Mann Whitney U Test Confidence Interval Calculator

The Mann-Whitney U test is a non-parametric statistical test used to compare two independent samples. This calculator helps you determine the confidence interval for the difference in medians between the two groups.

What is the Mann-Whitney U Test?

The Mann-Whitney U test (also known as the Wilcoxon rank-sum test) is a non-parametric alternative to the independent samples t-test. It's used when:

Your data doesn't meet the assumptions of a parametric test (normal distribution, equal variances)
You're comparing two independent groups
Your data is ordinal or ratio level

The test compares the ranks of the data points in the two groups to determine if there's a significant difference between them.

Null Hypothesis (H₀): There is no difference between the two groups.

Alternative Hypothesis (H₁): There is a difference between the two groups.

Confidence Interval

A confidence interval for the Mann-Whitney U test provides a range of values that is likely to contain the true difference in medians between the two groups. The confidence interval is calculated based on the observed U statistic and the sample sizes.

The confidence interval helps you understand the precision of your estimate and whether the difference between groups is statistically significant.

Common confidence levels are 90%, 95%, and 99%. Higher confidence levels provide wider intervals that are more likely to contain the true value.

How to Use the Calculator

Enter the sample size for Group 1 (n₁)
Enter the sample size for Group 2 (n₂)
Enter the observed U statistic
Select your desired confidence level (90%, 95%, or 99%)
Click "Calculate" to get the confidence interval

The calculator will display the confidence interval for the difference in medians between the two groups.

Interpreting Results

When interpreting the confidence interval:

If the interval includes zero, there is no significant difference between the groups
If the interval does not include zero, there is a significant difference
A wider interval indicates less precision in your estimate

Remember that the Mann-Whitney U test is sensitive to differences in sample sizes. Always consider the effect size along with the statistical significance.

Worked Example

Suppose you have two groups of students:

Group 1: 15 students with a median score of 72
Group 2: 12 students with a median score of 65

Using the calculator with these values and a 95% confidence level, you might find a confidence interval of [3.2, 12.8]. This suggests there is a statistically significant difference between the groups.

Example Data
Group	Sample Size	Median Score
Group 1	15	72
Group 2	12	65

FAQ

What is the difference between the Mann-Whitney U test and the Wilcoxon signed-rank test?: The Mann-Whitney U test compares two independent groups, while the Wilcoxon signed-rank test compares two related samples (paired data).
When should I use a confidence interval instead of just a p-value?: A confidence interval provides additional information about the precision of your estimate and the range of plausible values for the true difference.
What if my data has many tied ranks?: Tied ranks can reduce the power of the Mann-Whitney U test. Consider using alternative non-parametric tests if you have many ties.
Can I use this test for more than two groups?: No, the Mann-Whitney U test is specifically for comparing two independent groups. For more than two groups, consider the Kruskal-Wallis test.
What if my data is not normally distributed?: The Mann-Whitney U test is designed for non-normal data, making it a good alternative to the t-test in such cases.