[R] Between-group variance from ANOVA

[Mark Difford]

Hi Emma,

>> ...from this I can read the within-group variance. can anyone tell me how
>> i may find 
>> out the between-group variance?

But it's in the table, above the "within-group" variance. Remember that F is
the ratio of these two quantities, i.e. the mean of the group variances
divided by the mean of the within-group variances . I will work with my
example since you never set seed so your answers are different from mine
(which really does not help matters).

set.seed(7) 
TDat <- data.frame(response = c(rnorm(100, 5, 2), rnorm(100, 20, 2))) 
TDat$group <- gl(2, 100, labels=c("A","B"))
summary(aov(response ~ group, data=TDat))

11225.25/3.64
[1] 3083.86

There is some rounding error on the mean squares (i.e. mean variances) but F
is correct. Using estimates calculated by a different route we have:

11225.249057/3.639801
[1] 3084.028

Does this answer your question?

Regards, Mark.


emj83 wrote:
> 
> I have done this in R and this is the following ANOVA table I get:
> 
>> summary(aov(response ~ group, data=TDat))
>              Df  Sum Sq Mean Sq F value    Pr(>F)
> group         1 11203.5 11203.5  2505.0 < 2.2e-16 ***
> Residuals   198   885.5     4.5
> 
> The model is response(i,j)= group(i)+ error(i,j),
> 
> we assume that group~N(0,P^2) and error~N(0,sigma^2)
> 
> I know that sigma^2 is equal to 4.5, how do I find out P^2? 
> 
> In the problem that I am trying to apply this to, I have more than 2
> groups. I was hoping there would be a function that helps you do this that
> I don't know about.
> 
> 
> Thanks for your help Emma
> 
> 
> 
> 
> Mark Difford wrote:
>> 
>> Hi Emma,
>> 
>>>> 
>> 
>> R gives you the tools to work this out.
>> 
>> ## Example
>> set.seed(7)
>> TDat <- data.frame(response = c(rnorm(100, 5, 2), rnorm(100, 20, 2)))
>> TDat$group <- gl(2, 100, labels=c("A","B"))
>> with(TDat, boxplot(split(response, group)))
>> summary(aov(response ~ group, data=TDat))
>> 
>> Regards, Mark.
>> 
>> 
>> emj83 wrote:
>>> 
>>> can anyone advise me please?
>>> 
>>> 
>>> emj83 wrote:
>>>> 
>>>> I have done some ANOVA tables for some data that I have, from this I
>>>> can read the within-group variance. can anyone tell me how i may find
>>>> out the between-group variance?
>>>> 
>>>> Thanks Emma
>>>> 
>>> 
>>> 
>> 
>> 
> 
> 

-- 
View this message in context: http://www.nabble.com/Between-group-variance-from-ANOVA-tp24954045p25129942.html
Sent from the R help mailing list archive at Nabble.com.