U-Test Calculator (Mann-Whitney)
Perform the Mann-Whitney U test to compare two independent samples without assuming the data is normally distributed. This nonparametric test is a common alternative to the independent samples t-test.
The U-test (Mann-Whitney U test, also called the Wilcoxon rank-sum test) determines whether two independent groups come from the same distribution. It works by ranking all observations together and comparing the sum of ranks between groups.
How the U-Test Works:
- Combine all values from both samples
- Rank them from smallest to largest (average ties)
- Calculate U = n1 x n2 + n1(n1+1)/2 - R1
- For larger samples, approximate with a z-test using continuity correction
When to Use the U-Test:
- Your data is ordinal (ranked) rather than interval
- The normality assumption is violated
- You have outliers that would distort a t-test
- Sample sizes are small and you cannot verify normality
Interpreting Results:
A small p-value (below your chosen significance level) means the two groups differ significantly. The U statistic itself indicates how much one group tends to have larger values than the other. When U equals half of n1 x n2, the groups are perfectly balanced.