Type I and type II errors

nr_of_trials <- 100

calc_p <- Vectorize(
  function(effect_size, n) {
    y1 <- rnorm(n)
    y2 <- rnorm(n, effect_size)
    t.test(y1, y2)$p.value
  }
)

calc_p(1, 10)

[1] 0.01657786

dat <- tibble(effect_size = c(rep(0, nr_of_trials), rexp(nr_of_trials)),
              effect_present = rep(c('No', 'Yes'), each = nr_of_trials),
              n = 10,
              p = calc_p(effect_size, nr_of_trials))


plot(sort(dat$p))

dat |> 
  ggplot(aes(effect_size, p, colour = effect_present)) + 
  geom_point() +
  geom_smooth()

`geom_smooth()` using method = 'loess' and formula = 'y ~ x'