Hi,
I have sort of a newbie question. I've seriously put a lot of effort into
how to handle simple replicates in a repeated ANOVA design, but haven't had
much luck.
I really liked reading "Notes on the use of R for psychology experiments
and questionnaires", by Jonathan Baron and Yuelin Li (
http://www.psych.upenn.edu/~baron/rpsych/rpsych.html ) but still didn't run
across an example using simple replicates.
So, I made up the data below semi-borrowing the idea of a reaction time
experiment involving noise from Maxwell, S. E. & Delaney, H. D. (1990)
Designing Experiments and Analyzing Data: A model comparison perspective.
Pacific Grove, CA: Brooks/Cole., which was referenced in the Baron and Li link
above.
The experimental concept I'm trying to envision is 2 groups of subjects
(Treat and Control), 3 subjects in each. In one session, all 6 patients from
both groups are tested for reaction time by making 3 replicate tests on some
hypothetical RT test (I call this the "pre" testing phase below or one
could call this baseline ). In a second session (the "post" phase),
the subjects in the "Treat" Group are subjected to noise (or any
treatment), while the other 3 "Control" subjects are not, (i.e. the
Control subjects are basically tested exactly like they were in the
"pre" testing session).
I'm trying to set up the correct model for this experimental design to
simply understand whether "noise" (or treatment) has an effect on
reaction time. Can someone tell this newbie the proper name of this
experimental design?
By setting up the design this way, I'm hoping one could see if there was a
"pre" session to "post" session effect (using the Control
group) and then take into account any possible pre->post effect when deciding
whether there was a Treatment (noise) effect.
Unfortunately, whenever, I put the Group factor in the Error term (to take into
account subj:Group as a random effect), I get a singular result: (see the data
entry section below)
> rt.aov <- aov(rt ~ Group*prepost + Error(subj/(prepost*Group)),
data=rt.df)
Warning message:
Error() model is singular in: aov(rt ~ Group * prepost +
Error(subj/(prepost * Group)), data = rt.df)
plus, I'm not sure how to include the replicate factor ("rep") in
my Error() term -- should it be something like
...+Error(subj*rep/(Group*prepost))?
(this still gives the above error if Group is in the error term, but I'm
pretty sure it should be there since all interactions given the individual
subject are random effects, aren't they?)
In my hypothetical experiment, I'm assuming the replicates are independent
samples of reaction time -- although, admittedly, there could be a trend that
should be looked for if one assumes that the subject "gets better"
with each replicate.
Suggestions on aov() model welcome!
Thanks,
Michael
-----------------------------------------------------------------
Creating the hypothetical dataset...
> data <- c(
+ 287,283,261,298,302,280,
+ 211,272,222,285,253,252,
+ 266,252,287,266,255,269,
+ 299,310,285,296,310,301,
+ 288,265,273,285,252,259,
+ 295,299,285,288,281,303)
> rt.df <- data.frame(rt=data,
+ rep = factor(rep(paste("rep",1:3, sep=""),12)),
+ prepost = factor(rep(c(rep("pre",3),rep("post",3)),6)),
+ subj =
factor(rep(paste("subj",1:6,sep=""),c(6,6,6,6,6,6))),
+ Group = factor(c(rep("Treat",18),rep("Control",18))))
> rt.df
rt rep prepost subj Group
1 287 rep1 pre subj1 Treat
2 283 rep2 pre subj1 Treat
3 261 rep3 pre subj1 Treat
4 298 rep1 post subj1 Treat
5 302 rep2 post subj1 Treat
6 280 rep3 post subj1 Treat
7 211 rep1 pre subj2 Treat
8 272 rep2 pre subj2 Treat
9 222 rep3 pre subj2 Treat
10 285 rep1 post subj2 Treat
11 253 rep2 post subj2 Treat
12 252 rep3 post subj2 Treat
