Sample Size for More than Two Independent Means

Example clinical scenario

A randomized study compares mean HbA1c at six months across three dietary interventions using an overall test of the independent group means.

Formula and methodological note

This calculator uses a fixed-effects one-way ANOVA power calculation based on the noncentral F distribution. For each candidate total sample size, it calculates the allocation-weighted grand mean and noncentrality parameter, λ = Σ n_i(μ_i − μ̄_w)² / SD², with numerator degrees of freedom equal to the number of groups minus 1 and denominator degrees of freedom equal to total sample size minus the number of groups. It then searches for the smallest allocation that reaches the requested power.

Enter two to 50 anticipated group means and one common within-group SD. Equal allocation is supported, as are unequal allocations specified as positive whole-number ratios; the reported analysable group sizes preserve those ratios exactly. Any power and Type I error strictly between 0% and 100% can be entered. Dropout/non-response is applied separately to each group, with each recruitment target rounded upward.

The method assumes independent participants, a continuous outcome, a prespecified fixed-effects omnibus comparison, approximately Normally distributed within-group outcomes, and a common within-group SD. It does not plan post-hoc pairwise contrasts, repeated measurements, covariate adjustment, clustering, unequal variances, non-Normal outcomes, non-inferiority/equivalence designs, or interim monitoring. It supports research planning and does not replace statistical consultation.

Method references

1. Cohen J. Statistical Power Analysis for the Behavioral Sciences. 2nd ed. Lawrence Erlbaum Associates; 1988.
2. Chow SC, Shao J, Wang H, Lokhnygina Y. Sample Size Calculations in Clinical Research. 3rd ed. Chapman and Hall/CRC; 2017.