Sample Size for Nonparametric Tests Calculator

Calculator Form

Test type

Alpha

Target power

Tail option

Effect size

Use a standardized effect or anticipated rank correlation.

Number of groups

Allocation ratio

Group 2 divided by Group 1.

Expected dropout percentage

Round total to nearest multiple

Efficiency source

Custom ARE

Example Data Table

Scenario	Test	Effect size	Alpha	Power	Dropout
Two independent groups	Mann-Whitney U	0.50	0.05	0.80	10%
Paired baseline and follow-up	Wilcoxon signed-rank	0.45	0.05	0.90	12%
Three treatment groups	Kruskal-Wallis H	0.30	0.05	0.80	8%
Association study	Spearman correlation	0.35	0.05	0.85	5%

Formula Used

This tool uses asymptotic planning formulas. They convert familiar power expressions into rank-test targets through an efficiency factor called asymptotic relative efficiency, or ARE.

Mann-Whitney U / Wilcoxon rank-sum: N_total = (((1+r)^2)/r) × (Z_alpha + Z_power)^2 ÷ (ARE × d^2)

Wilcoxon signed-rank: N_pairs = (Z_alpha + Z_power)^2 ÷ (ARE × d^2)

Kruskal-Wallis H: N_total = (k-1) × (Z_alpha + Z_power)^2 ÷ (ARE × f^2)

Spearman correlation: N = (((Z_alpha + Z_power) ÷ atanh(rho))^2 + 3) ÷ ARE

Dropout adjustment: Adjusted N = Base N ÷ (1 - dropout rate)

These are planning approximations. They are useful for early protocol design, grant preparation, and feasibility review.

How to Use This Calculator

Select the nonparametric test that matches your design.
Enter alpha, target power, and one-sided or two-sided testing.
Provide the expected effect size. Use correlation for Spearman studies.
Set the group count for omnibus designs and allocation ratio for two-group studies.
Add expected dropout and a rounding multiple for operational planning.
Choose automatic ARE or supply your own value when justified.
Press calculate to show the result above the form.
Use the CSV and PDF buttons to save the output.

Frequently Asked Questions

1. What does this calculator estimate?

It estimates recruitment targets for common nonparametric tests. The result is a planning value, not a guarantee. It combines alpha, power, effect size, efficiency, dropout, and rounding.

2. Why use ARE in nonparametric planning?

ARE adjusts a familiar parametric planning expression to reflect rank-test efficiency. It gives a practical bridge when exact closed-form nonparametric planning methods are unavailable or inconvenient.

3. Which effect size should I enter?

Use a standardized location effect for Mann-Whitney, a paired standardized effect for Wilcoxon signed-rank, Cohen f style effect for Kruskal-Wallis, and absolute rho for Spearman correlation.

4. Is the result exact?

No. It is an asymptotic approximation for planning. Final protocol decisions should consider pilot data, simulation, missingness patterns, unequal variances, and consultation with a statistician.

5. Should I use one-sided or two-sided alpha?

Use two-sided alpha unless your study question and protocol justify a directional hypothesis before data collection. Two-sided planning is usually the safer default.

6. Why is dropout added after the base estimate?

The base estimate covers analyzable observations. Dropout inflates recruitment so the final retained sample is closer to the target after losses, withdrawals, or incomplete measurements.

7. What does the Plotly graph show?

It shows how the adjusted total sample changes across several target power levels while keeping your other assumptions fixed. This helps sensitivity review during planning.

8. When should I use a custom ARE?

Use a custom value only when you have defensible external evidence, simulation results, or subject-matter guidance supporting a different efficiency assumption for your outcome distribution.