# [R] quesion about SS of ANOVA

Bert Gunter gunter.berton at gene.com
Mon Feb 25 12:35:44 CET 2013

```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
> and provide commented, minimal, self-contained, reproducible code.

--

Bert Gunter
Genentech Nonclinical Biostatistics

Internal Contact Info:
Phone: 467-7374
Website: