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. Give a column name (unquoted or as a string), an expression such as
sampling_weight * 2, or a numeric vector with one weight per row.- mu
The hypothesized location shift of group 1 against group 2 (Default: 0, meaning no difference; this is the SPSS test). As in
wilcox.test(), group-1 values are shifted bymubefore ranking, so U, W, Z, r and p all refer to the same hypothesis. Onlymu = 0is available withweights.- alternative
Direction of the test:
"two.sided"(default): Test if groups are different. Z is reported as SPSS does, from the smaller U (never positive)."greater": Test if group 1 > group 2"less": Test if group 1 < group 2
For a one-sided test Z is directional (positive when group 1 tends to have higher values), so its sign matches the p-value.
- conf.level
Not used. Rank tests report no confidence interval (SPSS
NPAR TESTSneither); kept for backward compatibility.
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 (
r_effect, 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
0.1 to < 0.3: Small difference
0.3 to < 0.5: Medium difference
0.5 or higher: 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
Advantages Over t-test
Works with any data distribution
Not affected by outliers
Valid for ordinal data
No assumptions about variance
More robust for real-world data
Tips for Success
Each group should have at least 5 observations
The test compares distributions, not just means
Look at both p-values and effect sizes
Consider plotting the data to see the pattern
Weighted analyses
The weighted test is the design-based Lumley-Scott (2013) rank test
(Horvitz-Thompson midranks with a sandwich variance) and agrees with
survey::svyranktest(). Its U and W are design-based rank
quantities; Z and the p-value are the test result. Weighted results are
not compared with SPSS output; see vignette("spss-compatibility").
Use this for Likert scales and rating data
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 = 776732, Z = -0.164, p = 0.870, r = 0.003 (negligible), N = 2500
#> Use summary() for detailed output.
# Multiple variables
survey_data %>%
mann_whitney(age, income, life_satisfaction, group = region)
#> Mann-Whitney U Test: age by region
#> U = 462234.5, Z = -1.850, p = 0.064, r = 0.037 (negligible), N = 2500
#> Mann-Whitney U Test: income by region
#> U = 374226.5, Z = -0.226, p = 0.821, r = 0.005 (negligible), N = 2186
#> Mann-Whitney U Test: life_satisfaction by region
#> U = 452568.5, Z = -0.168, p = 0.867, r = 0.003 (negligible), N = 2421
#> Use summary() for detailed output.
# Using tidyselect helpers
survey_data %>%
mann_whitney(starts_with("trust_"), group = gender)
#> Mann-Whitney U Test: trust_government by gender
#> U = 678805.5, Z = -0.775, p = 0.438, r = 0.016 (negligible), N = 2354
#> Mann-Whitney U Test: trust_media by gender
#> U = 661523, Z = -2.320, p = 0.020 *, r = 0.048 (negligible), N = 2367
#> Mann-Whitney U Test: trust_science by gender
#> U = 697309, Z = -1.234, p = 0.217, r = 0.025 (negligible), N = 2398
#> Use summary() for detailed output.
# Weighted analysis
survey_data %>%
mann_whitney(income, group = region, weights = sampling_weight)
#> Mann-Whitney U Test: income by region [Weighted]
#> U = 386321.2, Z = -0.536, p = 0.592, r = 0.011 (negligible), N = 2201
#> Use summary() for detailed output.
# Grouped analysis (separate tests for each education level)
survey_data %>%
group_by(education) %>%
mann_whitney(life_satisfaction, group = gender)
#> [education = Basic Secondary]
#> Mann-Whitney U Test: life_satisfaction by gender
#> U = 81439, Z = -0.036, p = 0.971, r = 0.001 (negligible), N = 809
#> [education = Intermediate Secondary]
#> Mann-Whitney U Test: life_satisfaction by gender
#> U = 45218, Z = -1.001, p = 0.317, r = 0.040 (negligible), N = 618
#> [education = Academic Secondary]
#> Mann-Whitney U Test: life_satisfaction by gender
#> U = 45787.5, Z = -0.130, p = 0.897, r = 0.005 (negligible), N = 607
#> [education = University]
#> Mann-Whitney U Test: life_satisfaction by gender
#> U = 17319, Z = -1.281, p = 0.200, r = 0.065 (negligible), N = 387
#> Use summary() for detailed output.
# One-sided test
survey_data %>%
mann_whitney(life_satisfaction, group = region, alternative = "greater")
#> Mann-Whitney U Test: life_satisfaction by region
#> U = 452568.5, Z = 0.168, p = 0.433, r = 0.003 (negligible), N = 2421
#> Use summary() for detailed output.
# --- 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 = 592273.4, Z = -0.755, p = 0.450, r = 0.016 (negligible), N = 2201
#> Use summary() for detailed output.
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
#> - Alternative hypothesis: two.sided
#>
#>
#> --- income ---
#>
#> Male: rank mean = 1111.32, n = 1048
#> Female: rank mean = 1090.68, n = 1153
#>
#> Weighted Mann-Whitney U Test Results:
#> ---------------------------------------------------------------------
#> U W Z p value Effect r
#> ---------------------------------------------------------------------
#> Mann-Whitney U 592273.432 1257619.327 -0.755 .450 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: |r| < 0.1
#> - Small: 0.1 <= |r| < 0.3
#> - Medium: 0.3 <= |r| < 0.5
#> - Large: |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
#> - Alternative hypothesis: two.sided
#>
#>
#> --- income ---
#>
#> Male: rank mean = 1111.32, n = 1048
#> Female: rank mean = 1090.68, n = 1153
#>
#> Weighted Mann-Whitney U Test Results:
#> ---------------------------------------------------------------------
#> U W Z p value Effect r
#> ---------------------------------------------------------------------
#> Mann-Whitney U 592273.432 1257619.327 -0.755 .450 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