On 5 Dec 1999 07:45:51 -0800, [EMAIL PROTECTED] (dennis roberts) wrote:
< snip, detail >
> One-way Analysis of Variance
>
> Analysis of Variance
> Source DF SS MS F P
> Factor 1 252 252 1.54 0.231
> Error 18 2949 164
> Total 19 3201
>
> and the ancova shows:
>
> Analysis of Variance for TOTY, using Adjusted SS for Tests
>
> Source DF Seq SS Adj SS Adj MS F P
> TOTIQ 1 1539.9 2057.9 2057.9 39.26 0.000
> Group 1 770.0 770.0 770.0 14.69 0.001
> Error 17 891.0 891.0 52.4
> Total 19 3200.9
>
> in the handout, i showed that the adjusted SS(TOT) equals the sum of the
> 770 and 891 values for Group and Error in the Adj SS columns ... but where
> does the 2057 come from and, when you add to the 770 and 891 values .. you
> get a much larger value than the original 3201?
- The SS= 770 for Group has been boosted from its oneway SS of 252
by 518, owing to the (negative) confounding with TOTIQ. That is
exactly the SS boost for TOTIQ when it is regarded as the second
factor sequentially: labeled Adj SS.
The SS will add up if you take the factors sequentially, or if the
factors are uncorrelated. The SS can't add up if you credit the
"shared variance" of 518 -- or however you want to phrase it, in the
negative case -- to both factors. This compares to the usual example
where the shared variance wipes out the contribution of one or both
variables, and the sum of Adj SS is less than the Total SS.
--
Rich Ulrich, [EMAIL PROTECTED]
http://www.pitt.edu/~wpilib/index.html
