Mann Whitney U Test Web Calculator

Calculator Input

Sample A Values

Use commas, spaces, or new lines.

Sample B Values

Each sample must be independent.

Alternative Hypothesis

Alpha Level

Continuity Correction

Apply correction for normal approximation

Example Data Table

Scenario	Sample A	Sample B	Useful Tail
Training scores	12, 15, 14, 10, 18, 17	9, 11, 13, 8, 10, 12	Sample A tends higher
Wait times	18, 22, 21, 19, 25	24, 27, 29, 23, 26	Sample A tends lower
Two products	7, 8, 7, 9, 10	6, 8, 9, 11, 12	Two sided

Formula Used

Combine both samples, sort all values, and assign ranks. Ties receive the average of their rank positions.

Rank sum for Sample A is R₁. The statistic is U₁ = R₁ - n₁(n₁ + 1) / 2.

The second statistic is U₂ = n₁n₂ - U₁. For two sided tests, the smaller U is commonly reviewed.

The expected value is n₁n₂ / 2. The tie corrected variance is n₁n₂[N + 1 - Σ(t³ - t)/(N(N - 1))] / 12.

The rank biserial effect is 2U₁ / (n₁n₂) - 1. Positive values mean Sample A tends higher.

How To Use This Calculator

Enter Sample A values in the first box.
Enter Sample B values in the second box.
Select the alternative hypothesis that matches your research question.
Set alpha, usually 0.05, unless your study uses another level.
Use continuity correction when you want a conservative normal approximation.
Press Calculate Test and read the result above the form.
Download the CSV or PDF report for records.

Understanding the Mann Whitney U Test

The Mann Whitney U test compares two independent groups. It is useful when data are ordinal, skewed, or not safely modeled with a normal curve. The test does not compare raw averages. It compares rank positions after both samples are pooled together. Higher ranks suggest larger values in that group.

When This Test Helps

Use this test when each observation belongs to only one group. The groups should not be paired. Common examples include two treatments, two stores, two classrooms, or two machine settings. The method works well with small samples, but interpretation improves when the study design is clean. Outliers can still affect ranks, yet they usually have less influence than in a mean based test.

What The Calculator Does

This calculator parses two numeric samples. It ranks all values together. Tied values receive average ranks. It then finds rank sums, U statistics, the expected U value, the standard deviation, and the z score. It also estimates p values for one tailed or two tailed questions. For small untied samples, it can show an exact p value. For ties or larger samples, it uses a tie corrected normal approximation.

How To Read Results

Start with the p value and your chosen alpha level. A p value below alpha suggests a statistically significant group difference. Also review the rank biserial effect size. This value shows direction and strength. Values near zero suggest little separation. Larger absolute values suggest clearer separation between the two groups.

Practical Advice

Do not treat significance as practical importance. Always inspect the sample sizes, medians, ranges, and rank table. A small p value can occur with tiny differences when samples are large. A larger p value can appear when samples are small or noisy. Report the alternative hypothesis, U value, sample sizes, p value, and effect size. Explain what larger ranks mean in your study context.

Good Data Entry

Enter numbers only. You may separate values with commas, spaces, or new lines. Keep missing values out of the samples. Use the same measurement unit for both groups. Check labels before exporting. This prevents reversed conclusions. Save the CSV for audits. Save the report after reviewing assumptions and later peer review.

FAQs

What does the Mann Whitney U test compare?

It compares two independent samples by ranking all observations together. It tests whether one group tends to have larger values, or whether the groups differ in rank distribution.

Can I use this test for paired data?

No. Paired observations need a paired rank method, such as the Wilcoxon signed rank test. The Mann Whitney U test assumes independent groups.

What should I enter in each sample box?

Enter numeric observations from one group in each box. You may separate values with commas, spaces, or new lines. Do not include labels or units.

What does a two sided test mean?

A two sided test checks whether the two groups differ in either direction. It does not assume Sample A should be higher or lower before testing.

How are tied values handled?

Tied values receive average ranks. The normal approximation then uses a tie corrected variance, which improves the p value estimate when repeated values exist.

When is the exact p value shown?

The calculator shows an exact p value for small samples without ties. If samples are larger or ties exist, it reports the tie corrected normal approximation.

What is rank biserial effect size?

Rank biserial effect size describes direction and separation. Positive values mean Sample A tends higher. Negative values mean Sample A tends lower.

Should I report U1 or U2?

Report the statistic used by your chosen convention. Many reports include U, both sample sizes, p value, alternative hypothesis, and effect size for clarity.