Mann-Whitney U Test Calculator
Non-parametric test to compare two independent samples without assuming normal distribution
Test Configuration
Detected 0 valid values
Detected 0 valid values
Example: Treatment Effectiveness
Control Group (A)
Data: 2.1, 2.5, 1.8, 3.2, 2.9, 1.5, 2.7
Sample size: n₁ = 7
Median: 2.5
Treatment Group (B)
Data: 3.8, 4.5, 5.2, 4.1, 6.0, 4.8
Sample size: n₂ = 6
Median: 4.65
Expected Result
Treatment group shows higher values
Conclusion: Significant difference suggests treatment effectiveness
When to Use Mann-Whitney U Test
Two Independent Samples
Comparing two groups with different subjects
Non-Normal Data
Data doesn't follow normal distribution
Small Sample Sizes
Works well with small samples (n < 30)
Ordinal Data
Suitable for ranked or ordinal measurements
Test Assumptions
Independence: Observations within and between groups are independent
Ordinal Scale: Data measured on at least ordinal scale
Similar Shape: If comparing medians, distributions should have similar shapes
Random Sampling: Samples should be randomly selected from populations
Understanding the Mann-Whitney U Test
What is the Mann-Whitney U Test?
The Mann-Whitney U test (also known as the Wilcoxon rank-sum test) is a non-parametric statistical test used to determine whether two independent samples come from populations with the same distribution. Unlike the t-test, it doesn't assume normal distribution.
When to Use vs t-test
- •Use Mann-Whitney when: Data is not normally distributed, small sample sizes, ordinal data
- •Use t-test when: Data is normally distributed, large sample sizes, continuous data
Key Formulas
U Statistic
U₁ = R₁ - n₁(n₁ + 1)/2
R₁ = sum of ranks in sample 1
Normal Approximation
z = (U - μᵤ) / σᵤ
μᵤ = n₁n₂/2, σᵤ = √(n₁n₂(n₁+n₂+1)/12)
How it Works
- 1.Combine all observations from both samples and rank them
- 2.Calculate the sum of ranks for each sample
- 3.Compute U statistics: U₁ and U₂
- 4.Use the smaller U for testing significance
Interpretation Guidelines
- •p-value < α: Reject null hypothesis (significant difference)
- •p-value ≥ α: Fail to reject null hypothesis
- •Effect size (r): Magnitude of difference between groups
- •Consider: Practical significance beyond statistical significance