Calculator Form
Large screens use three columns, smaller screens use two, and mobile uses one.
Example Data Table
This sample dataset is preloaded when the page first opens.
| Observation | Group A | Group B |
|---|---|---|
| 1 | 12 | 19 |
| 2 | 15 | 17 |
| 3 | 14 | 21 |
| 4 | 10 | 20 |
| 5 | 16 | 18 |
| 6 | 18 | 16 |
| 7 | 11 | 22 |
| 8 | 13 | 15 |
Formula Used
The Brunner-Munzel test compares two independent samples without assuming equal variances. It works with pooled ranks and group-specific rank variability.
1) Pool both samples and assign average ranks for ties.
2) Compute mean pooled ranks: R̄A and R̄B.
3) Compute within-group rank variances:
S_A² = var(R_A - R_A*)
S_B² = var(R_B - R_B*)
4) Compute the test statistic:
W = [n_A n_B (R̄B - R̄A)] / [(n_A + n_B) √(n_A S_A² + n_B S_B²)]
5) Estimate degrees of freedom:
df = (n_A S_A² + n_B S_B²)² /
[ (n_A S_A²)²/(n_A - 1) + (n_B S_B²)²/(n_B - 1) ]
6) Relative effect estimate:
p̂ = [R̄B - (n_B + 1)/2] / n_A
Here, p̂ estimates the probability that a random value from the first sample is smaller than a random value from the second sample, counting ties as half.
How to Use This Calculator
- Enter or paste two independent samples into the value boxes.
- Use commas, spaces, or line breaks to separate observations.
- Choose the alternative hypothesis that matches your research question.
- Set the alpha level and preferred decimal precision.
- Click Calculate Test to place the result above the form.
- Review the statistic, p-value, relative effect, summary table, and graph.
- Use the export buttons to save a CSV file or a PDF report.
FAQs
1) What does the Brunner-Munzel test measure?
It tests whether one independent sample tends to produce larger values than another. It is rank-based and handles unequal variances better than many common nonparametric alternatives.
2) When should I prefer it over Mann-Whitney?
Use it when distributions may differ in spread or shape. The Brunner-Munzel method is often preferred when the equal-variance style assumptions behind simpler rank comparisons may not hold.
3) Does this calculator allow tied values?
Yes. It assigns average ranks to ties in the pooled data, then uses the rank structure inside the Brunner-Munzel calculation.
4) What does the relative effect mean?
It estimates how likely a random first-group value is smaller than a random second-group value, with ties split equally. A value near 0.50 suggests little stochastic advantage.
5) Can I use raw decimals and negative numbers?
Yes. The parser accepts integers, decimals, and negative values. Separate them with commas, spaces, semicolons, or line breaks.
6) What sample size is recommended?
Each sample needs at least two values to compute the test. Larger samples generally produce more stable estimates and more reliable inference.
7) Why might my p-value be large?
A large p-value usually means the observed rank separation could plausibly happen under the null hypothesis. It does not prove the groups are identical.
8) What does the graph show?
The Plotly chart displays both sample distributions as box plots with points. It helps you visually compare spread, center, overlap, and possible outliers.