Question

How can the SST (total sum of squares) be separated?

a) Into between-group and within-group sums of squares
b) Into regression and residual sums of squares
c) Into interaction and main effects sums of squares
d) Into fixed and random effects sums of squares

Answer 1

The SST can be separated into between-group and within-group sums of squares, where SSbetween reflects variance due to different group means and SSwithin reflects variance within each group due to random variation or individual differences.

Step-by-step explanation:

The total sum of squares (SST) can be separated into the between-group and within-group sums of squares. The SSbetween, or sum of squares between groups, showcases the variance due to the difference between the group means, and it represents the effect of the independent variable. The SSwithin, or sum of squares within groups, represents the variance that occurs within each group, which is typically due to random variation or individual differences not accounted for by the independent variable.

The mean squares (MS), which includes MSbetween and MSwithin, are found by dividing each sum of squares by its respective degrees of freedom. In the context of an ANOVA test, MSbetween can be influenced by differences among group means, while MSwithin is not affected by the difference in group means since it compares values within the same group. This distinction is crucial for understanding how the SST is partitioned in statistical analyses like ANOVA (Analysis of Variance).