In this post we prove that SStotal = SSBG + SSWG and νtotal = νBG + νWG, where s2=SStotal/νtotal – variance. These are well known equations, used, say, in ANOVA. They are not obvious although the proof is easy.
So we have:
- m groups, nj – sizes, Xj – means, j = 1, …, m
- J is joint group (union of all groups)
- Xij – i-th sample of j-th group
- N is size of J
So several definitions:
The first proof:
The seconf proof:
So our variance is:
perfstories 