Mann-Whitney U Test Calculator

Q: What is the difference between Mann-Whitney U and Wilcoxon signed-rank test?

The Mann-Whitney U test compares two INDEPENDENT samples (different subjects in each group), while the Wilcoxon signed-rank test compares two RELATED samples (same subjects measured twice, like before/after). Use Mann-Whitney U when groups are unrelated (e.g., treatment vs control groups with different people), and Wilcoxon signed-rank when groups are paired (e.g., the same patients measured before and after treatment).

Q: What is the effect size in Mann-Whitney U test?

The effect size for Mann-Whitney U test is typically reported as rank-biserial correlation (r), calculated as r = 1 - (2U)/(n1*n2). It ranges from -1 to +1, where: |r| = 0.5 indicates large effect. Effect size helps understand the practical significance beyond just statistical significance.

Q: What are the assumptions of the Mann-Whitney U test?

The Mann-Whitney U test assumes: (1) Independence - observations within each sample and between samples are independent, (2) Ordinal data - values can be meaningfully ranked, (3) Similar shape - both populations have the same shape of distribution (though not necessarily normal), (4) Random sampling - samples are randomly drawn from their respective populations. The test does NOT require normal distribution or equal variances.

Perform the Mann-Whitney U test (Wilcoxon rank-sum test) to compare two independent samples. Get U statistic, p-value, effect size, step-by-step calculations, and interactive visualizations.

Mann-Whitney U Test Calculator

Try Example Datasets

Test Scores Treatment Effect Product Rating Response Time

1 Sample 1 (e.g., Control Group)

2 Sample 2 (e.g., Treatment Group)

Alternative Hypothesis

Decimal Precision

Embed Mann-Whitney U Test Calculator Widget

About Mann-Whitney U Test Calculator

The Mann-Whitney U Test Calculator is a comprehensive statistical tool for comparing two independent samples using the nonparametric Mann-Whitney U test (also known as the Wilcoxon rank-sum test). This calculator provides U statistic, z-score, p-value, effect size, step-by-step calculations, and interactive visualizations to help you understand and interpret your results.

What is the Mann-Whitney U Test?

The Mann-Whitney U test is a nonparametric statistical test used to determine whether two independent samples come from the same distribution. Unlike the independent samples t-test, it does not assume normal distribution of data, making it ideal for:

Ordinal data (data that can be ranked but not meaningfully averaged)
Small sample sizes where normality cannot be verified
Data with outliers or skewed distributions
Non-continuous measurements

The test works by ranking all observations from both samples together, then comparing the sum of ranks for each sample. If one sample tends to have higher ranks, this suggests the populations differ.

Mann-Whitney U Formulas

U Statistic

$$U_1 = n_1 n_2 + \frac{n_1(n_1 + 1)}{2} - R_1$$ $$U_2 = n_1 n_2 + \frac{n_2(n_2 + 1)}{2} - R_2$$ $$U = \min(U_1, U_2)$$

Where:

n₁, n₂ = Sample sizes of Sample 1 and Sample 2
R₁, R₂ = Sum of ranks for Sample 1 and Sample 2
U = Mann-Whitney U statistic (smaller of U₁ and U₂)

Z-Score (for large samples)

$$z = \frac{U - \mu_U}{\sigma_U}$$ $$\mu_U = \frac{n_1 n_2}{2}$$ $$\sigma_U = \sqrt{\frac{n_1 n_2 (n_1 + n_2 + 1)}{12}}$$

How to Use This Calculator

Enter Sample 1 data: Input your first group's numerical values, separated by commas, spaces, or line breaks (e.g., control group).
Enter Sample 2 data: Input your second group's values (e.g., treatment group). Ensure samples are independent.
Select test parameters: Choose the alternative hypothesis (two-tailed or one-tailed) and decimal precision.
Calculate: Click the button to see U statistic, p-value, effect size, and detailed interpretation.
Review results: Examine visualizations and step-by-step breakdown to understand the analysis.

Interpreting the Results

U Statistic

The U statistic represents the number of times a value from one sample precedes (is less than) a value from the other sample when all values are ranked together. A smaller U value suggests greater difference between samples.

