[R] a question about lm on t-test.

[Eik Vettorazzi]

Hi Lao,
thats not the same test. The concept of linear regression applies here
(and you might take any introductory at your hand to refresh that
concept). The intercept is estimated from the whole sample not just
group==1, dfs are 20-2, not sum(group==1)-1!

best regards

Am 17.08.2011 09:57, schrieb Lao Meng:
> 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 at uke.uni-hamburg.de
> <mailto:E.Vettorazzi at 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]]
>     >
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> 
>     --
>     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
> 
> 

-- 
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