How is the SS Within calculated in an unequal n ANOVA?

The calculation of SS Within, also known as the sum of squares within groups or the error sum of squares, is essential in an ANOVA as it reflects the variability of individual scores around their respective group means. In the context of an unequal n ANOVA, the correct approach to calculating SS Within involves taking into account the treatment variances and the sample sizes for each treatment group.

By multiplying the treatment variance by the number of subjects in each treatment and summing these products, you effectively capture how much variability exists within each group while adjusting for the number of observations in each group. This calculation ensures that each group's contribution to the total within-group variance is proportional to its size, accounting for the unequal sample sizes.

This approach provides a more accurate estimate of variability due to the inherent differences within each treatment group, allowing the ANOVA to appropriately assess the differences between group means while controlling for this internal variability. Hence, this method ensures a robust analysis, particularly in situations where groups differ in size.