[R] Between-group variance from ANOVA
smartpink111 at yahoo.com
Wed Jul 25 14:56:56 CEST 2012
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.
----- 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.
> View this message in context: http://r.789695.n4.nabble.com/Between-group-variance-from-ANOVA-tp901535p4637686.html
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