Example Data Table
| Case | Sample A | Sample B | Suggested test |
|---|---|---|---|
| Independent scores | 12, 15, 14, 17, 20, 21, 19 | 10, 11, 13, 13, 16, 18, 17 | Mann Whitney U |
| Before and after | 82, 85, 88, 91, 90, 94 | 78, 83, 84, 89, 88, 91 | Wilcoxon signed rank |
| Ordinal survey | 4, 5, 5, 3, 4, 5 | 3, 4, 4, 2, 3, 4 | Mann Whitney U |
Formula Used
Mann Whitney U Test
Rank all observations together. Then sum ranks for Sample A.
U1 = R1 - n1(n1 + 1) / 2
U2 = n1n2 - U1
Mean U = n1n2 / 2
SD = sqrt{n1n2[(N + 1) - tie correction / N(N - 1)] / 12}
Wilcoxon Signed Rank Test
Find paired differences. Remove zero differences. Rank absolute differences.
W+ = sum of positive signed ranks
W- = sum of negative signed ranks
W = min(W+, W-)
Mean W+ = n(n + 1) / 4
SD = sqrt{n(n + 1)(2n + 1) / 24 - tie correction / 48}
P Value and Effect Size
z = (observed statistic - expected mean) / SD
r = |z| / sqrt(N)
Rank biserial correlation measures directional rank separation.
How to Use This Calculator
- Select independent groups or paired samples.
- Choose the alternative hypothesis before calculation.
- Enter Sample A and Sample B values.
- Use equal list lengths for paired data.
- Set alpha, decimal places, and continuity correction.
- Press Calculate to view the result above the form.
- Download CSV or PDF after the result appears.
Understanding the calculator
A nonparametric t test calculator is a practical name for rank based tests. These tests compare groups when normality is doubtful. They use ordered values, not raw mean assumptions. This page supports two common choices. Use the Mann Whitney U test for independent groups. Use the Wilcoxon signed rank test for paired readings. Both methods work well for small samples, skewed data, ordinal scores, and outlier heavy measurements.
Why rank methods help
A standard t test focuses on means. It also assumes a useful normal pattern. Real data often breaks that pattern. Survey ratings may be ordinal. Lab values may be skewed. Cost data may contain extreme values. Rank methods reduce that problem. They replace each value with its rank. The calculation then studies how ranks are distributed between groups. This makes the method more robust. It does not remove every assumption. Samples still need suitable independence. Paired data must be matched correctly.
Interpreting the output
The result panel shows sample sizes, medians, rank sums, test statistic, z value, p value, and effect size. The p value measures how unusual the observed rank pattern is under the null hypothesis. A small p value suggests stronger evidence against equal central tendency. The alpha setting marks a chosen decision threshold. Effect size helps explain practical importance. It should be read with context. A significant result can still be small. A non significant result can still matter when samples are limited.
Good data practice
Enter clean numeric values. Separate them with commas, spaces, or new lines. Do not mix units. For paired tests, keep both lists in the same order. The first value in group one must match the first value in group two. Review missing values before calculating. Report the selected test, alternative hypothesis, statistic, p value, sample sizes, and effect size. Download the CSV or PDF for records. Keep the original dataset too. Rechecking inputs is important when rankings include ties.
When to choose it
Choose the independent option when two unrelated groups are compared. Choose the paired option when each subject has two linked readings. Select two sided testing for any difference. Select greater or less only when the direction was planned before analysis. State this choice.
FAQs
1. Is a nonparametric t test a real test name?
It is a common informal phrase. The usual methods are Mann Whitney U for independent groups and Wilcoxon signed rank for paired data.
2. When should I use the Mann Whitney U test?
Use it when two groups are independent. It is useful for skewed, ordinal, or outlier heavy data.
3. When should I use the Wilcoxon signed rank test?
Use it when values are paired. Examples include before and after scores, matched subjects, or repeated measurements.
4. What does the p value mean?
It estimates how unusual the rank pattern is if the null hypothesis is true. Smaller values show stronger evidence.
5. What does effect size r show?
Effect size r shows practical strength. It helps judge whether the difference is meaningful beyond statistical significance.
6. Can I use decimal values?
Yes. Enter whole numbers, decimals, or negative values. Separate values with commas, spaces, semicolons, or new lines.
7. What happens with tied values?
The calculator assigns average ranks to tied values. It also applies tie correction in the normal approximation.
8. Can I export the result?
Yes. After calculation, use the CSV or PDF button to download a clean result summary.