13.1: Error de muestreo (Sección @ref {samplingerror})

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Aquí vamos a muestrear repetidamente de la variable Altura NHANES para obtener la distribución muestral de la media.

sampSize <- 50 # size of sample
nsamps <- 5000 # number of samples we will take

# set up variable to store all of the results
sampMeans <- tibble(meanHeight=rep(NA,nsamps))

# Loop through and repeatedly sample and compute the mean
for (i in 1:nsamps) {
  sampMeans$meanHeight[i] <- NHANES_adult %>%
    sample_n(sampSize) %>%
    summarize(meanHeight=mean(Height)) %>%
    pull(meanHeight)
}

Ahora vamos a trazar la distribución de muestreo. También se sobrepondremos la distribución muestral de la media predicha sobre la base de la media poblacional y la desviación estándar, para mostrar que describe adecuadamente la distribución muestral real.

# pipe the sampMeans data frame into ggplot
sampMeans %>% 
  ggplot(aes(meanHeight)) +
  # create histogram using density rather than count
  geom_histogram(
    aes(y = ..density..),
    bins = 50,
    col = "gray", 
    fill = "gray"
  ) +
  # add a vertical line for the population mean
  geom_vline(xintercept = mean(NHANES_adult$Height),
             size=1.5) +
  # add a label for the line
  annotate(
    "text",
    x = 169.6, 
    y = .4,
    label = "Population mean",
    size=6
  ) +
  # label the x axis
  labs(x = "Height (inches)") +
  # add normal based on population mean/sd
  stat_function(
      fun = dnorm, n = sampSize,
      args = list(
        mean = mean(NHANES_adult$Height),
        sd = sd(NHANES_adult$Height)/sqrt(sampSize)
      ), 
      size = 1.5,
      color = "black",
      linetype='dotted'
    )