Explore the distribution of p-values

pvalues.Rmd

---
title: "On the distribution of p-values"
output: html_notebook
---

```{r}
sample.sizes <- seq(5, 100, 10)
num.trials <- 1000
num.experiments <- 1
null.mu <- 0.0
alternative.mu <- 0.1
sig.level <- 0.05
p.values <- array(data=NA, dim=num.trials)
for (n in sample.sizes) {
  for (i in 1:num.trials) {
    p.values.all.experiments <- array(data=NA, dim=num.experiments)
    for (j in 1:num.experiments) {
      x <- rnorm(n, mean=alternative.mu)
      p.values.all.experiments[j] <- t.test(
        x, alternative = "greater", var.equal=TRUE
      )$p.value
    }
    p.values[i] <- min(p.values.all.experiments)
  }
  mc.prob.reject <- mean(p.values < sig.level)
  power.results <- power.t.test(
    n = n,
    delta = alternative.mu - null.mu,
    sig.level = sig.level,
    type = "one.sample",
    alternative = "one.sided"
  )
  title <- paste(
    "Min. p-values for sample size =", n, "over", num.experiments, "experiments",
    "\nPower =", power.results$power, "; MC prob. reject =", mc.prob.reject
  )
  hist(p.values, main=title)
```