9  Box Plots

9.1 Introduction

NoteWhy this chart

Box plots compress a distribution into median, quartiles and outliers for fast group comparison.

WarningCommon pitfall

Hiding sample size misleads; a slim box from n=5 looks as confident as one from n=5000.

In this chapter, we will learn to:

  • build box plots
  • modify box
    • color
    • fill
    • alpha
    • line size
    • line type
  • modify outlier
    • color
    • shape
    • size
    • alpha

The box plot is a standardized way of displaying the distribution of data. It is useful for detecting outliers and for comparing distributions and shows the shape, central tendancy and variability of the data.

9.2 Structure

  • the body of the boxplot consists of a “box” (hence, the name), which goes from the first quartile (Q1) to the third quartile (Q3)
  • within the box, a vertical line is drawn at the Q2, the median of the data set
  • two horizontal lines, called whiskers, extend from the front and back of the box
  • the front whisker goes from Q1 to the smallest non-outlier in the data set, and the back whisker goes from Q3 to the largest non-outlier
  • if the data set includes one or more outliers, they are plotted separately as points on the chart

9.3 Data

We are going to use two different data sets in this chapter. Both the data sets have the same data but are in different formats.

daily_returns <- readr::read_csv('https://raw.githubusercontent.com/rsquaredacademy/datasets/master/tickers.csv')
daily_returns
# A tibble: 250 × 5
      AAPL   AMZN      FB    GOOG    MSFT
     <dbl>  <dbl>   <dbl>   <dbl>   <dbl>
 1  1.38    24.2   2.12    22.4    1.12  
 2  2.83     3.25 -0.860    5.99   0.767 
 3 -0.0394   9.91  1.45     6.75   0.973 
 4  0.108    3.76 -0.770  -10.7   -0.285 
 5  1.64    19.8   4.75     8.66   0.501 
 6  0.0689   5.33 -0.300   -0.930  0.256 
 7 -0.561   -5.21 -0.630   -7.28  -0.708 
 8  0.551    0.25 -0.460    0.690  0.128 
 9 -0.217  -13.6   0.0300   6.56   0.0786
10 -0.108   -4.25  0.460    2.60   0.472 
# ℹ 240 more rows

9.4 Single Plot

If you are not comparing the distribution of continuous data, you can create box plot for a single variable. Map the variable to y and add geom_boxplot(). In the below example, we examine the distribution of stock returns of Apple.

ggplot(daily_returns) +
  geom_boxplot(aes(y = AAPL))

Tip

Older code (including earlier editions of this book) used aes(x = factor(1)) as a dummy grouping variable for single boxplots. That workaround is no longer needed but still renders, so you may encounter it in the wild.

9.5 Compare Distributions

9.5.1 Data

For the rest of the chapter, we will use the below data set. Instead of 5 columns, we have two columns. One for the stock names and another for returns.

tidy_returns <- 
  read_csv('https://raw.githubusercontent.com/rsquaredacademy/datasets/master/tidy_tickers.csv',
  col_types = list(col_factor(levels = c('AAPL', 'AMZN', 'FB', 'GOOG', 'MSFT')), col_double()))
tidy_returns
# A tibble: 1,254 × 2
   stock returns
   <fct>   <dbl>
 1 AAPL   1.38  
 2 AAPL   2.83  
 3 AAPL  -0.0394
 4 AAPL   0.108 
 5 AAPL   1.64  
 6 AAPL   0.0689
 7 AAPL  -0.561 
 8 AAPL   0.551 
 9 AAPL  -0.217 
10 AAPL  -0.108 
# ℹ 1,244 more rows

With the above data, let us create a box plot where we compate the distribution of stock returns of different companies. We map X axis to the column with stock names and Y axis to the column with stock returns. Note that, the column names are wrapped inside aes().

ggplot(tidy_returns) +
  geom_boxplot(aes(x = stock, y = returns))

To create a horizontal bar plot, we can use coord_flip() which will flip the coordinate axes.

