Mann Whitney U Test Calculator GraphPad Style

Rank two groups, handle ties, and estimate p values. Check effect size and assumptions clearly. Export clean reports for quick GraphPad style review today.

Calculator

Use independent samples only. Do not use paired measurements here.

Example Data Table

Example Group A Group B Suggested Tail Purpose
Clinical score 12, 15, 17, 19, 21, 22, 24 9, 10, 14, 16, 18, 20, 23 Two sided Compare independent score distributions.
Lab response 4.1, 5.2, 5.5, 6.3, 6.7 3.8, 4.4, 4.9, 5.1, 5.6 Group A greater Test whether Group A tends higher.
Survey rating 2, 3, 3, 4, 5, 5 1, 2, 2, 3, 4, 4 Two sided Handle ordinal values and ties.

Formula Used

All observations are pooled and ranked from smallest to largest. Tied values receive average ranks.

Rank sums:

R1 = sum of ranks for Group A

R2 = sum of ranks for Group B

U statistics:

U1 = R1 - n1(n1 + 1) / 2

U2 = R2 - n2(n2 + 1) / 2

U = min(U1, U2)

Normal approximation:

Mean U = n1n2 / 2

Variance U = n1n2 / 12 × [(N + 1) - Σ(t³ - t) / {N(N - 1)}]

Z = adjusted difference between U1 and Mean U, divided by SD U.

Effect size:

Rank biserial correlation = (U1 - U2) / (n1n2)

Hodges Lehmann estimate = median of all pairwise differences Ai - Bj.

How to Use This Calculator

  1. Enter a label for each independent group.
  2. Paste numeric values into the two data boxes.
  3. Separate values with commas, spaces, semicolons, or new lines.
  4. Select a two sided or one sided alternative.
  5. Choose automatic, exact, or normal approximation.
  6. Set the alpha level and decimal precision.
  7. Click Calculate to show results above the form.
  8. Use CSV or PDF buttons to download the report.

About 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 treated as normal. The method ranks all values together. Then it checks whether ranks from one group tend to be higher than ranks from the other group.

Why This Calculator Helps

This calculator follows a GraphPad style workflow. You enter two samples, choose a tail, and decide whether to use exact or normal approximation. The tool handles ties with average ranks. It also reports U values, rank sums, z score, p value, effect size, and a Hodges Lehmann median difference. These outputs help you review both significance and practical size.

Interpreting Results

A small p value suggests the groups differ in distribution. It does not prove that medians differ in every setting. The test mainly evaluates whether observations from one group are generally larger than observations from the other group. The rank biserial correlation shows direction and strength. Positive values mean Group A tends to be larger. Negative values mean Group B tends to be larger.

Data Quality Notes

Each group should contain independent observations. Do not enter paired before and after data. Use a paired rank test for that design. Outliers are allowed, but they still affect ranks. Ties are accepted, although many ties make exact methods less suitable. The normal approximation becomes more stable as sample sizes increase.

Reporting the Test

A clear report should include group sizes, U statistic, p value, tail choice, and effect size. Also mention whether exact or normal approximation was used. If your work must match a journal or classroom requirement, check that the same tail and continuity correction are selected. Different settings can change the p value slightly.

When to Choose It

Use this test when two unrelated samples are measured on the same scale. It is common for clinical scores, survey ratings, laboratory values, and small experimental studies. The calculator is not a replacement for study design. It gives a fast statistical check, but your conclusion should also consider sampling, measurement quality, and the real question being asked. Save exports when you need transparent records for later review. Keep raw data with every reported result.

FAQs

What does the Mann Whitney U test compare?

It compares two independent groups using ranks. It checks whether values from one group tend to be higher or lower than values from the other group.

Can I use this for paired data?

No. This test is for independent samples. For paired before and after data, use a Wilcoxon signed rank test instead.

What does a small p value mean?

A small p value suggests the two groups differ in their ranked distributions. It does not automatically prove a meaningful practical difference.

How are tied values handled?

Tied values receive average ranks. The normal approximation also uses a tie correction in the variance formula.

When is exact p value used?

Exact calculation is used automatically for small untied samples when available. Larger samples or tied data use the normal approximation.

What is rank biserial correlation?

It is an effect size for the test. Positive values favor Group A. Negative values favor Group B.

What is the Hodges Lehmann estimate?

It is the median of all pairwise differences between Group A and Group B values. It gives a useful shift estimate.

Why may results differ from other tools?

Different tools may use different tails, continuity correction, exact rules, or tie handling. Match the settings before comparing outputs.

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