Paired Mann Whitney U Test Calculator

Example Data Table

Formula Used

Independent Mann Whitney U

Rank all observations together. Average tied ranks.

U_A = R_A - n_A(n_A + 1) / 2

U_B = n_An_B - U_A

Mean U = n_An_B / 2

z = (U - Mean U) / SD

Paired Signed Rank

Difference = A - B

Rank absolute nonzero differences. Keep the original sign.

W⁺ = sum of positive signed ranks

W^- = sum of negative signed ranks

W = smaller of W⁺ and W^-

Effect size r = z / square root of sample count

How to Use This Calculator

1. Enter Sample A values in the first box.
2. Enter Sample B values in the second box.
3. Choose paired mode for matched observations.
4. Choose independent mode for separate groups.
5. Select the alternative hypothesis.
6. Set alpha and decimal precision.
7. Press Calculate to view results above the form.
8. Use CSV or PDF buttons to save the report.

Understanding the Paired Rank Method

This calculator helps compare two related score lists. It also supports the independent Mann Whitney U method. Many users enter before and after data. Others compare matched subjects, paired machines, or repeated readings. The paired option uses signed ranks. It studies the size and direction of each difference.

Why Ranks Matter

Rank tests reduce the effect of extreme values. They do not require normal data. Each value is converted into an ordered position. For paired data, the tool ranks absolute differences. For independent data, it ranks all observations together. Ties receive average ranks. Zero paired differences are removed before ranking. This keeps the test focused on actual change.

What Results Mean

The result includes the main statistic, expected value, standard deviation, z score, and p value. It also shows effect size. The p value is compared with your alpha level. A small p value suggests stronger evidence against the null idea. The effect size helps explain practical strength. It is useful when sample size changes the p value.

Advanced Checks

The calculator reports ties, zero differences, sample counts, and rank totals. Small samples may receive an exact p value. Larger samples use a normal approximation. Continuity correction can be enabled for conservative reporting. The Hodges Lehmann estimate gives a simple location shift estimate. It is based on median paired differences or median pairwise differences.

Best Use Cases

Use paired mode for before after studies. Use it for matched patients, repeated lab readings, or paired ratings. Use independent mode when two groups contain different subjects. Examples include two classes, two brands, or two treatment groups. Do not mix the designs. The choice changes the statistic and interpretation.

Reporting Tips

Report the method, sample size, statistic, p value, and effect size. Include the alternative hypothesis. Mention whether exact or approximate p values were used. Keep raw data available for review. The CSV file gives compact output. The PDF button creates a readable summary. These exports help with assignments, lab reports, and audit notes.

Data Quality Notes

Use clean numeric entries only. Avoid units inside the boxes. Check decimal points before running the test. Missing paired values should be removed from both lists. This protects rank order well.

FAQs

1. Is Mann Whitney U a paired test?

No. Mann Whitney U is for independent groups. For paired observations, the common rank based choice is the Wilcoxon signed rank test. This calculator includes both modes.

2. When should I use paired mode?

Use paired mode when each A value matches one B value. Examples include before and after scores, matched patients, repeated readings, or paired machine tests.

3. When should I use independent mode?

Use independent mode when values come from separate groups. The subjects should not be matched. The calculator then computes Mann Whitney U from combined ranks.

4. What does the p value show?

The p value shows how unusual the observed ranks are under the null hypothesis. A smaller value gives stronger evidence against no difference.

5. What are tied ranks?

Tied ranks happen when equal values occur. The calculator assigns their average rank. It also adjusts the approximate variance when ties affect the test.

6. What is effect size r?

Effect size r divides the z score by the square root of sample count. It helps describe practical strength, not only statistical significance.

7. Why are zero paired differences removed?

Zero differences have no positive or negative direction. The signed rank method removes them before ranking, so the test focuses on real changes.

8. Can I export my result?

Yes. Use the CSV button for spreadsheet work. Use the PDF button for a readable report that includes summary results and rank details.