank mean = 1090.7, n = 1153.1
#>
#>
#> Weighted Mann-Whitney U Test Results:
#> ------------------------------------------------------------
#> Test U W Z p_value effect_r sig
#> Mann-Whitney U 592,273 1,257,619 -0.755 0.45 0.016
#> ------------------------------------------------------------
#>
#>
#> Note: Weighted analysis uses design-based rank test (Lumley & Scott, 2013).
#> U and W are descriptive statistics derived from weighted ranks.
#>
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05