R help - Jul 2012 - Between-group variance from ANOVA

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.

If anyone can add something to this, please do.
ted




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There is nothing about R in your question, hence it is not appropriate
for this list. Please consult with a local statistician, or post on a
stats help list such as http://stats.stackexchange.com/

On Tue, Jul 24, 2012 at 8:55 PM, tedtoal <twtoal at ucdavis.edu>
wrote:
> 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.
>
> If anyone can add something to this, please do.
> ted
>
>
>
>
> --
> View this message in context:
http://r.789695.n4.nabble.com/Between-group-variance-from-ANOVA-tp901535p4637686.html
> Sent from the R help mailing list archive at Nabble.com.
>
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