Re: ANOVA with empty cells

[Isaac Neuhaus]

Thanks Mike. That is the same answer that I get. I can get the correct 
answer for the interaction but I cannot figure how to get the same SAS 
answer for the fixed  effects. Thanks for your help . I hope somebody 
can take a look at this in more detail.

Isaac

C1 = [0,1,0,0,0,0;
    0,0,1,0,0,0;
    0,0,0,1,0,0]    pval = 0.0178    (in SAS 0.0203)

C2 = [0,0,0,0,1,0]    pval = 0.0550    (in SAS 0.0561)

C3 = [0,0,0,0,0,1]    pval = 0.2254    (the same in SAS)



Mike Miller wrote:

> On Mon, 11 Apr 2005, Isaac Neuhaus wrote:
>
> Here are the basic data:
>
>
> >    f1   f2   response
> > S1    1    1    7
> > S6    1    2    9
> > S8    1    2    10
> > S2    2    1    1
> > S3    3    1    4
> > S5    3    2    5
> > S7    3    2    5
> > S4    4    2    5
> >
> > X =  [ 1,  1,  0,  0,  1,  0;
> >        1,  1,  0,  0, -1,  0;
> >        1,  1,  0,  0, -1,  0;
> >        1,  0,  1,  0,  1,  0;
> >        1,  0,  0,  1,  1,  1;
> >        1,  0,  0,  1, -1, -1;
> >        1,  0,  0,  1, -1, -1;
> >        1, -1, -1, -1, -1,  1];
>
>
> > Y = [7;9;10;1;4;5;5;5]
>
>
>
> I was looking at residual sums of squares (RSS) like this:
>
> b=X\Y; e=Y-X*b; e'*e
>
> octave:48> b=X\Y; e=Y-X*b; e'*e
> ans = 0.500000000000000
>
> That is the correct error SS and it is equal to the answer given by 
> SAS (it is on 2 df, so MSE = 0.50/2 = 0.25).  See below.
>
>
> octave:49> b=X(:,1:5)\Y; e=Y-X(:,1:5)*b; e'*e
> ans = 1.25000000000000
>
> That is the RSS for the interaction term.  Subtract the error SS and 
> you'll have 0.75, which is again the SAS answer.
>
>
> But then I run into a problem computing Type III SS for the other 
> effects, probably because I'm doing it the wrong way.  I've really got 
> to return to some other work now.  Maybe someone else on the list can 
> figure this out. We're trying to get this:
>
>
> > Source   DF     Type III SS     Mean Square    F Value    Pr > F
> > R         3     36.30000000     12.10000000      48.40    0.0203
> > T         1      4.08333333      4.08333333      16.33    0.0561
> > R*T       1      0.75000000      0.75000000       3.00    0.2254
>
>
>
> From these data:
>
> Y = [7;9;10;1;4;5;5;5]
>
> X = [ 1, 1, 0, 0, 1, 0;
>      1, 1, 0, 0,-1, 0;
>      1, 1, 0, 0,-1, 0;
>      1, 0, 1, 0, 1, 0;
>      1, 0, 0, 1, 1, 1;
>      1, 0, 0, 1,-1,-1;
>      1, 0, 0, 1,-1,-1;
>      1,-1,-1,-1,-1, 1]
>
> Where the first column of X is for the intercept, the next three 
> columns are for R, the 5th column is for T and the last column is for 
> R*T.
>
> Mike




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