This is a basic statistics question and off topic here. Talk to a statistician (i.e. someone with a good statistics background) or start reading. You need an extensive statistics tutorial that I believe is too much for online forums like stats.stackexchange.com.
-- Cheers, Bert On Sun, Feb 24, 2013 at 8:07 PM, meng <laomen...@163.com> wrote: > Hi all: > I have a quesion about ANOVA: Is SS(Sum of Square) of a specific factor > constant with the number of factors changing? > > dat1 includes one factor g1,and g1's SS is called SS_g1_dat1. > dat2 includes two factors g1,g2,and g1's SS is called SS_g1_dat2. > > My quesion is: Is SS_g1_dat1 equals to SS_g1_dat2? > > I have both "yes" and "no" reasons for the quesion,but don't know which one > is correct,which need your precious help. > > The reasion for SS_g1_dat1 equals to SS_g1_dat2: > The formula for computing SS is:sum(sample size of level(i)*(mean of > level(i)-TotalMean)^2),with i refers to each level in SS_g1_dat1 and > SS_g1_dat2. > Every element of the formula is constant,so SS is constant. > > Using the dataset "warpbreaks" from R: > anova(lm(breaks~wool)) > Analysis of Variance Table > Response: breaks > Df Sum Sq Mean Sq F value Pr(>F) > wool 1 450.7 450.67 2.6684 0.1084 > Residuals 52 8782.1 168.89 > > anova(lm(breaks~wool+tension)) > Analysis of Variance Table > Response: breaks > Df Sum Sq Mean Sq F value Pr(>F) > wool 1 450.7 450.67 3.3393 0.073614 . > tension 2 2034.3 1017.13 7.5367 0.001378 ** > Residuals 50 6747.9 134.96 > > anova(lm(breaks~tension+wool)) > Analysis of Variance Table > Response: breaks > Df Sum Sq Mean Sq F value Pr(>F) > tension 2 2034.3 1017.13 7.5367 0.001378 ** > wool 1 450.7 450.67 3.3393 0.073614 . > Residuals 50 6747.9 134.96 > > >From above,wool's SS is always 450.7 not matter the number and order of > >factors. > > > The reasion for SS_g1_dat1 NOT equals to SS_g1_dat2: > The total SS is constant,so SS for each factor is decreasing with the number > of factors increasing. > But when I use dataset "warpbreaks" to comfirm, it failed to confirm.The > result shows that wool's SS is always 450.7 not matter the number and order > of factors. > > So which reason of the above two is correct then? > > Many thanks for your help. > > 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. -- Bert Gunter Genentech Nonclinical Biostatistics Internal Contact Info: Phone: 467-7374 Website: http://pharmadevelopment.roche.com/index/pdb/pdb-functional-groups/pdb-biostatistics/pdb-ncb-home.htm ______________________________________________ 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.
