# [R] how to calculate interaction contrast

szhan at uoguelph.ca szhan at uoguelph.ca
Tue Jul 3 20:45:56 CEST 2007

```Hello, R experts,
Sorry for asking this question again since I really want a help!

I have a two-factor experiment data and like to calculate estimates of
interation contrasts say factor A has levels of a1, a2, and B has
levels of b1, b2, b3, b4, and b5 with 3 replicates. I am not sure the
constrast estimate I got is right using the script below:

score<-c(7.2,6.5,6.9,6.4,6.9,6.1,6.9,5.3,7.2,5.7,5.1,5.9,7.6,6.9,6.8,
7.2,6.6,6.9,6.4,6.0,6.0,6.9,6.9,6.4,7.5,7.7,7.0,8.6,8.8,8.3)

A <- gl(2, 15, labels=c("a1", "a2"))
B <- rep(gl(5, 3, labels=c("b1", "b2", "b3", "b4", "b5")), 2)

contrasts(B)<-cbind(c(-4,rep(1,4)),c(rep(-3,2),rep(2,3)),
+  c(rep(-2,3),rep(3,2)),c(rep(-1,4), rep(4,1)))
fit1 <- aov(score ~ A*B)
summary(fit1, split=list(B=1:4), expand.split = TRUE)
Df Sum Sq Mean Sq F value    Pr(>F)
A            1 3.2013  3.2013 15.1483 0.0009054 ***
B            4 8.7780  2.1945 10.3841 0.0001019 ***
B: C1      1 0.0301  0.0301  0.1424 0.7099296
B: C2      1 2.0335  2.0335  9.6221 0.0056199 **
B: C3      1 1.2469  1.2469  5.9004 0.0246876 *
B: C4      1 5.4675  5.4675 25.8715 5.637e-05 ***
A:B          4 5.3420  1.3355  6.3194 0.0018616 **
A:B: C1    1 0.7207  0.7207  3.4105 0.0796342 .
A:B: C2    1 2.6068  2.6068 12.3350 0.0021927 **
A:B: C3    1 1.9136  1.9136  9.0549 0.0069317 **
A:B: C4    1 0.1008  0.1008  0.4771 0.4976647
Residuals   20 4.2267  0.2113
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Now I like to get interaction contrast estimate for b1 and b2 vs b3, b4 and b5
cont <- c(1, -1)[A] * c(-3, -3, 2, 2, 2)[B]

estimat<-sum(cont*score) # value of the contrast estimate for A:B C2

> estimat
[1] -24.1

I am not sure the estimate for A:B C2 contrast  (-24.1) is correct
because the F value given the output above(12.3350) does not equal to
those I calculate below (15.2684):

t.stat <- sum(cont*score)/se.contrast(fit1, as.matrix(cont))
> t.stat^2
Contrast 1
15.2684

interaction contrast and corresponding F value?
Joshua

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