repeated measures ANOVA
Christian,
You need, first to factor() your factors in the data frame P.PA,
and then denote the error-terms in aov correctly, as follows:
> group <- rep(rep(1:2, c(5,5)), 3)
> time <- rep(1:3, rep(10,3))
> subject <- rep(1:10, 3)
> p.pa <- c(92, 44, 49, 52, 41, 34, 32, 65, 47, 58, 94, 82, 48, 60, 47,
+ 46, 41, 73, 60, 69, 95, 53, 44, 66, 62, 46, 53, 73, 84, 79)
> P.PA <- data.frame(subject, group, time, p.pa)
> # added code:
> P.PA$group=factor(P.PA$group)
> P.PA$time=factor(P.PA$time)
> P.PA$subject=factor(P.PA$subject)
> summary(aov(p.pa~group*time+Error(subject/time),data=P.PA))
Error: subject
Df Sum Sq Mean Sq F value Pr(>F)
group 1 158.7 158.7 0.1931 0.672
Residuals 8 6576.3 822.0
Error: subject:time
Df Sum Sq Mean Sq F value Pr(>F)
time 2 1078.07 539.03 7.6233 0.004726 **
group:time 2 216.60 108.30 1.5316 0.246251
Residuals 16 1131.33 70.71
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
On 28-Feb-06, at 4:00 AM, r-help-request at stat.math.ethz.ch wrote:
Dear list members: I have the following data: group <- rep(rep(1:2, c(5,5)), 3) time <- rep(1:3, rep(10,3)) subject <- rep(1:10, 3) p.pa <- c(92, 44, 49, 52, 41, 34, 32, 65, 47, 58, 94, 82, 48, 60, 47, 46, 41, 73, 60, 69, 95, 53, 44, 66, 62, 46, 53, 73, 84, 79) P.PA <- data.frame(subject, group, time, p.pa) The ten subjects were randomly assigned to one of two groups and measured three times. (The treatment changes after the second time point.) Now I am trying to find out the most adequate way for an analysis of main effects and interaction. Most social scientists would call this analysis a repeated measures ANOVA, but I understand that mixed- effects model is a more generic term for the same analysis. I did the analysis in four ways (one in SPSS, three in R): 1. In SPSS I used "general linear model, repeated measures", defining a "within-subject factor" for the three different time points. (The data frame is structured differently in SPSS so that there is one line for each subject, and each time point is a separate variable.) Time was significant. 2. Analogous to what is recommended in the first chapter of Pinheiro & Bates' "Mixed-Effects Models" book, I used library(nlme) summary(lme ( p.pa ~ time * group, random = ~ 1 | subject)) Here, time was NOT significant. This was surprising not only in comparison with the result in SPSS, but also when looking at the graph: interaction.plot(time, group, p.pa) 3. I then tried a code for the lme4 package, as described by Douglas Bates in RNews 5(1), 2005 (p. 27-30). The result was the same as in 2. library(lme4) summary(lmer ( p.pa ~ time * group + (time*group | subject), P.PA )) 4. The I also tried what Jonathan Baron suggests in his "Notes on the use of R for psychology experiments and questionnaires" (on CRAN): summary( aov ( p.pa ~ time * group + Error(subject/(time * group)) ) ) This gives me yet another result. So I am confused. Which one should I use? Thanks Christian
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