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## Re: ANOVA with empty cells

**From**: |
Mike Miller |

**Subject**: |
Re: ANOVA with empty cells |

**Date**: |
Mon, 11 Apr 2005 17:12:13 -0500 (CDT) |

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
--
Michael B. Miller, Ph.D.
Assistant Professor
Division of Epidemiology and Community Health
and Institute of Human Genetics
University of Minnesota
http://taxa.epi.umn.edu/~mbmiller/
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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*, `2005/04/11`
**Re: ANOVA with empty cells**, *Mike Miller*, `2005/04/11`
*Message not available**Message not available**Message not available**Message not available**Message not available***Re: ANOVA with empty cells**,
*Mike Miller* **<=**
**Re: ANOVA with empty cells**, *Isaac Neuhaus*, `2005/04/11`
**ANOVA with empty cells**, *Isaac Neuhaus*, `2005/04/12`