That is a speciality of your model - it is actually an ANOVA-model (with 2 groups). Even so the variance of the intercept is estimated from the whole sample, not only for group==1 (thats why the statistics and p-values differ) - and that analysis is equivalent to a t-test with common variance (aka classical t-test).
A different kettle of fish is a regression with continuous predictors like (s1<-summary(lm(extra~as.numeric(group),data=sleep))) where your estimates depend on the coding of group. cheers. Am 18.08.2011 08:50, schrieb Lao Meng: > Well,since the intercept is the same as mean of group1,I take it for > granted that the 1-sample ttest must test based on group==1... > > If the intercept is estimated from the whole sample,why does the > intercept is the same as mean of group1? > > > > > 2011/8/17 Eik Vettorazzi <e.vettora...@uke.uni-hamburg.de > <mailto:e.vettora...@uke.uni-hamburg.de>> > > 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.vettora...@uke.uni-hamburg.de > <mailto:e.vettora...@uke.uni-hamburg.de> > > <mailto:e.vettora...@uke.uni-hamburg.de > <mailto:e.vettora...@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 <mailto:R-help@r-project.org> > <mailto:R-help@r-project.org <mailto: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 > > > > > > -- > 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 Department of Medical Biometry and Epidemiology University Medical Center Hamburg-Eppendorf Martinistr. 52 20246 Hamburg T ++49/40/7410-58243 F ++49/40/7410-57790 ______________________________________________ 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.
