In a one-way ANOVA, effect size can be expressed as SS_between / SS_total. What interpretation corresponds to this ratio?

In a one-way ANOVA, effect size can be expressed as SS_between / SS_total. What interpretation corresponds to this ratio?

• A. The proportion of total variance accounted for by the between-group differences
• B. The proportion of variance due to error
• C. The ratio of within-group to total variance
• D. The F-statistic value

Answer: (A)

This ratio shows how much of the total variability in the data is explained by the differences between the groups. In one-way ANOVA, the total sum of squares is the sum of the between-groups sum of squares and the within-groups (error) sum of squares. Therefore SS_total = SS_between + SS_within. When you take SS_between divided by SS_total, you get the portion of the total variance that is attributed to the grouping factor, which is a measure of effect size known as eta-squared. It ranges from 0 to 1, with larger values meaning the group differences account for more of the total variance. The other options describe different quantities: SS_within / SS_total is the proportion due to error, SS_between / SS_total is not the within-to-total ratio, and the F-statistic is the ratio of mean squares (MS_between / MS_within), not a ratio of sums of squares.

This ratio shows how much of the total variability in the data is explained by the differences between the groups. In one-way ANOVA, the total sum of squares is the sum of the between-groups sum of squares and the within-groups (error) sum of squares. Therefore SS_total = SS_between + SS_within. When you take SS_between divided by SS_total, you get the portion of the total variance that is attributed to the grouping factor, which is a measure of effect size known as eta-squared. It ranges from 0 to 1, with larger values meaning the group differences account for more of the total variance. The other options describe different quantities: SS_within / SS_total is the proportion due to error, SS_between / SS_total is not the within-to-total ratio, and the F-statistic is the ratio of mean squares (MS_between / MS_within), not a ratio of sums of squares.