100000 samples with N=20 and no difference in population sampled from

gistfile1.txt

library(tidyverse)

df <- NULL
set.seed(1111)
sample_size = 20

for (i in 1:100000) {
  a <- rnorm(sample_size, mean = 10, sd = 2)
  b <- rnorm(sample_size, mean = 10, sd = 2)
  a <- cbind(a, rep ("A", sample_size), rep (i, sample_size))
  b <- cbind(b, rep("B", sample_size), rep (i, sample_size))
  df <- as.tibble(rbind(df, (rbind(a, b))))
}

colnames(df) <- c("Score","Condition", "Sample")
df$Score <- as.numeric(df$Score)

data <- NULL
for (i in 1:100000) {
  toa <- as.tibble(cbind(filter(df, Sample==i & Condition=="A")$Score, 
                         filter(df, Sample==i & Condition=="B")$Score))
  data <- rbind(data, tidy(t.test(toa$V1, toa$V2)))
}

ggplot(data, aes(x = p.value)) + geom_histogram()