R Normalize then plot two histograms together in R

Question

I realize there have been several posts for people asking how to plot two histograms together side by side (as in one plot with the bars next to each other) and overlaid in R and also on how to normalize data. Following the advice that I've found, I'm able to do one or the other, but not both operations.

Here's the setup. I have two data frames of different lengths and would like to plot the volume of the objects in each df as a histogram. Eg how many in data frame 1 are between .1-.2 um^3 and compare it with how many in data frame 2 are between .1 and .2 um^3 and so on. Overlaid or Side by Side would be great to do this.

Since there are more measurements in one data frame than the other, obviously I have to normalize, so I use:

read.csv(ctl)
read.csv(exp)
h1=hist(ctl$Volume....)
h2=hist(exp$Volume....

#to normalize#

h1$density=h1$counts/sum(h1$counts)*100
plot(h1,freq=FALSE....)
h2$density=h2$counts/sum(h2$counts)*100
plot(h2,freq=FALSE....)

Now I've been successful overlaying the un-normalized data using this method: http://www.r-bloggers.com/overlapping-histogram-in-r/ and also with this method: plotting two histograms together

but I'm stuck when it comes to how to overlay normalized data

Answer 1

ggplot2 makes it relatively straightforward to plot normalized histograms of groups with unequal size. Here's an example with fake data:

library(ggplot2)

# Fake data (two normal distributions)
set.seed(20)
dat1 = data.frame(x=rnorm(1000, 100, 10), group="A")
dat2 = data.frame(x=rnorm(2000, 120, 20), group="B")
dat = rbind(dat1, dat2)

ggplot(dat, aes(x, fill=group, colour=group)) +
  geom_histogram(breaks=seq(0,200,5), alpha=0.6, 
                 position="identity", lwd=0.2) +
  ggtitle("Unormalized")

ggplot(dat, aes(x, fill=group, colour=group)) +
  geom_histogram(aes(y=..density..), breaks=seq(0,200,5), alpha=0.6, 
                 position="identity", lwd=0.2) +
  ggtitle("Normalized")

If you want to make overlayed density plots, you can do that as well. adjust controls the bandwidth. This is already normalized by default.

ggplot(dat, aes(x, fill=group, colour=group)) +
  geom_density(alpha=0.4, lwd=0.8, adjust=0.5) 

UPDATE: In answer to your comment, the following code should do it. (..density..)/sum(..density..) results in the total density over the two histograms adding up to one, and the total density of each individual group adding up to 0.5. So you have multiply by 2 in order for the total density of each group to be individually normalized to 1. In general, you have to multiply by n, where n is the number of groups. This seems kind of kludgy and there may be a more elegant approach.

library(scales) # For percent_format()

ggplot(dat, aes(x, fill=group, colour=group)) +
  geom_histogram(aes(y=2*(..density..)/sum(..density..)), breaks=seq(0,200,5), alpha=0.6, 
                 position="identity", lwd=0.2) +
  scale_y_continuous(labels=percent_format())