Comparing Medians and Inter-Quartile Ranges Using the Box Plot

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The box plot is useful for comparing the quartiles of quantitative variables. More specifically, lower and upper ends of a box (the hinges) are defined by the first (Q1) and third quartile (Q3). The median (Q2) is shown as a horizontal line within the box. Additionally, outliers are indicated by the whiskers of the boxes whose definition is implementation-dependent. For example, in geom_boxplot of ggplot2, whiskers are defined by the inter-quartile range (IQR = Q3 – Q1), extending no further than 1.5 * IQR.

Creating a box plot in native R

We will use the warpbreaks data set to exemplify the use of box plots. In native R, a box plot can be obtained via boxplot.

# create positions for tick marks, one more than number of bars
x <- warpbreaks$breaks
# create labels
x.labels <- paste0(warpbreaks$wool, "-", warpbreaks$tension)
# specify colors for groups
group.cols <- c("darkred", "red", "darksalmon", 
                "darkblue", "blue", "lightblue")
cols <- c(rep(group.cols[1], 9), rep(group.cols[2], 9), 
        rep(group.cols[3], 9), rep(group.cols[4], 9), 
        rep(group.cols[5], 9), rep(group.cols[6], 9))
boxplot(x ~ warpbreaks$wool + warpbreaks$tension, col = group.cols)
legend("topright", legend = c(unique(x.labels)), 
        col = group.cols, pch = 20)

Creating a box plot with ggplot

We could compare the tensions for each type of wool using facet_wrap in the following way:

ggplot(warpbreaks, aes(x = tension, y = breaks)) +
    geom_boxplot() + facet_wrap(.~wool) +
    ggtitle("Breaks for wool A and B")

ggplot(warpbreaks, aes(x = tension, y = breaks, fill = wool)) +
    geom_boxplot() + 
    ggtitle("Breaks for wool A and B")

Showing all points

To view the individual measurements associated with the box plot, we set outlier.shape = NA to prevent duplicates and call geom_point.

ggplot(warpbreaks, aes(x = tension, y = breaks, fill = wool)) +
    geom_boxplot(outlier.shape = NA) + 
    ggtitle("Breaks for wool A and B") +
    # dodge points horizontally (there are two bars per tick)
    # and jitter points horizontally so that they don't overlap
    geom_point(position = position_jitterdodge(jitter.width = 0.1))

Showing all the points helps us to identify whether the sample size is sufficient. In this case, most pairs of wool and tension exhibit high variabilities (especially wool A with tension L). Thus, the question would be whether this level of variability is inherent to the data or a result of the small number of samples (n = 9). Note that you can combine a box plot with a beeswarm plot to optimize the locations of the points.

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