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
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.
Deater-Deckard et al. (2017). Within- and between-person and group variance in behavior and beliefs in cross-cultural longitudinal data. Journal of Adolescence. 62. 10.1016/j.adolescence.2017.06.002. Retrieved from https://www.researchgate.net/publication/317940722_Within-_and_between-person_and_group_variance_in_behavior_and_beliefs_in_cross-cultural_longitudinal_data on August 17, 2018.
Garbin, Cal. Between Groups and Within Groups ANOVA. Lecture Notes. Retrieved from http://psych.unl.edu/psycrs/941/q3/bg-wg.pdf on August 17, 2018.
Jones, James. Statistics Lecture Notes: One Way Anova.
Retrieved from https://people.richland.edu/james/lecture/m170/ch13-1wy.html on August 17, 2018.
Webb, Barbara. ANOVA – Analysis of Variance
Retrieved from http://homepages.inf.ed.ac.uk/bwebb/statistics/ANOVA1.pdf on August 17, 2018.