**StATS: **Unequal group sizes (created 2001-11-02)

*Dear Professor Mean, I am comparing several groups of subjects, but the number of subjects
in each group differ quite a bit. How does this affect the assumptions in analysis of variance.*

Equal group sizes are not a requirement for ANOVA. Some of the post hoc tests in ANOVA require equal sample sizes, but there are ways to work around this.

With unequal group sizes comes a loss of power, because the precision of your estimates is dominated by the smaller (smallest) group sample size. Still there are plenty of situations where unequal group sizes are recommended. If, for example, the cost of sampling a control subject is much smaller than the cost of sampling a treated subject, then you can justify sampling a greater number of control subjects because it produces the most precision for the money.

You should look closely at your assumption of equal variances, however, since a violation of this assumption is more problematic when the group sizes are not equal.

So my recommendation is to not worry too much about group sizes that are not equal.

This page was written by Steve Simon while working at Children's Mercy Hospital. Although I do not hold the copyright for this material, I am reproducing it here as a service, as it is no longer available on the Children's Mercy Hospital website. Need more information? I have a page with general help resources. You can also browse for pages similar to this one at Category: Analysis of variance.