\documentclass{article}
\usepackage{sober}
\usepackage[utf8]{inputenc}
\title{Various ways to compare histograms}
\author{Ben Bolker}
\date{\today}
\newcommand{\code}[1]{{\tt #1}}
\begin{document}
\maketitle

Graphically comparing distributions, especially with small
samples, is a challenge.  Here are some approaches.

\SweaveOpts{fig.width=5,fig.height=5,out.width="0.7\\textwidth"}

<<echo=FALSE>>=
library(ggplot2)
theme_set(theme_bw())
@

Example data:
<<>>=
set.seed(1001)
z1 <- rnorm(100,mean=20,sd=2)
z2 <- rnorm(100,mean=25,sd=2)
@

The \code{multhist} function from the \code{plotrix} package:
<<>>=
library(plotrix)
m <- multhist(list(z1,z2),
              breaks=seq(9.5,30.5),names.arg=10:30)
box(bty="l")
@

Or overlay histograms with transparent colors:
<<fig.keep="last">>=
trred <- rgb(1,0,0,0.5)  ## transparent red
trblue <- rgb(0,0,1,0.5) ## transparent blue
hist(z1,col=trred,breaks=14:35,main="",ylim=c(0,30))
par(new=TRUE)
hist(z2,col=trblue,breaks=14:35,main="",ylim=c(0,30))
@

Comparing density estimates instead:
<<>>=
plot(density(z1),ylim=c(0,0.25),xlim=c(10,35))
lines(density(z2),col=2)
@

Alternative code:
<<>>=
d1 = density(z1,from=10,to=35)
d2 = density(z2,from=10,to=35)
matplot(d1$x,cbind(d1$y,d2$y),lty=1,col=1:2,type="l")
@

Using lattice or ggplot2 packages requires that we
combine the data into a single data frame:
<<>>=
dat <- data.frame(z=c(z1,z2),grp=factor(rep(1:2,each=100)))
library(lattice)
print(histogram(~z|grp,data=dat))
@


The \code{groups} argument works for density plots, not
histograms (from \code{?histogram}:
``Note that the default panel function for
`histogram’ does not support grouped displays, whereas the
one for ‘densityplot’ does.'').

<<>>=
densityplot(~z,groups=grp,data=dat)
@

\code{ggplot} is the new hotness.
<<>>=
library(ggplot2)
## overlapping/transparent
ggplot(dat,aes(x=z,group=grp,fill=grp))+
  geom_histogram(colour="gray",binwidth=0.5,alpha=0.5,
                 position="identity")
@
(Note that lattice plots have the \code{groups} argument,
but ggplot uses the \code{group} aesthetic.
I used \verb+theme_set(theme_bw())+ to change
to my preferred plot style.)

Superimpose histograms (scaled to prob. density)
and density lines:
<<>>=
ggplot(dat,aes(x=z,group=grp,fill=grp,colour=grp))+
  stat_bin(colour="gray",binwidth=0.5,alpha=0.5,
                 position="identity",aes(y=..density..))+
  geom_density(fill=NA)

@

Put the bars next to each other:
<<>>=
ggplot(dat,aes(x=z,group=grp,fill=grp))+
  geom_histogram(colour="gray",binwidth=0.5,
                 position="dodge")+theme_bw()
@

The same thing but without gray borders on the
bars (seem to overlap slightly??)
<<>>=
ggplot(dat,aes(x=z,group=grp,fill=grp,colour=grp))+
  geom_histogram(binwidth=0.5,
                 position="dodge")+theme_bw()
@

Separate graphs:
<<>>=
ggplot(dat,aes(x=z,group=grp,fill=grp))+
  geom_histogram(colour="gray",binwidth=0.5)+facet_wrap(~grp)+
  theme_bw()
@

For more than two groups one should probably look into vertical
presentations of the data, i.e. boxplots/violin plots/bean plots \ldots
\end{document}