P value simulations

null_true_p <- function(n) {
  null <- c(runif(n))
  result <- quantile(null, probs = c(0.00, 0.025, 0.05, 0.25, 0.50, 0.75, 0.95, 0.975, 1) )
  hist(null)
  result
}

null_false_p <- function(sample, sim_size) {
  reject <- numeric(sim_size)
    for (i in 1:sim_size) {
      x <- rnorm(sample, 100, 15)
      y <- rnorm(sample, 108, 15)
      reject[i] <- t.test(x,y,alternative="greater")$p.value
      result <- quantile(reject, probs = c(0.00, 0.025, 0.05, 0.25, 0.50, 0.75, 0.95, 0.975, 1))
     }
    hist(reject)
    result
}

true_null_meta <- function(sample, sim_size ) {
  stouffer <- numeric(sim_size)
  for (i in 1:sim_size) {
    null <- runif(sample)
    z_score <- c(qnorm(null))
    stouffer[i] <- sum( z_score/sqrt(sample) )
    result <- quantile(stouffer, probs = c(0.00, 0.025, 0.05, 0.25, 0.50, 0.75, 0.95, 0.975, 1))
  }
  hist(stouffer)
  result
}

false_null_meta <- function(sample, sim_size) {
  z_scores <- numeric(sample)
  p_vals   <- numeric(sample)
  stouffer <- numeric(sim_size)
  for (i in 1:sim_size) {
    x <- rnorm(sample, 100, 15)
    y <- rnorm(sample, 108, 15)
    p_vals[i]   <- t.test(x,y, alternative = "greater")$p.value
    z_scores[i] <- c(qnorm(p_vals[i]))
    stouffer[i] <- sum( z_scores / sqrt(sample) )
    result_z    <- quantile(z_scores, probs = c(0.00, 0.025, 0.05, 0.25, 0.50, 0.75, 0.95, 0.975, 1))
  }
   hist(stouffer)
   print(result_z)
   result_s
}