In a one-way ANOVA, the F-statistic compares which variances?

In a one-way ANOVA, the F-statistic compares which variances?

• A. Between-group variance to within-group variance.
• B. Total variance to explained variance.
• C. Within-group variance to between-group variance.
• D. Model variance to residual variance.

Answer: (C)

In a one-way ANOVA, you separate total variation into two parts: how much the group means differ from the overall mean (between-group variation) and how much individual observations vary inside each group (within-group variation). The F-statistic is the ratio of the mean square for between-group differences to the mean square for within-group differences. This means you’re testing whether the differences among group means are large compared to the random variation you’d expect within each group. If all group means are the same, the two sources of variation are similar and F is around 1; if the means differ, between-group variation grows and F becomes larger. The ratio of within-group to between-group variation would be the reciprocal of F, which is not what the F-statistic uses.

In a one-way ANOVA, you separate total variation into two parts: how much the group means differ from the overall mean (between-group variation) and how much individual observations vary inside each group (within-group variation). The F-statistic is the ratio of the mean square for between-group differences to the mean square for within-group differences. This means you’re testing whether the differences among group means are large compared to the random variation you’d expect within each group. If all group means are the same, the two sources of variation are similar and F is around 1; if the means differ, between-group variation grows and F becomes larger. The ratio of within-group to between-group variation would be the reciprocal of F, which is not what the F-statistic uses.