[R] Between-group variance from ANOVA

[Mark Difford]

Hi Emma,

...

I forgot to add the tabular ouput, which doesn't help either:

T.sum <- summary(aov(response ~ group, data=TDat))
print(T.sum)

             Df  Sum Sq Mean Sq F value    Pr(>F)    
group         1 11225.2 11225.2    3084 < 2.2e-16 ***
Residuals   198   720.7     3.6                      
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

unlist(T.sum)

unlist(T.sum)[5]/unlist(T.sum)[6]
Mean Sq1 
3084.028

Regards, Mark.


Mark Difford wrote:
> 
> 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
>>>>> 
>>>> 
>>>> 
>>> 
>>> 
>> 
>> 
> 
> 

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