P-Value

p < 0.05: Statistically significant difference (reject null hypothesis)
p ≥ 0.05: No significant difference detected (fail to reject null hypothesis)

Effect Size (Rank-Biserial Correlation)

The effect size helps interpret the practical significance of your results:

Small Effect

|r| < 0.3: Minimal practical difference between groups

Medium Effect

0.3 ≤ |r| < 0.5: Moderate practical difference

Large Effect

|r| ≥ 0.5: Substantial practical difference

When to Use Mann-Whitney U Test vs T-Test

Criterion	Mann-Whitney U Test	Independent T-Test
Data distribution	No normality requirement	Requires normal distribution
Sample size	Works well with small samples	Needs n > 30 per group ideally
Data type	Ordinal or continuous	Continuous only
Outliers	Robust to outliers	Sensitive to outliers
Power	Slightly less powerful	More powerful when assumptions met

Assumptions of the Mann-Whitney U Test

Independence: Observations within and between samples must be independent
Ordinal data: Values must be at least ordinal (can be meaningfully ranked)
Similar shape: Both populations should have the same shape of distribution (though not necessarily normal)
Random sampling: Samples should be randomly drawn from their respective populations

Frequently Asked Questions

What is the Mann-Whitney U test?

The Mann-Whitney U test (also called Wilcoxon rank-sum test) is a nonparametric statistical test used to compare two independent samples to determine whether they come from the same distribution. It is an alternative to the independent samples t-test when the data do not meet normality assumptions. The test compares the ranks of values rather than the values themselves.

When should I use the Mann-Whitney U test?

Use the Mann-Whitney U test when: (1) You have two independent samples to compare, (2) The data are at least ordinal (can be ranked), (3) The data violate normality assumptions required for a t-test, (4) You have small sample sizes where normality cannot be verified, or (5) You are working with ranked or ordinal data rather than continuous measurements.

How do I interpret the Mann-Whitney U test results?

Interpret the results by examining the p-value: if p < 0.05 (or your chosen significance level), reject the null hypothesis and conclude the samples differ significantly. The U statistic represents the number of times a value from one sample precedes a value from the other sample when all values are ranked together. The effect size (rank-biserial correlation) indicates the magnitude of the difference.

What is the difference between Mann-Whitney U and Wilcoxon signed-rank test?

The Mann-Whitney U test compares two INDEPENDENT samples (different subjects in each group), while the Wilcoxon signed-rank test compares two RELATED samples (same subjects measured twice, like before/after). Use Mann-Whitney U when groups are unrelated, and Wilcoxon signed-rank when groups are paired.

What is the effect size in Mann-Whitney U test?

The effect size for Mann-Whitney U test is typically reported as rank-biserial correlation (r), calculated as r = 1 - (2U)/(n₁*n₂). It ranges from -1 to +1, where: |r| < 0.3 indicates small effect, 0.3 ≤ |r| < 0.5 indicates medium effect, and |r| ≥ 0.5 indicates large effect.

What are the assumptions of the Mann-Whitney U test?

The Mann-Whitney U test assumes: (1) Independence - observations within each sample and between samples are independent, (2) Ordinal data - values can be meaningfully ranked, (3) Similar shape - both populations have the same shape of distribution (though not necessarily normal), (4) Random sampling - samples are randomly drawn from their respective populations.

Additional Resources

Reference this content, page, or tool as:

"Mann-Whitney U Test Calculator" at https://MiniWebtool.com/mann-whitney-u-test-calculator/ from MiniWebtool, https://MiniWebtool.com/

by miniwebtool team. Updated: Jan 15, 2026

You can also try our AI Math Solver GPT to solve your math problems through natural language question and answer.

Related MiniWebtools:

AI Content DetectorNew

AI Token CounterNew

ANOVA Calculator

Character Counter

Chi-Square Test Calculator

Divisibility Test Calculator

F-Test / F-Distribution CalculatorNew

Kruskal-Wallis Test Calculator

Series Convergence Test CalculatorNew

Mann-Whitney U Test Calculator

About Mann-Whitney U Test Calculator

What is the Mann-Whitney U Test?

Mann-Whitney U Formulas

How to Use This Calculator

Interpreting the Results

U Statistic

P-Value

Effect Size (Rank-Biserial Correlation)

When to Use Mann-Whitney U Test vs T-Test

Assumptions of the Mann-Whitney U Test

Frequently Asked Questions

What is the Mann-Whitney U test?

When should I use the Mann-Whitney U test?

How do I interpret the Mann-Whitney U test results?

What is the difference between Mann-Whitney U and Wilcoxon signed-rank test?

What is the effect size in Mann-Whitney U test?

What are the assumptions of the Mann-Whitney U test?

Additional Resources

Related MiniWebtools:

Statistics And Data Analysis:

Top & Updated: