# [R] summary of aov fit on a contrast basis

John Fox jfox at mcmaster.ca
Tue Oct 23 14:43:47 CEST 2001

```Dear Jarek,

There are probably other ways to do this, but one way is to assign the
contrasts to the factor; using the data in your data frame x:

> attach(x)
>
> con <- matrix(c(2,  2, -1, -1, -1, -1,
+                 0,  0,  3, -1, -1, -1,
+                 1, -1,  0,  0,  0,  0,
+                 0,  0,  0, -2,  1,  1,
+                 0,  0,  0,  0,  1, -1),
+                 6, 5)
>
> con
[,1] [,2] [,3] [,4] [,5]
[1,]    2    0    1    0    0
[2,]    2    0   -1    0    0
[3,]   -1    3    0    0    0
[4,]   -1   -1    0   -2    0
[5,]   -1   -1    0    1    1
[6,]   -1   -1    0    1   -1
>
> contrasts(G) <- con
>
> summary(lm(X ~ G))

Call:
lm(formula = X ~ G)

Residuals:
Min         1Q     Median         3Q        Max
-1.000e+00 -1.000e+00 -5.551e-17  1.000e+00  1.000e+00

Coefficients:
Estimate Std. Error  t value Pr(>|t|)
(Intercept)  4.000e+00  2.357e-01   16.971 9.40e-10
G1           1.401e-16  1.667e-01 8.41e-16 1.000000
G2           2.000e+00  1.667e-01   12.000 4.84e-08
G3          -2.000e+00  4.082e-01   -4.899 0.000367
G4           2.318e-33  2.357e-01 9.83e-33 1.000000
G5           1.813e-16  4.082e-01 4.44e-16 1.000000

Residual standard error: 1 on 12 degrees of freedom
Multiple R-Squared: 0.9333,     Adjusted R-squared: 0.9056
F-statistic:  33.6 on 5 and 12 DF,  p-value: 1.179e-006

I used lm rather than aov to get the one-df t-tests for each contrast
coefficient; these are simply sqrt(F) from your approach. Note that the
contrast matrix is given by columns.

Is that what you wanted?

John

At 10:47 AM 10/23/2001 +0200, J.Sobieszek at elka.pw.edu.pl wrote:
>Hello,
>
>In a book (David W. Stockburger, "Multivariate Statistics: Concepts,
>Models, and Applications", chapter 12 "Contrasts, Special and
>Otherwise", available online at http://www.psychstat.smsu.edu/multibook)
>I've found some examples of doing analysis of variance on a contrast
>basis.
>
>I attach my solution (in R, the book uses SPSS) to this problem.
>
>Am I computing the same thing, and is there a simpler way of doing that?
>
>I would greatly appreciate any comments.
>
>Thanks,
>
>Jarek

-----------------------------------------------------
John Fox
Department of Sociology
McMaster University
email: jfox at mcmaster.ca
phone: 905-525-9140x23604
web: www.socsci.mcmaster.ca/jfox
-----------------------------------------------------

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```