Simulating one-factor ANOVAs

Section 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 containing a column for the group factor levels, and a column for the DV. Then, we run the ANOVA and print it out.

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Remark 11.4.1. R Code.

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))

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Table 11.4.2. Simulated One-Factor ANOVA Results

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	Df	Sum Sq	Mean Sq	F value	Pr(>F)
groups	2	111.2747	55.63735	0.1989719	0.8196821
Residuals	297	83048.3738	279.62415	NA	NA

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

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Remark 11.4.3. R Code.

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

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