Between-group variance from ANOVA

Hi,

From the ANOVA results, you could get MSE and MS of group.  MSE is basically sigma^2 error.  MS group of MS between group contains sigma^2 error+replication*sigma^2group (please check the formula.  It can be slightly different when the model complexity increases).  


Once, you get sigma^2 group, I guess you know how to calculate Vg and Vp. 


Once, you have all the values, except sigma^2 group, you can subtract and divide it by replication to get sigma^2 group.  In SAS, proc glm also shows the output with formula.

A.K.

----- Original Message -----
From: Ista Zahn <istazahn at gmail.com>
To: tedtoal <twtoal at ucdavis.edu>
Cc: r-help at r-project.org
Sent: Wednesday, July 25, 2012 6:21 AM
Subject: Re: [R] Between-group variance from ANOVA

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




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