How to Shade Under a Normal Density in R

The easiest-to-find method for shading under a normal density is to use the polygon() command. That link is to the first hit on Google for "Shading Under a Normal Curve in R." It works (like a charm), but it is not the most intuitive way to let users produce plots of normal densities.

In response to the standard polygon() approach, I wrote a function called shadenorm() that will produce a plot of a normal density with whatever area you want shaded. The code is available here (in a newer post; I updated the function slightly).

Copy into an R script and run all of it if you want to use the shadenorm() command. To show you how to use it, I also recorded a video tutorial in R to demonstrate how to use the shadenorm() command.




Here is the code I use in the video:

	## ---------------------- ##
	## Shading under a Normal ##
	## in R ##
	## ---------------------- ##
	shadenorm() ## Defaults mu = 0, sig = 1, pcts = c(0.025, 0.975)
	## Below, Above, Outside and Between
	shadenorm(below=-1.5) ## Sets lower endpoint at -1.5
	shadenorm(below=-1.5,justbelow=TRUE) ## Just plots the lower tail
	shadenorm(above=1.5) ## Sets upper endpoint at 1.5
	shadenorm(above=1.5, justabove=TRUE) ## Similar to below
	shadenorm(below=-1.5,above=1.5) ## Plots "outside" of -1.5 and 1.5
	shadenorm(outside = c(2.5, -2.5)) ## Alternative "outside" plotter
	shadenorm(outside = c(1, 2, -1, -0.2, 2.4)) ## works by taking min and max
	shadenorm(between = c(2.5, -2.5)) ## Plots between specified points
	shadenorm(between = c(-1.75, 0, 2, 0.5, -1)) ## Plots between specified points
	## Can specify different means and standard deviations with mu and sig arguments
	shadenorm(mu=2, sig=10)
	shadenorm(mu=2, sig=10, between=c(-2, 14)) ## works with between and outside
	shadenorm(mu=2, sig=10, outside=c(-5, 14))
	## Can Apply different colors and densities... color and dens
	shadenorm(mu=2, sig=10, outside=c(-3, 12), col="blue")
	shadenorm(mu=2, sig=10, outside=c(-3, 12), col="blue",dens=15) ## Dens default is 40
	shadenorm(mu=2, sig=10, outside=c(-3, 12), col="blue",dens=150)
	## Can plot one and then another ontop of it using lines = TRUE
	shadenorm(mu=2, sig=10, outside=c(-3, 12), dens=15)
	shadenorm(mu=2, sig=15, between=c(-3, 12),lines=TRUE, col="blue",dens=15)
	## Example: Plotting a Hypothesis Test for the mean
	## Truth: mu.true = 8
	## Hypothesis: mu.ho = 6
	## Generate Data Under Truth
	mu.true = 5 ## Alternative Mean
	mu.ho = 6
	sig = 8
	N = 250 ## Sample Size
	std.err = sig/sqrt(N)
	crits = qnorm(c(0.025,0.975),mean=mu.ho, sd = std.err)
	shadenorm(outside = crits, mu = mu.ho, sig = std.err,dens=15)
	shadenorm(between = crits, mu = mu.true, sig = std.err, lines=TRUE, color="green",dens=15)

view raw IntroducingShadenorm.R hosted with ❤ by GitHub

There are a lot of applications where you may want to produce a plot with a normal density with some region shaded. I hope you find this function useful.