On Feb 25, 2013, at 12:35 , Bert Gunter wrote: > 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
True. On the other hand, once we are in R, try removing one observation: > anova(lm(breaks~wool+tension, data=warpbreaks, subset=-1)) Analysis of Variance Table Response: breaks Df Sum Sq Mean Sq F value Pr(>F) wool 1 472.3 472.31 3.5293 0.0662491 . tension 2 2198.3 1099.16 8.2133 0.0008391 *** Residuals 49 6557.5 133.83 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 > anova(lm(breaks~tension+wool, data=warpbreaks, subset=-1)) Analysis of Variance Table Response: breaks Df Sum Sq Mean Sq F value Pr(>F) tension 2 2143.8 1071.92 8.0098 0.0009777 *** wool 1 526.8 526.79 3.9364 0.0528683 . Residuals 49 6557.5 133.83 --- Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ Now the results are order-dependant. The difference is that tension and wool are no longer orthogonal factors. For further enlightening, consult the literature as Bert suggests. -pd > > 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. -- Peter Dalgaard, Professor Center for Statistics, Copenhagen Business School Solbjerg Plads 3, 2000 Frederiksberg, Denmark Phone: (+45)38153501 Email: pd....@cbs.dk Priv: pda...@gmail.com ______________________________________________ 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.