Boxplot: Matlab displays different graphic in respect of R?

Question

I plotted a simple data matrix

39  135 249 1   91  8   28  0   0   74  17  65  560
69  0   290 26  254 88  31  0   18  53  4   63  625
66  186 344 0   9   0   0   0   18  54  0   74  554
80  41  393 0   0   0   2   0   6   51  0   65  660
271 112 511 1   0   274 0   0   0   0   16  48  601
88  194 312 0   110 0   0   0   44  13  2   76  624
198 147 367 0   15  0   0   3   9   44  3   39  590

using a standard boxplot (i.e. where whiskers extend 1.5 x IRQ from Q1 and Q3). Each column is a variable, each row an observation.

Nevertheless I obtained two different graphics using R (RStudio 1.0.44) and Matlab2018. In particular, whiskers extend in a different way.

In Matlab I'm using the following code:

% clearing workspace
clear all;
close all;
clc;

%entering in current directory where I find the txt data file 
tmp = matlab.desktop.editor.getActive;
cd(fileparts(tmp.Filename));
clear tmp;

%reading data
df = readtable('pippo.txt', 'Delimiter', '\t', 'ReadVariableNames',false);
df = table2array(df)

figure(1);
boxplot(df(:, 1:end-1), 'Whisker', 1.5);
ylim([0 600]);

which produces the following graph:

In R I'm using the following code:

rm(list = ls())

# getting the current directory
working_dir <-dirname(rstudioapi::getActiveDocumentContext()$path)

# setting the working directory where I finf the txt file with data
setwd(working_dir)

df <- read.table("pippo.txt")
jpeg('r_boxplot.jpg')
boxplot(df[,1:12], las=2, ylim=c(0,600), range=1.5)
dev.off()

which produces the following graph:

Observation 1: if I omit the parameters 'whiskers' and 'range' from both scripts I obtain the same graphics; it is expected as 1.5 seems to be the default whiskers value.

Observation 2: both matlab and R seem to read data in the correct way, I mean both workspaces visualise the same matrix

What Am I missing? Which graph should I trust?

Hojo.Timberwolf Hojo.Timberwolf · Accepted Answer · 2019-03-19T10:03:56

explanation for R boxplot code

MATLAB code for boxplots

So going through both functions I found that they both appear to be calculating the exact same thing even down to how they define the IQR

R claims to be doing the following for the boxplot

upper whisker = min(max(x), Q_3 + 1.5 * IQR)
lower whisker = max(min(x), Q_1 – 1.5 * IQR)
where IQR = Q_3 – Q_1, the box length.

MATLAB claims to be doing this for their boxplot

p75 + w(p75 – p25) 
p25 – w(p75 – p25)
where p25 and p75 are the 25th and 75th percentiles, respectively.

Even how they define whisker extension is the same with Matlab stating

%   The plotted whisker extends to the adjacent value, which is the most 
%   extreme data value that is not an outlier. Set whisker to 0 to give 
%   no whiskers and to make every point outside of p25 and p75 an outlier.

And R states

Range determines how far the plot whiskers extend out from the box. If range is 
positive, the whiskers extend to the most extreme data point which is no more than 
range times the interquartile range from the box. A value of zero causes the whiskers 
to extend to the data extremes.

Personally, I feel that it has to do with some underlying way the computations are performed. Edit After messing with the code, I can confirm it has everything to do with the underlying computations.

R code

quantile(a,c(.25, .75))
25% 75% 
301 380 
> 380+1.5*(380-301)
[1] 498.5
> 301-1.5*(380-301)
[1] 182.5

Matlab code

prctile(te,[25,75])
ans =

  295.5000  386.5000

W75 = p75 + 1.5*(p75-p25)
W25 = p25 - 1.5*(p75-p25)

W75 =

   523


W25 =

   159

I used the 3rd column of your data to test and see how the quantiles are being calculated. As you can see the 25% and 75% are not very different but just different enough to result in larger whisker cutoffs in the matlab code.

Boxplot: Matlab displays different graphic in respect of R?

2 Answers