What is Mann-Whitney U Test?
The Mann-Whitney U test is a non-parametric statistical test used to compare two independent groups when the data isn't normally distributed. It helps determine if there's a significant difference between the groups by ranking all values and comparing the sum of ranks. Commonly used in medical research, social sciences, and business analytics, it's an alternative to the t-test for non-normal distributions or ordinal data.
Calculator
Formula
U = n₁n₂ + n₁(n₁+1)/2 - R₁
Where n₁/n₂ = sample sizes, R₁ = sum of ranks for group 1
How to Use
1. Enter comma-separated values for both groups
2. Click Calculate to get U statistic and p-value
3. Interpret results: U value shows group difference, p-value < 0.05 indicates significance
4. Use Clear to reset inputs
Ensure minimum 3 samples per group. Values are automatically converted to numbers and sorted.
Development Process
1. Designed UI with input fields and buttons
2. Implemented JavaScript ranking algorithm
3. Added U statistic calculation using standard formula
4. Integrated p-value calculation with normal approximation
5. Created result display system
6. Added validation and error handling
7. Developed FAQ section with common queries
8. Optimized for responsiveness and accessibility
FAQs
When should I use Mann-Whitney U test?
Use when comparing two independent groups with non-normal distributions or ordinal data. It's ideal for small sample sizes or when parametric assumptions aren't met. Commonly used in medical research for comparing patient groups and in social sciences for survey analysis.
How to interpret U value?
The U statistic represents the number of times a value from one group precedes a value from the other group. A smaller U indicates greater difference between groups. Compare calculated U with critical values table or use p-value for significance determination.
What are the test assumptions?
Assumptions include: 1) Independence between groups 2) Ordinal or continuous data 3) Similar shape distributions. The test doesn't require normal distribution but assumes the distributions being compared are similar in shape.
How does it handle tied ranks?
Tied ranks receive average of their positions. The calculator automatically handles ties by assigning average ranks. Multiple identical values get the mean of their potential ranks, ensuring accurate statistical calculations.
Minimum sample size required?
Works with small samples (n ≥3). For samples larger than 20, normal approximation becomes more accurate. For very small samples, exact critical value tables should be consulted rather than p-value approximation.