Are the procedures for finding SS Between and SS Within the same in an unequal n summary data ANOVA?

The procedures for finding the Sum of Squares Between (SS Between) and the Sum of Squares Within (SS Within) in an ANOVA setup with unequal sample sizes are different.

When calculating SS Between, you focus on the variability due to the differences between the group means. This involves taking the overall mean and calculating how much each group's mean deviates from that overall mean, weighting these deviations by the number of observations in each group. Since the groups have unequal sample sizes, this weighting will influence the calculation.

Conversely, when calculating SS Within, you account for the variability within each group. This involves summing the squared deviations of each observation from its own group mean, which again will be influenced by the unequal number of observations in each group.

As a result, the presence of unequal sample sizes means that the procedures for calculating these two sums of squares differ in terms of the weighting applied to the group means and the individual observations. This distinction is key to understanding the impact of sample size on the ANOVA calculations. Therefore, the correct answer is that the methods for finding SS Between and SS Within are not the same in the context of unequal sample sizes.