How do you calculate the df Within for an unequal n ANOVA?

To calculate the degrees of freedom (df) within for an unequal n ANOVA, the correct approach involves understanding how degrees of freedom are derived from sample sizes associated with each treatment group.

In an ANOVA, the degrees of freedom within (df Within) reflects the variability within each group and is calculated by taking the sum of the degrees of freedom for each treatment group. Since treatment groups can have unequal sample sizes, for each group, you subtract 1 from the sample size (n) associated with that group. This accounts for the estimation of the group mean from the data. By summing these individual degrees of freedom from all treatment groups, you achieve the total degrees of freedom within.

This method effectively captures the inherent variability within each treatment group while properly adjusting for the fact that different groups may contain different numbers of observations. Thus, the correct computation is to sum the values of (n - 1) for all treatment groups, which aligns perfectly with the chosen answer, emphasizing the importance of recognizing how unbalanced designs must be handled carefully in statistical analyses.