13 266 rep1 pre subj3 Treat
14 252 rep2 pre subj3 Treat
15 287 rep3 pre subj3 Treat
16 266 rep1 post subj3 Treat
17 255 rep2 post subj3 Treat
18 269 rep3 post subj3 Treat
19 299 rep1 pre subj4 Control
20 310 rep2 pre subj4 Control
21 285 rep3 pre subj4 Control
22 296 rep1 post subj4 Control
23 310 rep2 post subj4 Control
24 301 rep3 post subj4 Control
25 288 rep1 pre subj5 Control
26 265 rep2 pre subj5 Control
27 273 rep3 pre subj5 Control
28 285 rep1 post subj5 Control
29 252 rep2 post subj5 Control
30 259 rep3 post subj5 Control
31 295 rep1 pre subj6 Control
32 299 rep2 pre subj6 Control
33 285 rep3 pre subj6 Control
34 288 rep1 post subj6 Control
35 281 rep2 post subj6 Control
36 303 rep3 post subj6 Control
On 4/13/07, Michael Stevens <mstevens1107 at yahoo.com> wrote:> Hi, > I have sort of a newbie question. I've seriously put a lot of effort into how to handle simple replicates in a repeated ANOVA design, but haven't had much luck. > I really liked reading "Notes on the use of R for psychology experiments and questionnaires", by Jonathan Baron and Yuelin Li ( http://www.psych.upenn.edu/~baron/rpsych/rpsych.html ) but still didn't run across an example using simple replicates. > So, I made up the data below semi-borrowing the idea of a reaction time experiment involving noise from Maxwell, S. E. & Delaney, H. D. (1990) Designing Experiments and Analyzing Data: A model comparison perspective. Pacific Grove, CA: Brooks/Cole., which was referenced in the Baron and Li link above. > > The experimental concept I'm trying to envision is 2 groups of subjects (Treat and Control), 3 subjects in each. In one session, all 6 patients from both groups are tested for reaction time by making 3 replicate tests on some hypothetical RT test (I call this the "pre" testing phase below or one could call this baseline ). In a second session (the "post" phase), the subjects in the "Treat" Group are subjected to noise (or any treatment), while the other 3 "Control" subjects are not, (i.e. the Control subjects are basically tested exactly like they were in the "pre" testing session). > > I'm trying to set up the correct model for this experimental design to simply understand whether "noise" (or treatment) has an effect on reaction time. Can someone tell this newbie the proper name of this experimental design? > > By setting up the design this way, I'm hoping one could see if there was a "pre" session to "post" session effect (using the Control group) and then take into account any possible pre->post effect when deciding whether there was a Treatment (noise) effect. > > Unfortunately, whenever, I put the Group factor in the Error term (to take into account subj:Group as a random effect), I get a singular result: (see the data entry section below) > > > rt.aov <- aov(rt ~ Group*prepost + Error(subj/(prepost*Group)), data=rt.df) > Warning message: > Error() model is singular in: aov(rt ~ Group * prepost + Error(subj/(prepost * Group)), data = rt.df) > > plus, I'm not sure how to include the replicate factor ("rep") in my Error() term -- should it be something like > ...+Error(subj*rep/(Group*prepost))? > (this still gives the above error if Group is in the error term, but I'm pretty sure it should be there since all interactions given the individual subject are random effects, aren't they?) > In my hypothetical experiment, I'm assuming the replicates are independent samples of reaction time -- although, admittedly, there could be a trend that should be looked for if one assumes that the subject "gets better" with each replicate. >[output deleted] I'm not sure if this is exactly what you want but a model with fixed effects for Group and prepost