Hello everyone,
I am trying to run a repeated measures Anova in R followed by some specific
contrasts on that dataset. So far I think the correct approach would be to use
Anova() from the car package.
Â
Lets illustrate my question with the example taken from ?Anova using the
OBrienKaiser data:
We have a design with 2 between subjects factor, treatment (3 levels: control,
A, B) and gender (M vs. F), and 2 repeated-measures (within subjects) factors,
phase (3 levels: pretest, posttest, followup) and hour (5 levels: 1 to 5).
The standard ANOVA table is given by (in difference to example(Anova) I switched
to Type 3 Sums of Squares, that is what my field wants):
require(car)
phase <- factor(rep(c("pretest", "posttest", "followup"), c(5, 5, 5)),
levels=c("pretest", "posttest", "followup"))
hour <- ordered(rep(1:5, 3))
idata <- data.frame(phase, hour)
mod.ok <- lm(cbind(pre.1, pre.2, pre.3, pre.4, pre.5, post.1, post.2, post.3,
post.4, post.5, fup.1, fup.2, fup.3, fup.4, fup.5) ~Â treatment*gender,
data=OBrienKaiser)
av.ok <- Anova(mod.ok, idata=idata, idesign=~phase*hour, type = 3)
summary(av.ok, multivariate=FALSE)
Now, imagine that the highest order interaction would have been significant
(which is not the case) and we would like to explore it further with the
following contrasts:
Is there a difference between hours 1&2 versus hours 3 (contrast 1) and between
hours 1&2 versus hours 4&5 (contrast 2) in the treamtment conditions (A&B
together)? In other words, how do I specify these contrasts: 1. ((treatment %in%
c("A", "B")) & (hour %in% 1:2)) versus ((treatment %in% c("A", "B")) & (hour
%in% 3))
2. ((treatment %in% c("A", "B")) & (hour %in% 1:2)) versus ((treatment %in%
c("A", "B")) & (hour %in% 4:5))
My idea would be to run another ANOVA ommitting the non-needed treatment
condition (control). However, I still have no idea how to set up the appropriate
within-subject contrast matrix comparing hours 1&2 with 3 and 4&5, respectively.
And I am not sure if ommitting the non-needed treatment group is indeed a good
idea as it changes the overall errorterm.
Before going for Anova() I was also thinking going for lme. However, there are
small differences in F and p values between textbook ANOVA and what is returned
from anove(lme) (see my question here:
http://stats.stackexchange.com/q/14088/442). I also tried using Anova() with lme
objects, but Anova() seems to only returns Chi² values for lme objects. So I
ended up giving all my hope in John Fox and Anova().
I hope this question on contrsats is okay. I tried to understand Venables &
Ripley on model matrices (chapter 6.2, pp. 144, 4th ed.) but this did not help
me at all.
Thanks in advance,
Henrik
--
Dipl. Psych. Henrik Singmann
PhD Student
Institute of Psychology
Albert-Ludwigs-Universität Freiburg
http://www.psychologie.uni-freiburg.de/Members/singmann
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