9.6 Horizontal Box Plot

ggplot(tidy_returns) +
  geom_boxplot(aes(x = stock, y = returns)) +
  coord_flip()

9.6.1 Notch

Notches are used to compare medians. You can use the notch argument and set it to TRUE.

ggplot(tidy_returns) +
  geom_boxplot(aes(x = stock, y = returns),
    notch = TRUE)

9.6.2 Jitter

Just for comparison, let us plot the returns as points on top of the box plot using geom_jitter(). We modify the color of the points using the color argument and the spread using the width argument.

ggplot(tidy_returns, aes(x = stock, y = returns)) +
  geom_boxplot() +
  geom_jitter(width = 0.2, color = 'blue')

9.7 Outliers

To highlight extreme observations, we can modify the appearance of outliers using the following:

  • color
  • shape
  • size
  • alpha

To modify the color of the outliers, use the outlier.color argument. The color can be specified either using its name or the associated hex code.

ggplot(tidy_returns) +
  geom_boxplot(aes(x = stock, y = returns), outlier.color = 'red')

The shape of the outlier can be modified using the outlier.shape argument. It can take values between 0 and 25.

ggplot(tidy_returns) +
  geom_boxplot(aes(x = stock, y = returns), outlier.shape = 23)

The size of the outlier can be modified using the outlier.size argument. It can take any value greater than 0.

ggplot(tidy_returns) +
  geom_boxplot(aes(x = stock, y = returns), outlier.size = 3)

You can play around with the transparency of the outlier using the outlier.alpha argument. It can take values between 0 and 1.

ggplot(tidy_returns) +
  geom_boxplot(aes(x = stock, y = returns), outlier.color = 'blue', outlier.alpha = 0.3)

9.8 Aesthetics

The appearance of the box can be controlled using the following:

  • color
  • fill
  • alpha
  • line type
  • line width

9.8.1 Specify Values

The background color of the box can be modified using the fill argument. The color can be specified either using its name or the associated hex code.

ggplot(tidy_returns) +
  geom_boxplot(aes(x = stock, y = returns), fill = c('blue', 'red', 'green', 'yellow', 'brown'))

To modify the transparency of the background color, use the alpha argument. It can take any value between 0 and 1.

ggplot(tidy_returns) +
  geom_boxplot(aes(x = stock, y = returns), fill = 'blue', alpha = 0.3)

The color of the border can be modified using the color argument. The color can be specified either using its name or the associated hex code.

ggplot(tidy_returns) +
  geom_boxplot(aes(x = stock, y = returns), color = c('blue', 'red', 'green', 'yellow', 'brown'))

The width of the border can be changed using the linewidth argument. It can take any value greater than 0.

ggplot(tidy_returns) +
  geom_boxplot(aes(x = stock, y = returns), linewidth = 1.5)

To change the line type of the border, use the linetype argument. It can take any value between 0 and 6.

ggplot(tidy_returns) +
  geom_boxplot(aes(x = stock, y = returns), linetype = 2)

9.9 Map Variables

Instead of specifying values, we can map fill and color to variables as well. In the below example, we map fill to the variable stock. It assigns different colors to the different stocks.

ggplot(tidy_returns) +
  geom_boxplot(aes(x = stock, y = returns, fill = stock))

Let us map color to the variable stock. It will assign different colors to the box borders.

ggplot(tidy_returns) +
  geom_boxplot(aes(x = stock, y = returns, color = stock))

9.10 Exercises

  1. Draw mileage by cylinders from mtcars.
  2. Draw a single-variable boxplot of mpg using modern syntax (no factor(1)).
  3. Rewrite the grouped plot with a message-first title and no redundant legend.

Worked solutions in solutions/box.md (attempt first).

Where to go next

  • ggplot2 book (ggplot2-book.org) for theory behind this layer
  • Claus Wilke, Fundamentals of Data Visualization, for perception guidance