17.2: Simulación de valores p

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En este ejercicio realizaremos pruebas de hipótesis muchas veces para comprobar si los valores p proporcionados por nuestra prueba estadística son válidos. Muestrearemos datos de una distribución normal con una media de cero, y para cada muestra realizaremos una prueba t para determinar si la media es diferente de cero. Luego contaremos la frecuencia con la que rechazamos la hipótesis nula; ya que sabemos que la verdadera media es cero, estos son por definición errores de Tipo I.

nRuns <- 5000

# create input data frame for do()
input_df <- tibble(id=seq(nRuns)) %>%
  group_by(id)

# 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))
  return(tibble(pvalue=tt.result$p.value))
}

# perform simulations

sample_ttest_result <- input_df %>%
  do(sample_ttest())

p_error <-
  sample_ttest_result %>%
  ungroup() %>%
  summarize(p_error = mean(pvalue<.05)) %>%
  pull()

p_error

## [1] 0.048

Deberíamos ver que la proporción de muestras con $p$ es de aproximadamente 5%.

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