Calculate Mann-Whitney U Test by Hand
The Mann-Whitney U test, also known as the Wilcoxon rank-sum test, is a non-parametric test used to compare the distributions of two independent samples. It’s particularly useful when the data is not normally distributed. Calculating it by hand can help you understand the underlying logic and build your statistical skills.
How to Use This Calculator
- Enter the values of the two samples and their sizes.
- Click ‘Calculate’.
- View the results and interpretation below.
Formula & Methodology
The Mann-Whitney U test involves ranking all observations together, then comparing the sum of ranks for each sample. The formula for U is:
U = n1*n2/2 – (n1*(n1+1)/2 – R1)
where n1 and n2 are the sizes of the two samples, and R1 is the sum of ranks for the first sample.
Real-World Examples
Data & Statistics
| Sample 1 | Sample 2 |
|---|---|
| 12 | 15 |
| 15 | 18 |
| 18 | 21 |
| Rank | Sample 1 | Sample 2 |
|---|---|---|
| 1 | 12 | 15 |
| 2 | 15 | 18 |
| 3 | 18 | 21 |
Expert Tips
- Always check the assumptions of the test before using it.
- Consider using a different test if the data is paired or the samples are related.
- Remember that the Mann-Whitney U test is a two-tailed test, so you need to consider both tails when interpreting the results.
Interactive FAQ
What are the assumptions of the Mann-Whitney U test?
The assumptions are: independence of observations, random sampling, and identical shapes of the distributions for the two groups.