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17.2: Simulating p-values

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  • In this exercise we will perform hypothesis testing many times in order to test whether the p-values provided by our statistical test are valid. We will sample data from a normal distribution with a mean of zero, and for each sample perform a t-test to determine whether the mean is different from zero. We will then count how often we reject the null hypothesis; since we know that the true mean is zero, these are by definition Type I errors.

    nRuns <- 5000
    # create input data frame for do()
    input_df <- tibble(id=seq(nRuns)) %>%
    # create a function that will take a sample
    # and perform a one-sample t-test
    sample_ttest <- function(sampSize=32){
      tt.result <- t.test(rnorm(sampSize))
    # perform simulations
    sample_ttest_result <- input_df %>%
    p_error <-
      sample_ttest_result %>%
      ungroup() %>%
      summarize(p_error = mean(pvalue<.05)) %>%
    ## [1] 0.048

    We should see that the proportion of samples with p<.05p < .05 is about 5%.

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