Ordering boxes in an R boxplot()

Exercise 6.3.2.

These notes concern box-whisker plots and in particular how you can rearrange the order of the boxes in such plots.

• Introduction
• Data in sample layout
  • Order columns using a summary function
• Data in a list
• Data in scientific recording layout
  • Order a factor using a function
  • Order a factor using an explicit order

The boxplot() command is one of the most useful graphical commands in R. The box-whisker plot is useful because it shows a lot of information concisely. However, the boxes do not always appear in the order you would prefer. These notes show you how you can take control of the ordering of the boxes in a boxplot().

There are four main methods, which in turn depend on the layout of the data:

• Use order() to select column order when you have separate samples (i.e. vectors, columns in a data.frame or a list).
• Use [row, column] to select an explicit column order when you have separate samples.
• Use reorder() to change the order of a factor variable according to a function (e.g. mean), when you have response and predictor variables.
• Use ordered() to make a custom ordered factor variable when you have response and predictor variables.

There are subtle differences between these methods but essentially you are creating an index, which you can use in the boxplot() command to control the order the boxes appear in the plot.

If your data are in a list you can use the same principles but need a slightly modified procedure:

hogl = list(U = hog3$Upper, M = hog3$Mid, L = hog3$Lower)
hogl

$U
[1] 3 4 5 9 8 10 9

$M
[1] 4 3 7 9 11 NA NA

$L
[1] 11 12 9 10 11 NA NA

Use the lapply() command to work out the median over the list elements.

m <- lapply(hogl, median, na.rm = TRUE)

If you try to order() the result you get an error, so you must unlist() the result first:

order(unlist(m))
[1] 2 1 3

Now save the new order and use it in the plot.

o <- order(unlist(m))
boxplot(hogl[o])

Note that you don’t use [row, column] for the list, just give [element], as the list is one-dimensional.

When your data are in scientific recording format you will have a column for each variable and will have response variables and predictor variables e.g.

hog2
   count  site
1      3 Upper
2      4 Upper
3      5 Upper
4      9 Upper
5      8 Upper
6     10 Upper
7      9 Upper
8      4   Mid
9      3   Mid
10     7   Mid
11     9   Mid
12    11   Mid
13    11 Lower
14    12 Lower
15     9 Lower
16    10 Lower
17    11 Lower

These are the same data as before but in a more “sensible” layout. However, when you try a boxplot() you get the boxes plotted in alphabetical order.

You can use the reorder() command to reorder a predictor variable by a function applied to the response variable. In other words, you can determine the order of the boxes using a median or other function. Use the following general process:

Use reorder(predictor, response, FUN) to determine an order for the predictor variable.

Use the result of reorder() in place of the original predictor variable in the boxplot() command.

bpm <- with(hog2, reorder(site, count, FUN = median))
boxplot(count ~ bpm, data = hog2)

Here the with() command is used to “see inside” the hog2 data. You could use:

attach(hog2)
bpm <- reorder(site, count, FUN = median)
detach(hog2)

The result is ordered ascending. If you want a descending order simply add a minus sign in front of the response variable:

bpm <- with(hog2, reorder(site, -count, FUN = median))
boxplot(count ~ bpm, data = hog2)

The procedure works with multiple predictors but you can only reorder() one at a time.

You can use the reorder() command to reorder a predictor variable by a function applied to the response variable. In other words, you can determine the order of the boxes using a median or other function. Use the following general process:

Use reorder(predictor, response, FUN) to determine an order for the predictor variable.

Use the result of reorder() in place of the original predictor variable in the boxplot() command.

bpm <- with(hog2, reorder(site, count, FUN = median))
boxplot(count ~ bpm, data = hog2)

Here the with() command is used to “see inside” the hog2 data. You could use:

attach(hog2)
bpm <- reorder(site, count, FUN = median)
detach(hog2)

The result is ordered ascending. If you want a descending order simply add a minus sign in front of the response variable:

bpm <- with(hog2, reorder(site, -count, FUN = median))
boxplot(count ~ bpm, data = hog2)

The procedure works with multiple predictors but you can only reorder() one at a time.

You can make a factor variable into an explicit order using the ordered() command. You just give the name of the factor you want to order and then the names of the levels in the order you want.

The result of the ordered() command is an ordered factor. The upshot is that the order you set will take precedent over the default alphabetical order.

o <- ordered(hog2$site, levels = c("Upper", "Lower", "Mid"))
o
[1] Upper Upper Upper Upper Upper Upper Upper Mid   Mid   Mid   Mid   Mid
[13] Lower Lower Lower Lower Lower
Levels: Upper < Lower < Mid

boxplot(count ~ o, data = hog2)