and for their interaction and with random effects for subj can be fit using the lme4 package as shown in the enclosed. (If your next question is, "Yes, but how do I get p-values?" I'll defer to others on that. It's a long story.) P.S. for Debian/Ubuntu experts. How do I set up the Mime types so that the system knows that a file with a .Rout extension is text/plain? Or is this a property of Firefox or Gmai.com? The immediate problem is that when I try to attach a file with extension .Rout to a message sent from gmail.com under Firefox off a Ubuntu system it gets encoded as a binary file and stripped by the mailing list software. I need to move it to a name ending in .txt before it gets encoded as text/plain. -------------- next part -------------- R version 2.5.0 beta (2007-04-14 r41163) Copyright (C) 2007 The R Foundation for Statistical Computing ISBN 3-900051-07-0 R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. Natural language support but running in an English locale R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R.> library(lme4)Loading required package: Matrix Loading required package: lattice> > data <- c(+ 287,283,261,298,302,280, + 211,272,222,285,253,252, + 266,252,287,266,255,269, + 299,310,285,296,310,301, + 288,265,273,285,252,259, + 295,299,285,288,281,303)> > rt.df <- data.frame(rt=data,+ rep = factor(rep(paste("rep",1:3, sep=""),12)), + prepost = factor(rep(c(rep("pre",3),rep("post",3)),6)), + subj = factor(rep(paste("subj",1:6,sep=""),c(6,6,6,6,6,6))), + Group = factor(c(rep("Treat",18),rep("Control",18))))> > fm1 <- lmer(rt ~ Group*prepost + (1|subj), rt.df) > fm1Linear mixed-effects model fit by REML Formula: rt ~ Group * prepost + (1 | subj) Data: rt.df AIC BIC logLik MLdeviance REMLdeviance 293.4 301.3 -141.7 307.6 283.4 Random effects: Groups Name Variance Std.Dev. subj (Intercept) 239.81 15.486 Residual 245.46 15.667 number of obs: 36, groups: subj, 6 Fixed effects: Estimate Std. Error t value (Intercept) 286.111 10.354 27.632 GroupTreat -12.778 14.643 -0.873 prepostpre 2.667 7.386 0.361 GroupTreat:prepostpre -15.889 10.445 -1.521 Correlation of Fixed Effects: (Intr) GrpTrt prpstp GroupTreat -0.707 prepostpre -0.357 0.252 GrpTrt:prps 0.252 -0.357 -0.707> > proc.time()user system elapsed 6.956 0.188 7.140 -------------- next part -------------- An embedded and charset-unspecified text was scrubbed... Name: Stevens_R.txt Url: https://stat.ethz.ch/pipermail/r-help/attachments/20070414/26654fa2/attachment.txt
Michael,
You have mis-specified the aov() call. It should be:
rt.aov=aov(rt~Group*rep*prepost+Error(subj/(prepost*rep)),data=rt)
yielding:
summary(rt.aov)
Error: subj
Df Sum Sq Mean Sq F value Pr(>F)
Group 1 3864.7 3864.7 2.2941 0.2044
Residuals 4 6738.6 1684.6
Error: subj:prepost
Df Sum Sq Mean Sq F value Pr(>F)
prepost 1 250.69 250.69 0.9934 0.3753
Group:prepost 1 568.03 568.03 2.2509 0.2079
Residuals 4 1009.44 252.36
Error: subj:rep
Df Sum Sq Mean Sq F value Pr(>F)
rep 2 325.50 162.75 0.4882 0.6309
Group:rep 2 74.39 37.19 0.1116 0.8958
Residuals 8 2667.11 333.39
Error: subj:prepost:rep
Df Sum Sq Mean Sq F value Pr(>F)
rep:prepost 2 463.39 231.69 0.9295 0.4336
Group:rep:prepost 2 338.72 169.36 0.6794 0.5339
Residuals 8 1994.22 249.28
On 14-Apr-07, at 4:00 AM, r-help-request at stat.math.ethz.ch wrote:
> Unfortunately, whenever, I put the Group factor in the Error term
> (to take into account subj:Group as a random effect), I get a
> singular result: (see the data entry section below)
>
>> rt.aov <- aov(rt ~ Group*prepost + Error(subj/(prepost*Group)),
>> data=rt.df)
> Warning message:
> Error() model is singular in: aov(rt ~ Group * prepost +
> Error(subj/(prepost * Group)), data = rt.df)