In a one-factor ANOVA, the total sum of squares is equal to:
A)the sum of squares within groups plus the sum of squares between groups.
B)the sum of squares within groups times the sum of squares between groups.
C)the sum of squares within groups divided by the sum of squares between groups.
D)the means of all the groups squared.

Question

Quizplus · Accepted Answer

The total sum of squares (SS total) represents the total variability in the data. It is calculated by summing the squared deviations of each individual score from the grand mean. The sum of squares within groups (SS within) represents the variability that is due to differences within each group and is calculated by summing the squared deviations of each individual score from their group mean. The sum of squares between groups (SS between) represents the variability that is due to differences between the groups and is calculated by summing the squared deviations of each group mean from the grand mean. Therefore, the total sum of squares is equal to the sum of squares within groups plus the sum of squares between groups.

In a One-Factor ANOVA, the Total Sum of Squares Is