Between Group Variation: Definition, Formula


Between group variation is used in ANOVA (analysis of variance) to measure variation between separate groups of interest. Unlike within group variation, where the focus is on the differences between a population and its mean, between group variation is concerned with finding how the means of groups differ from each other.

Between Group Variation Formula

The formula for between-group variation is:
Between Group Variation Formula

and is called the sum of squares between groups, or SS(B).

This measures the interaction between the groups or samples. If the group means don’t differ greatly from each other and the grand mean, the SS(B) will be small.

Note that for k groups, there will be k-1 degrees of freedom. The between groups variance is the variation, or SS(B), divided by its degree of freedom. We sometimes refer to the between groups variance as sb 2.

Between Group Variation, Within Group Variation, and the F-ratio

Between group variation is important in ANOVA because it is compared to within group variation to determine treatment effect.

We can calculate the “F-ratio” as (between group variation)/(within group variation). This is equivalent to (treatment effect + error)/(error). If the treatment effect goes to zero, the F ratio will be (error)/(error) and go to 1. If the treatment effect increases toward infinity, the F ratio will also go towards infinity.


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Webb, Barbara. ANOVA – Analysis of Variance
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