KONSİLCalculator · deterministic
Mann-Whitney U test sample size calculator
Skewed outcome or small sample: n for the non-parametric two-group comparison.
Calculator
No AI, no sign-up — the arithmetic runs in the server-side deterministic solver, validated against G*Power and R pwr.
When to use it
You are comparing two independent groups, but the outcome is clearly skewed (length of stay, cost, some biomarkers) or the sample is too small to lean on normality. The rank-based Mann-Whitney test is the standard alternative to the t test here.
Where the inputs come from
- d equivalent: derived exactly as for the two-group t test — the path on the t-test page applies.
- If the distribution is heavily skewed, think in terms of the median difference and spread; pick the closest d scenario and run a sensitivity range.
Worked example
For a d equivalent of 0.50, two-sided α = 0.05 and 80% power, the solver requires 67 per arm, 134 in total — slightly more than the 128 a t test needs at the same effect; that is the price of dropping the parametric assumptions. At 20% attrition, recruit 168.
How to write it in the protocol
“As the primary outcome [measure] is skewed, the primary analysis was planned as a Mann-Whitney U test. A d equivalent of [value] [with source], two-sided α = 0.05 and 80% power required [n] per arm (t-test n inflated by ARE = 0.955).”
Sources
- Cohen J. Statistical Power Analysis for the Behavioral Sciences, 2nd ed. Lawrence Erlbaum; 1988.
- Faul F, Erdfelder E, Lang A-G, Buchner A. G*Power 3: a flexible statistical power analysis program. Behav Res Methods. 2007;39:175–191.
- Champely S. pwr: Basic Functions for Power Analysis (R package).