How many p-values just under threshold.R

# simulate true effect sizes vs p in 0.01-0.05 range
library(tidyverse)

SUBJECT_COUNT = 16
TEST_COUNT = 16

# test if the p-value is in the specified range
inRange = function(p) {
  (p > 0.01) & (p < 0.05)
}

# simulate one t-test
simulate_one = function(d) {
  a = rnorm(SUBJECT_COUNT, 0)
  b = rnorm(SUBJECT_COUNT, 0 + d)
  t.test(a, b)$p.value
}

# simulate multiple t-tests
simulate_many = function(d) {
  replicate(TEST_COUNT, simulate_one(d)) %>% inRange() %>% sum()
}

# run the simulation for a few cohen's d values
simulation_data = expand_grid(
  d = c(0, 0.25, 0.5, 0.75, 1, 1.25),
  rep_index = 1:10000,
  ps_in_range = NA
) %>% 
  rowwise() %>% 
  mutate(ps_in_range = simulate_many(d))

#plot it
ggplot(simulation_data %>% mutate(d_label = paste("Cohen's d = ", d))) +
  aes(x = ps_in_range, fill = d) +
  geom_vline(xintercept = 9, color="red") +
  geom_histogram(binwidth = 1) +
  scale_x_continuous(expand = c(0,0), breaks = 0:16) + expand_limits(x=16) +
  facet_wrap(d_label ~ ., ncol = 1, strip.position = "top") +
  theme_light(18) + theme(panel.grid.major = element_blank(), panel.grid.minor.y = element_blank()) +
  guides(fill = "none") +
  labs(title = "How many simulated t-tests have 0.01 < p < 0.05?",
       subtitle = "16 t-tests simulated 10k times for each Cohen's d",
       x = NULL, y = NULL)