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

The calculation of the sum of squares between groups (SS Between) in an unequal n ANOVA is correctly described by the process of subtracting the grand mean from each treatment mean, squaring that difference, and then summing these squared differences across all treatments. This method allows for the assessment of how much the treatment means deviate from the overall grand mean, which represents the overall average across all groups.

This approach is essential because it accounts for the variability between different treatments (or groups) within the dataset, providing insight into whether the means of the treatments differ significantly from the overall mean. The calculated SS Between reflects the potential effects of the independent variable on the dependent variable by highlighting the variability attributed to the different groups.

In comparison, some other approaches listed do not accurately reflect how SS Between is determined in ANOVA. For instance, methods involving squaring treatment means without considering the grand mean or simply adding variances do not directly capture the essence of between-group variance as needed for this analysis. The correct approach focuses on summarizing the systematic variance explained by the treatment conditions, which is fundamental in hypothesis testing for differences among group means.