Mann-Whitney U Test Calculator
Introduction & Importance
The Mann-Whitney U Test is a statistical test used to compare the medians of two independent samples. It’s a non-parametric alternative to the independent samples t-test. This calculator helps you perform the Mann-Whitney U Test easily and understand its results.
How to Use This Calculator
- Enter the values of the two samples in the respective input fields.
- Enter the sizes of the two samples.
- Click the ‘Calculate’ button.
Formula & Methodology
The Mann-Whitney U Test is based on the sum of ranks of one sample. The formula for U is:
U = n1 * n2 + (n1 * (n1 + 1)) / 2 – R1
Where:
- n1 and n2 are the sizes of the two samples.
- R1 is the sum of ranks of the first sample.
Real-World Examples
Let’s consider three examples…
Data & Statistics
| Sample 1 | Sample 2 | U Statistic | p-value |
|---|---|---|---|
| 10, 15, 20 | 12, 18, 22 | 3.0 | 0.429 |
| 5, 10, 15 | 8, 12, 16 | 0.0 | 0.062 |
Expert Tips
- Always ensure your samples are independent.
- Consider the distribution of your data. The Mann-Whitney U Test is robust but not distribution-free.
- Use a significance level of 0.05 for most applications.
Interactive FAQ
What does the p-value represent?
The p-value represents the probability of observing a test statistic as extreme as the one calculated from the sample data, assuming that the null hypothesis is true.
What is the alternative hypothesis for the Mann-Whitney U Test?
The alternative hypothesis is that the median of the first sample is different from the median of the second sample.