Mann-Whitney U Test Calculator
Find the Mann-Whitney U statistic for two small samples.
The Mann-Whitney U test compares two independent samples without assuming normality.
How the Math Works
The Mann-Whitney U Test Calculator uses the formula U = R - n(n+1)/2 for each group, where R is the sum of ranks for that group and n is the sample size. First, all observations from both groups are combined and ranked from smallest to largest. Then, separate rank sums are calculated for each group. The U statistic for each group is computed by subtracting n(n+1)/2 from its rank sum. The smaller of the two U values is reported because it provides the most conservative test of whether one group tends to have larger values than the other, making it ideal for small sample comparisons.
Practical Applications
To use this calculator, enter the values from your two independent samples into the designated fields. The tool will automatically rank all observations, compute rank sums for each group, apply the U formula to both groups, and return the smaller U statistic along with relevant sample information. This is particularly useful when comparing two small groups (typically n < 30) where you want to determine if one group stochastically dominates the other, such as comparing test scores from two different teaching methods or reaction times from two experimental conditions.
Day-to-Day Use
This statistical test helps you make data-driven decisions in everyday situations involving group comparisons. For example, you could use it to determine if a new recipe consistently produces better results than an old one, whether a daily walking routine leads to lower blood pressure readings than a sedentary lifestyle, or if customers prefer one product version over another. By providing an objective measure of difference between small groups, it removes guesswork from personal experiments, consumer choices, and small-scale research questions that don't require complex statistical software but still need rigorous analysis.
Worked example
Two 3-4 value groups give a U you compare to the critical value table.
FAQ
When use it over a t-test?
When data is ordinal or not normally distributed.