Boxplots: R Does Them Right

In this post, I define a Tukey boxplot, review the history of boxplots in Excel and walk through an R script for making a proper Tukey boxplot. A link to the source data and R script files is provided.

Tukey Boxplot

“… a boxplot (also known as a box-and-whisker diagram or plot) is a convenient way of graphically depicting groups of numerical data through their five-number summaries  (the smallest observation,   lower  quartile  (Q1), median (Q2), upper quartile (Q3), and largest observation). A boxplot may also indicate which observations, if any, might be considered outliers. The boxplot was invented in 1977 by the American statistician John Tukey.”  Wikipedia

Naomi Robbins’  in her book,  Creating More Effective Graphs  explains the proper layout of a boxplot:

“The rectangle shows the interquartile range (IQR); it goes from the first quartile (the 25th percentile) to the third quartile (the 75th percentile). The whiskers go from the minimum value to the maximum value unless the distance from the minimum value to the first quartile is more than 1.5 times the IQR. In that case the whisker extends out to the smallest value within 1.5 times the IQR from the first quartile. A similar rule is used for values larger than 1.5 times IQR from the third quartile. A special symbol shows the values, called outliers, which are smaller or larger than the whiskers.” pg.91

Boxplots and Excel

Since Excel does not provide a boxplot option, hundreds of Excel users have asked for boxplot capabilities over the years.  In October, 2002, Duncan Williamson posted a tutorial on how to make box and whisker plots in Excel.  Duncan’s method was a modification of the Tukey boxplot.

Duncan Williamson’s  July, 2003 follow-up post on boxplots describes how he found out that his October, 2002 boxplot page “ is, unbeknownst to me, inadequate. ” Duncan learned from a reader, Nikolai Graae, that he was not correctly calculating the whisker values and needed to show outliers for a proper Tukey box and whisker plot.

John Walkenbach, in his 2003 book, Excel Charts, also showed how to make a modified boxplot.  I say modified, because John’s boxplot, like Duncan’s,  used the minimum and maximum values to calculate the whisker values and did not plot outliers.  In April of 2006, I showed how to make a modified boxplot in Excel on my ProcessTrends.com website. 

Jon Peltier created a downloadable Excel workbook of a modified boxplot in October, 2002.  Jon placed the following note in his workbook: 

“Note: there are several different ways that box and whisker plot depict sample data.  The whiskers may alternatively show a more rigorously defined upper control limit, and special markers may be used to indicate outliers beyond these.  Any such alternatives are beyond the scope of this exercise.”

In July, 2007, Jon Peltier updated his boxplot utility to include an option to construct a proper Tukey boxplot that uses the 1.5 IQR definition for the whiskers and outliers. 

The significance of the differences between the Tukey boxplot and modified boxplot methods depends on the distribution of the data being analyzed.  If the minimum and maximum values lie outside the 1.5 IQR, then the modified boxplot becomes problematic because it misses the presence of outliers in the data.

Excel users who want to make a proper Tukey boxplot in Excel should use Jon Peltier’s add-in that includes an option to use the proper whisker definition and outliers. 

R Boxplot

Here’s a comparison of my original Excel ProcessTrends.com modified boxplot and a proper Tukey boxplot that I made with R. 

 

 

 

The R boxplot has the 1.5 IQR Tukey whiskers as well the outliers for points outside the whiskers. 

R Script Overview

Here’s an image of the R script for this R boxplot. 

The 26 lines of R script include 4 lines of comments, 2 library and  attach statements,  and 4 function calls. This script can be reused over and over to make proper Tukey box plots by adjusting the source data file link, variable names,  titles and color selections.  

Let’s walk through the script to see how R handles boxplots. The script is set up in the 4 steps I have described before. I have deliberately arranged the script to highlight the arguments for each function to help me be able to reuse the script from chart to chart and help both you and I understand the options for each function. 

Step 1 – Setup 

library(lattice)
link<- c("C:\\R_Home\\Charts & Graphs Blog\\Box_Whisker
   \\fluoride.csv")

The first line loads the lattice library.
The second line establishes the variable link that I use to specify the source data file path and file name. 

Step 2 – Read Data 

my_Data <- read.table(link,
     skip = 0, sep = ",", dec=".",
     row.names = NULL, header = FALSE,
     colClasses=c("numeric","factor","NULL","numeric"),
     comment.char="#",na.strings=c(-99.9,-999.9),
     col.names=c("week","week_dt","ignore","fluoride"))
attach(my_Data)

This first function reads the data file specified by link. I have added arguments to indicate how many lines to skip in data file (skip = 0), decimal indicator (dec=”.”), specify that there are no row.names, indicate that there is no header, specify the colClasses (character, factor, logical, NULL,  or numeric) for the each input variable, specify the comment.char =”#”, specify the missing data strings (na.strings = “-99.9, -999.9), and specify the col.names.

The second function allows me to use the variable names directly without having to include the data.frame name (my_Data).

Step 3 – Data Manipulation 

# reorder week_dt factor to sort by week number
by_week <- with(my_Data,(reorder(week_dt, week, mean)))
trellis.par.set(box.rectangle = list(col="grey"),
    box.dot =list(col = "grey", pch = 16, cex = 0.5),  
    box.umbrella= list(col = "grey", lty= "solid"), 
    plot.symbol=list(col="red", pch= 6 , cex=.5))

I want to make a plot by week, so I have specified the week_dt as a factor. Since factors will appear in alphabetical order be default, I have reordered the data.frame by week. I have also set several trellis par values for box and symbol specifications.

Step 4 – Make Boxplot

xyplot(fluoride ~ by_week, my_Data,
         main = "Box & Whisker Plot: Weekly Results \n 
           Fluoride Concentrations \n
           (10/1/02 - 1/20/03)",
    par.settings=list(axis.text=list(cex=0.9),
    fontsize=list(text=9)),
    panel = panel.bwplot, horizontal = FALSE,
    ylab = "Fluoride Concentration - mg/l",
    xlab = "Week Begining " ,
    box.ratio =0.5)

This function makes the boxplot, one for each of the 16 weeks. The title and axis labels are specified as well as text font size and the ratio of box width to height.

Note that I use the lattice library xyplot function. I specify the boxplot with the panel = panel.bwplot argument.

Here’s a link to the source data and R script file so that you can try it for yourself. Be sure to correct the link in the R script so that it points to the path and file name that you give your copy of the source data file.

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