Visualizing Sampling Distributions in ggplot2: Adding area under the curve

Thank you ggplot2tutor for solving one of my struggles. Apparently this is all it takes:

ggplot(NULL, aes(x = c(-3, 3))) +
  stat_function(fun = dnorm, geom = "line")

I can’t begin to count how often I have wanted to visualize a (normal) distribution in a plot. For instance to show how my sample differs from expectations, or to highlight the skewness of the scores on a particular variable. I wish I’d known earlier that I could just add one simple geom to my ggplot!

Want a different mean and standard deviation, just add a list to the args argument:

ggplot(NULL, aes(x = c(0, 20))) +
  stat_function(fun = dnorm,
                geom = "area",
                args = list(
                  mean = 10,
                  sd = 3
                ))

Need a different distribution? Just pass a different distribution function to stat_function. For instance, an F-distribution, with the df function:

ggplot(NULL, aes(x = c(0, 5))) +
  stat_function(fun = df,
                geom = "area",
                args = list(
                  df1 = 2,
                  df2 = 10
                ))

You can make it is complex as you want. The original ggplot2tutor blog provides this example:

ggplot(NULL, aes(x = c(-3, 5))) +
  stat_function(
    fun = dnorm,
    geom = "area",
    fill = "steelblue",
    alpha = .3
  ) +
  stat_function(
    fun = dnorm,
    geom = "area",
    fill = "steelblue",
    xlim = c(qnorm(.95), 4)
  ) +
  stat_function(
    fun = dnorm,
    geom = "line",
    linetype = 2,
    fill = "steelblue",
    alpha = .5,
    args = list(
      mean = 2
    )
  ) +
  labs(
    title = "Type I Error",
    x = "z-score",
    y = "Density"
  ) +
  scale_x_continuous(limits = c(-3, 5))