Statistics for Business: Decision Making and Analysis, 3rd Edition

26.4 Groups of Different Size

An ANOVA regression does not require an equal number of cases in each group. The calculation and interpretation of the associated regression proceed as with balanced data. For instance, the intercept remains the mean of the baseline group, and the F-test compares the means of the J populations.

The effect of unequal group sizes is that more is known about the means of some categories than others. The standard error of an average of n observations is $\sigma /\sqrt{n}$ If one group has, say, 36 observations whereas another has 9, then the standard error of the mean of the larger group (σ/6) is half the size of the standard error of the mean of the smaller group (σ/3).

Because of the different sample sizes, unbalanced data produce ...