# [R] Multiple tests on 2 way-ANOVA

From: Grathwohl, Dominik, LAUSANNE, NRC-BAS <dominik.grathwohl_at_rdls.nestle.com>
Date: Wed 12 Jul 2006 - 00:52:15 EST

I have a question about multiple testing. Here an example that puzzles me:
All matrixes and contrast vectors are presented in treatment contrasts.

1. example: library(multcomp) n<-60; sigma<-20
# n = sample size per group
# sigma standard deviation of the residuals

cov1 <- matrix(c(3/4,-1/2,-1/2,-1/2,1,0,-1/2,0,1), nrow = 3, ncol=3, byrow=TRUE,

dimnames = list(c("A", "B", "C"), c("C.1", "C.2", "C.3")))
# cov1 = variance covariance matrix of the beta coefficients of a
# 2x2 factorial design (see Piantadosi 2005, p. 509)

cm1 <- matrix(c(0, 1, 0, 0, 0, 1), nrow = 2, ncol=3, byrow=TRUE,

dimnames = list(c("A", "B"), c("C.1", "C.2", "C.3")))
# cm1 = contrast matrix for main effects

v1 <- csimint(estpar=c(100, 6, 5), df=4*n-3, covm=cov1*sigma^2/n, cmatrix=cm1, conf.level=0.95) summary(v1)

The adjusted p-values are almost the Bonferroni p-values. If I understood right: You need not to adjust for multiple testing on main effects in a 2x2 factorial design assuming the absence of interaction.
I do not think that there is a bug,
I want to understand, why multcomp does adjust for multiple tests having all information about the design of the trial (variance covariance matrix)? Or do I have to introduce somehow more information?

2. example:
And I have second question: How do I proper correct for multiple testing if I want to estimate in the presence of interaction the two average main effects. Can some one point me to some literature where I can learn these things? Here the example, 2x2 factorial with interaction, estimation of average main effects:

cov2 <- matrix(

```c(1,-1,-1, 1,
-1, 2, 1,-2,
-1, 1, 2,-2,
1,-2,-2, 4)
```

, nrow=4, ncol=4, byrow=TRUE)
cm2 <- matrix(c(0, 1, 0, 1/2, 0, 0, 1, 1/2), nrow = 2, ncol=4, byrow=TRUE,

dimnames = list(c("A", "B"), c("C.1", "C.2", "C.3", "C.4"))) v2 <- csimint(estpar=c(100, 6, 5, 2), df=4*n-4, covm=cov2*sigma^2/n, cmatrix=cm2, conf.level=0.95) summary(v2)

platform i386-pc-mingw32

```arch     i386
os       mingw32
system   i386, mingw32
status
major    2
minor    2.1
year     2005
month    12
day      20
svn rev  36812
```

language R

R-help@stat.math.ethz.ch mailing list