[R] Between-group variance from ANOVA

[peter dalgaard]

On Jul 25, 2012, at 14:56 , arun wrote:

> 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.
> 

Beware, though, that this works for balanced designs only (identical group sizes). For unequal replication, you need to go the lme/lmer route.

-pd


> 
> 
> 
> ----- 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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>> 
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> 
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-- 
Peter Dalgaard, Professor,
Center for Statistics, Copenhagen Business School
Solbjerg Plads 3, 2000 Frederiksberg, Denmark
Phone: (+45)38153501
Email: pd.mes at cbs.dk  Priv: PDalgd at gmail.com