In this post I show some R-examples on how to perform power analyses for mixed-design ANOVAs. The first example is analytical — adapted from formulas used in G*Power (Faul et al., 2007), and the second example is a Monte Carlo simulation. The source code is embedded at the end of this post.
Both functions require a dataframe, containing the parameters that will be used in the power calculations. Here is an example using three groups and three time-points.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | # design -------# mus
CT <- c(34.12,21,17.44)
BA <- c(36.88,16.82,8.75)
ADM <- c(35.61,14.39,7.78)
study <- data.frame("group"= gl(3,3, labels=c("CT","BA","ADM")))
study$time <- gl(3,1,9, labels=c("Intake","8 weeks","16 weeks"))
study$DV <- c(CT, BA, ADM)
study$SD <-10
ggplot(study, aes(time, DV, group=group, linetype=group, shape=group))+
geom_line()+
geom_point() |
Here is a plot of our hypothetical study design.
Now, we will use this design to perform a power analysis usinganova.pwr.mixed and anova.pwr.mixed.sim.
1 2 3 | # analytical ----------
anova.pwr.mixed(data = study, Formula ="DV ~ time*group",
n=10, m=3, rho=0.5) |
1 2 3 4 | Terms power n.needed b group 0.197 NA w1 time 1.000 NA w2 time:group 0.617 NA |
1 2 3 | # monte carlo ------------
anova.pwr.mixed.sim(data=study, Formula="DV ~ time*group + Error(subjects)",
FactorA="group", n=10, rho=0.5, sims=100) |
1 2 3 4 | terms power 1 group 0.19 2 time 1.00 3 time:group 0.64 |
Comparison of analytical and monte carlo power analysis
Now let's compare the two functions' results on the time x group-interaction. Hopefully, the two methods will yield the same result.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | # compare
samples <- seq(10,50,3)# n's to use
analytical <- matrix(ncol=2, nrow=length(samples))
colnames(analytical)<- c("power","n")for(i in samples){
j <- which(samples == i)
analytical[j,1]<- anova.pwr.mixed(data = study, Formula ="DV ~ time*group", n=i, m=3, rho=0.5)$power[3]
analytical[j,2]<- i}
MC <- matrix(ncol=2, nrow=length(samples))
colnames(MC)<- c("power","n")for(i in samples){
j <- which(samples == i)
MC[j,1]<- anova.pwr.mixed.sim(data=study, Formula="DV ~ time*group + Error(subjects)", FactorA="group", n=i, rho=0.5, sims=500)$power[3]
MC[j,2]<- i}# plot
MC <- data.frame(MC)
MC$method <-"MC"
analytical <- data.frame(analytical)
analytical$method <-"analytical"
df <- rbind(analytical, MC)
ggplot(df, aes(n, power, group=method, color=method))+ geom_smooth(se=F)+ geom_point() |
Luckily, the analytical results are consistent with the Monte Carlo
results.
References
Faul, F., Erdfelder, E., Lang, A. G., & Buchner, A. (2007). G* Power 3: A flexible statistical power analysis program for the social, behavioral, and biomedical sciences.Behavior research methods, 39(2), 175-191.