# Unequal Sample Size Effect on Power Calculation

I am new to power analysis and have been experimenting with one-way fixed effects Anova in G*Power (Fixed effects, omnibus, one-way, Post hoc power).

When dealing with unbalanced design, the effect size is affected. When power of such a test is computed, is it also affected by unequal sample sizes (I mean besides the effect size)?

• Could you clarify if your question is about how to conduct a power analysis (i.e., how many observations should I collect?), or is your question about how to conduct ANOVA (i.e., does it matter if my group sizes are different?). In other words, have you already collected your data, or are you making a plan to collect data? – 5ayat May 17 '16 at 15:07
• I would like to know how power calculation for an unbalanced design differs from calculation for a balanced one (fixed one-way Anova, 4 groups). For those familiar with G*Power I can further explain where my question stems from: the program allows to compute an effect size given unequal sample sizes; when the computed effect size is used to calculate power, and given that total sample size is not a multiple of the number of groups, the program bases its calculation on average group size. I'd like to know whether unequal sample sizes directly affect the power calculation. – Gregory May 17 '16 at 18:07

## 1 Answer

There is an easy rule of thumb for ANOVA: Unequality in sample sizes deteriorates the power. The reason is that the power depends mostly on the variance of the effect estimator, i.e. the mean differences between the groups. These mean differences have the least variance (given a total sample size) if all the sample sizes are equal.

• Thank you for your answer @Horst Grünbusch. GPower outputs a message whenever the total sample size is not a multiple of the number of groups, saying that "the analysis was based on the average group size". Does this imply that the GPower calculation is correct only for samples of equal size? – Gregory Jun 2 '16 at 15:00