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Re: ANOVA with empty cells
From: |
Isaac Neuhaus |
Subject: |
Re: ANOVA with empty cells |
Date: |
Mon, 11 Apr 2005 14:14:54 -0400 |
User-agent: |
Mozilla Thunderbird BMS-en M6r11d (Windows/20041005) |
Please see bellow.
Mike Miller wrote:
On Mon, 11 Apr 2005, Isaac Neuhaus wrote:
How does SAS do it?
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
You'll have to look at their manuals to figure out what they are
doing. Note that you have 3 df for R, 1 df for T, but only one df for
R*T. It must be fitting a model with a sort of partial interaction
effect. In a full model, you would have 3*1 = 3 df for interaction.
Yes.... this is because there are two empty cells in the design, but how
are they calculating it?
Looking more closely, you can only fit an interaction to the part of
the model where f1 is 1 or 3. So that must be what it is doing. You
can do this in Octave using dummy codes. You need three dummy codes
for f1, one for f2, and one for (arbitrary choice here) when f1=1,
f2=1. Once you have that done, you can use the '\' operator and other
functions to solve this,
That is pretty much what I did but I do not get the same answer although
it is close. Here is my design matrix:
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]
And here are my contrast matrices and their results (which I believe are
not approximation errors):
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)
Isaac
but I'm sure someone has developed a little regression or ANOVA
package to make this easier.
Mike
Your data....
f1 f2 response
S1 1 1 7
S2 2 1 1
S3 3 1 4
S4 4 2 5
S5 3 2 5
S6 1 2 9
S7 3 2 5
S8 1 2 10
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- ANOVA with empty cells, Isaac Neuhaus, 2005/04/11
- Re: ANOVA with empty cells, Mike Miller, 2005/04/11
- Re: ANOVA with empty cells, Isaac Neuhaus, 2005/04/11
- Re: ANOVA with empty cells, Mike Miller, 2005/04/11
- Re: ANOVA with empty cells,
Isaac Neuhaus <=
- Re: ANOVA with empty cells, Mike Miller, 2005/04/11
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- Re: ANOVA with empty cells, Mike Miller, 2005/04/11
- Re: ANOVA with empty cells, Isaac Neuhaus, 2005/04/11
- ANOVA with empty cells, Isaac Neuhaus, 2005/04/12