Illustrate mean and standard deviation in ggplot2 density plot

Question

I'm trying to construct a plot where I plot normally distributed variables showing their mean on the x-axis and the standard deviation (SD) on the y-axis. Kinda like a density plot, but instead of having the density on the y-axis I want to have the SD (value).

I'm working with the data below,

set.seed(1)
mu1 <- rnorm(10^5, mean = 1, sd = 1)
mu3 <- rnorm(10^5, mean = 3, sd = 2)

two normally distributed variables. Here their mean and sd,

# install.packages("tidyverse", dependencies = TRUE)
require(tidyverse)
tibble(mu1, mu3) %>% summarise_all(funs(mean, sd))
#> # A tibble: 1 x 4
#>    mu1_mean mu3_mean    mu1_sd   mu3_sd
#>       <dbl>    <dbl>     <dbl>    <dbl>
#> 1 0.9993454 3.000825 0.9982848 1.998234

I've played around with ggplot2, and other tidyverse packages, to get closer to what I want. I've also tried copying this function from a box-plot doing something similar, having succeeded yet.

Here is my start,

tibble(mu1, mu3) %>% gather() %>% ggplot() + 
  geom_density(aes(x = value, colour = key)) + 
  labs(x = 'mean', y = 'currently density, but I would like sd')

Do you have an example of the plot you have in mind? (Could be a drawing). What message should your plot convey? — Heroka
I more or less want what's in the plot you see, but I want the standard deviation on the y-axis instead of the density. Does that make sense? — Eric Fail
Not really to me, as the sd is only one number. It doesn't vary along the distribution (as the density does). — Heroka
You are plotting the density (which is what geom_density() is for) and neither the x- nor the y-axis show the mean or the standard deviation. The boxplot from the example you linked is actually conveying a similar message as the density plot, but in a different way. It, too, does not have mean of standard deviation as one of its axes. I really don't understand your question... — Stibu

eipi10 eipi10 · Accepted Answer · 2016-02-06T20:21:18

The mean and standard deviation are measured on the x-scale, so you'd need to plot them along the x-axis. The y-axis is the density of points within a given x-interval, and is analogous to the height of the bars in a histogram.

Maybe this will give you something like what you were looking for: The code below adds a horizontal line that spans the standard deviation of each density plot, along with droplines to mark their location on the x-axis. The sd line is located at y-value where the width of the distribution is equal to the standard deviation. If you wish, you could in addition (or instead) fill the region spanned by the standard deviation.

library(dplyr)

# Densities
n = 2^10
df = data.frame(x = c(density(foo,n=n)$x, density(bar,n=n)$x),
                y = c(density(foo,n=n)$y, density(bar,n=n)$y),
                group=rep(c("foo","bar"), each=n))

## Mean and SD
msd =  melt(data.frame(foo=foo, bar=bar)) %>% 
         group_by(group=variable) %>% summarise(mean=mean(value), sd=sd(value))

# Find y value (of density) where sd has same width as density
msd$y = unlist(lapply(unique(df$group), function(g) {
  d = df[df$group==g,]
  d$y[which.min(abs(d$x - (msd$mean[msd$group==g] - msd$sd[msd$group==g])))]
}))

ggplot(df, aes(x=x, y=y, colour=group)) + 
  geom_line() + labs(x = NULL) +
  geom_segment(data=msd, aes(y=y,yend=y, x=mean - sd, xend=mean + sd), lty="21") +
  geom_point(data=msd, aes(y=y, x=mean)) +
  geom_segment(data=msd, aes(x=mean-sd, xend=mean-sd, y=0, yend=y), alpha=0.5, lty="21") +
  geom_segment(data=msd, aes(x=mean+sd, xend=mean+sd, y=0, yend=y), alpha=0.5, lty="21")

Illustrate mean and standard deviation in ggplot2 density plot

1 Answers