[R] coefs from summary.lm of an aov object

[David Winsemius]

On Feb 4, 2010, at 1:02 PM, Martin Ivanov wrote:

> Dear R users,
>
> This is probably a very stupid question, nevertheless I obviously am  
> not qualified enough
> to cope with it. I do not understand what the coefficients are that  
> are output by running
> summary.lm on an aov object. I thought they should be the  
> differential effects for the levels of the factor and the overall  
> mean, but they are obviously not, as illustrated by the following  
> simple example:
>
> x <- c(1:15); y <- factor(c(rep("a", 5), rep("b", 10)))
>> tapply(X=x, INDEX=y, FUN=mean)
>   a    b
> 3.0 10.5
>
>> mean(x)
> [1] 8
>
>> a <- aov(x ~ y)
>> summary.lm(a)$coef
>            Estimate Std. Error  t value     Pr(>|t|)
> (Intercept)      3.0   1.192928 2.514821 0.0258555905
> yb               7.5   1.461032 5.133357 0.0001921826
>
>
>> model.tables(a)
> Tables of effects
>
> y
>     a    b
>    -5  2.5
> rep  5 10.0
>
> Besides, I fit a factor with two levels, "a" and "b", but there is  
> only the "yb" coefficient for the "b" level, no "ya" coefficient for  
> the "a" factor level.

R reports treatment contrasts (at least by default) so the base level,  
"a" in your case, is reported as the "Intercept". The "yb effect" is  
the difference between the mean yb estimate and the baseline. So your  
estimated mean for a subject with yb="b" would be "Intercept" +  
beta(yb) = 10.5

So all is right in stats-land.


> I read a lot of materials on anova with R, but I could not find what  
> are these coefficients. I would be grateful if someone gives me some  
> clue. And what is the intercept term? I though it should be the  
> overall mean, but it is obviously not.

-- 
David.