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 <laomeng_3 at 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 at 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