In celiaflorea/statslab2022:

knitr::opts_chunk$set(echo = TRUE)

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library(tidyverse)

df <- data.frame (A= c("A1", "A1", "A2", "A2"), 
                 B = c(1, 2, 1, 2), 
                 dv = c(0, 0, 0.5, 0.25))


ggplot(df, aes(y=dv, x=B, fill = A))  + 
  geom_bar(stat = "identity", position = "dodge")+
  geom_point()+
  geom_line()

N <- 550



A_pvalue <- c()
B_pvalue <- c()
AB_pvalue <- c()
for(i in 1:1000){
  IVA <- rep(rep(c("1","2"), each=2),N)
  IVB <- rep(rep(c("1","2"), 2),N)
  DV <- c(replicate(N,c(rnorm(1,0,1), # means A1B1
                        rnorm(1,0,1), # means A1B2
                        rnorm(1,.5,1), # means A2B1
                        rnorm(1,.25,1)  # means A2B2
          )))
  sim_df <- data.frame(IVA,IVB,DV)

  aov_results <- summary(aov(DV~IVA*IVB, sim_df))
  A_pvalue[i]<-aov_results[[1]]$`Pr(>F)`[1]
  B_pvalue[i]<-aov_results[[1]]$`Pr(>F)`[2]
  AB_pvalue[i]<-aov_results[[1]]$`Pr(>F)`[3]
}

length(A_pvalue[A_pvalue<0.05])/1000
#> [1] 0.88
length(B_pvalue[B_pvalue<0.05])/1000
#> [1] 0.036
length(AB_pvalue[AB_pvalue<0.05])/1000
#> [1] 0.046