The F-test partitions the total variance into within-group variance and between-group variance.

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The F-test, also known as the ANOVA (analysis of variance) test, does indeed partition the total variance into within-group variance (variance within each group or sample) and between-group variance (variance between the samples or groups being compared). This allows for the calculation of an F-statistic, which tests whether the between-group variance is significant relative to the within-group variance, and hence whether the means of the groups are significantly different from each other.

The F-Test Partitions the Total Variance into Within-Group Variance and Between-Group