11.4 Simulating one-factor ANOVAs

The following builds simulated data for a one-factor ANOVA, appropriate for a between subjects design. We build the data frame containg a column for the group factor levels, and a column for the DV. Then, we run the ANOVA an print it out.

N <- 10
groups <- rep(c("A","B","C"), each=10)
DV <- c(rnorm(100,10,15),   # means for group A
        rnorm(100,10,15),   # means for group B
        rnorm(100,20,15)    # means for group C
        )
sim_df<-data.frame(groups,DV)

aov_results <- summary(aov(DV~groups, sim_df))

library(xtable)
knitr::kable(xtable(aov_results))

In this next example, we simulate the same design 100 times, save the $p$-values, and the determine the proportion of significant simulations.

N <- 10

save_p<-length(100)
for(i in 1:100){
  groups <- rep(c("A","B","C"), each=10)
  DV <- c(rnorm(100,10,15),   # means for group A
          rnorm(100,10,15),   # means for group B
          rnorm(100,20,15)    # means for group C
          )
  sim_df<-data.frame(groups,DV)
  
  aov_results <- summary(aov(DV~groups, sim_df))
  save_p[i]<-aov_results[[1]]$`Pr(>F)`[1]
}

length(save_p[save_p<0.05])/100

[1] 0.08

Adapted from Answering Questions with Data: Introductory Statistics for Psychology Students, by Matthew J. C. Crump (Brooklyn College of CUNY), crumplab.com/statistics, licensed under CC BY-SA 4.0. Portions adapt Danielle Navarro's Learning Statistics with R (CC BY-SA). Changes were made; this adaptation is distributed under the same license. License: CC-BY-SA-4.0.