Histogram without groups

First, let’s generate some fake data.

x<-1:10
y<-rep(c("a","b"), times=5)
dat<-data.frame(x,y)

This dataset contains only 10 values without duplicates, and they are divided into two groups a and b labelled by variable x.

plt<-ggplot(dat, aes(x=x)) + geom_histogram(binwidth = 1, color="red", fill="yellow")
plt + ggtitle("binwidth=1, count")

Here we specified binwidth=1, so there are 10 bins and each bin is expected to have only 1 count, and this is exact what we observed. Now let’s try a different binwidth, say 0.5. This will create 20 bins, but half of them will be empty.

plt<-ggplot(dat, aes(x=x)) + geom_histogram(binwidth = 0.5, color="red", fill="yellow")
plt + ggtitle("binwidth=0.5, count")

If we use fraction, we expect each fraction is being 0.1, because there are only 10 values and each non-empty bin has 1 value. To do so, we can use the function after_stat(density*width), where the density is the density value in each bin, and width is the binwidth.

plt<-ggplot(dat, aes(x=x)) + geom_histogram(aes(y=after_stat(density*width)), binwidth = 0.5, color="red", fill="yellow")
plt + ggtitle("binwidth=0.5, fraction")

The plot shows up as expected and each fraction is 0.1.

Good, now let’s introduce groups.

Histogram with groups

plt<-ggplot(dat, aes(x=x, fill=y)) + geom_histogram(aes(y=after_stat(density*width)), binwidth = 0.5, color="red")
plt + ggtitle("binwidth=0.5, fraction")

The two groups are filled in different colors, and the fraction in each bin is 0.2. This makes sense, because in each group, there are only 5 values and each non-empty bin has 1 value, accounting 0.2 of the total 5.

On the internet, there is another way to calculate fractions using after_stat(count), which works for cases without groups, but not for histograms with groups. Here we can see it:

plt<-ggplot(dat, aes(x=x, fill=y)) + geom_histogram(aes(y=after_stat(count/sum(count))), binwidth = 0.5, color="red")
plt + ggtitle("binwidth=0.5, calculated fraction")

As you can see, each bin has fraction 0.1. This is because the sum(count) gives the total number, not the total per group.

Density plot with groups

Another way to compare the distributions of multiple groups is to use density plot, as shown below:

# a bit change to update figures
plt<-ggplot(dat, aes(x=x, fill=y)) + geom_density(alpha=0.5)
plt + ggtitle("density plot")

Happy plotting 😄