# [R] Between-group variance from ANOVA

tedtoal twtoal at ucdavis.edu
Wed Jul 25 02:55:10 CEST 2012

```I'm trying also to understand how to get the between-group variance out of a
one-way ANOVA, but I'm beginning to think that in a sense, the variance does
not exist.  Emma said:

*The model is response(i,j)= group(i)+ error(i,j)*

Yes, if by group(i) you mean intercept + coefficient[i].

*we assume that group~N(0,P^2) and error~N(0,sigma^2) *

Only the error is assumed to be a random variable.  Group is a fixed effect,
not a random variable, and therefore it has no variance associated with it.
The model does not predict a variance for it.  One could compute the
variance of the coefficients and call this a group variance, but it seems to
me that isn't the right way to think about it.

I'm trying to calculate a heritability value for a trait in an organism,
defined as Vg/Vp, where Vg = variance due to genotype and Vp = total
variance.  The model is p~g,  or p[i,j] = intercept + g_coefficient[i] +
error[i,j].  But to get Vg, I think it is actually necessary to use a
different model, where g is modelled as a random variable (a random effect),
so the model can estimate a variance associated with it.