Simulate multiple comparisons to show that an adjustment is needed

multiple comparison simulation.R

COUNT = 100000

# How often does a single t-test of random data yield p<0.05?
replicate(COUNT, 
  t.test(rnorm(20))$p.value < 0.05
) %>% mean()

#> 0.05073
# 5% false positive rate


# How often will at least one of 10 t-tests of random data yield p<0.05?
replicate(COUNT, 
  replicate(10,
    t.test(rnorm(20))$p.value < 0.05
  ) %>% any()
) %>% mean()

#> 0.4017
# 40% false positive rate