Thanks Eik.
As to your words:"The intercept in lm is tested against 0 (one sample
t-test)"

So, I perform the following test:
t.test(extra[group==1],mu=0)

Since goup1 is regarded as reference,I do the 1-sample ttest based on
group1's mean vs 0.
But the result:
t value= 1.3257
p-value = 0.2176

And t value and p value of s1 is:
t value= 1.249
p value= 0.2276

So the t value and p value are different between 1-sample ttest of
group1'mean vs 0  and s1(lm's result).

What's the reason for the difference then?

Thanks a lot for your help.

My best.


2011/8/16 Eik Vettorazzi <E.Vettorazzi@uke.uni-hamburg.de>

> Hi,
> you may have noticed, that your t-test and lm had not the same p-values
> for the difference in means, which is calculated for group2 when you use
> treatment contrasts and that is what R does by default (see
> ?contr.treatment). This is because R uses Welsh test by default. Pros
> and cons are beyond this post, but look at
>
> (t1<-t.test(extra~group,data=sleep,var.equal=T))
> (s1<-summary(lm(extra~group,data=sleep)))
> all.equal(s1$coef["group2","Pr(>|t|)"],t1$p.value)
>
> The intercept in lm is tested against 0 (one sample t-test),
> so the t-statistic is (mean-0)/sd, having n-k (sample size - number of
> parameters) degrees of freedom.
>
> cc<-s1$coef["(Intercept)",1:2]
> 2*(1-pt(cc[1]/cc[2],df=18))
>
>
> hth.
>
> Am 16.08.2011 07:25, schrieb Lao Meng:
> > Hi all:
> > I have a question about lm on t-test.
> >
> > data(sleep)
> >
> > I wanna perform t-test to test the difference between the 2 groups:
> >
> > I can use:
> > t.test(extra~group)
> >
> > The t.test result shows that:t = -1.8608; mean1=0.75,mean2=2.33
> >
> >
> > But I still wanna use:
> > summary(lm(extra~group))
> >
> > Intercept=0.75,which is mean1,just the same as t.test.
> > group2=1.58 means the difference of the 2 groups,so
> > mean2=1.58+0.75=2.33,just the same as t.test.
> > And some parameters of group2(t value,Pr) are the same as t.test,since
> > group2 is the difference of the 2 groups.
> >
> > My question is:
> > How the "t value" of Intercept(group1 acturally) is calculated?
> >
> >
> > Thanks a lot.
> >
> > My best
> >
> >       [[alternative HTML version deleted]]
> >
> > ______________________________________________
> > R-help@r-project.org mailing list
> > https://stat.ethz.ch/mailman/listinfo/r-help
> > PLEASE do read the posting guide
> http://www.R-project.org/posting-guide.html
> > and provide commented, minimal, self-contained, reproducible code.
>
> --
> Eik Vettorazzi
> Institut für Medizinische Biometrie und Epidemiologie
> Universitätsklinikum Hamburg-Eppendorf
>
> Martinistr. 52
> 20246 Hamburg
>
> T ++49/40/7410-58243
> F ++49/40/7410-57790
>

	[[alternative HTML version deleted]]

