scatter plot over boxplot using Matlab - matlab

Question

I've plotted a simple boxplot of a vector y (1xN) using Matlab. I used multiple grouping variables: x1, x2, x3
x1 (1xN) represents length (0.5, 1 , 2 or 3)
x2 (1xN) represents gauge (26 or 30)
x3 (1xN cell array) represents the name of the vendor.
close all; clc;
N = 1000;
% measurements values: they represent some kind of an
% electrical characteristic of a cable.
y = randn(N,1);
% each cable being measured can be of length 1m, 2m, or 3m:
x1 = randi(3,N,1);
% each cable being measured have a gauge of 1awg or 2awg:
x2 = randi(2,N,1);
% each cable can be produced by a different vendor. for instance: 'SONY' or
% 'YAMAHA'
x3 = cell(N,1);
for ii = 1:N
if mod(ii,3) == 0
x3{ii} = 'SONY';
else
x3{ii} = 'YAMAHA';
end
end
figure(1)
boxplot(y,{x1,x2,x3});
I would like to plot a scatter plot over this boxplot in order to show the relevant values of y that create the boxplot, but I could not find a function that groups the values as the boxplot function does.
the closest thing I've found is the following function but it only accepts a single grouping variable.
any help?

Answer 1

The box of the boxplot is determined by the IQR. The data between boxes and outliers is everything in a range of 1.5*IQR from the upper and lower quartile. You can filter the data manually.
For instance...
% data generation
data=randn(100,3);
%%
datas=sort(data);
datainbox=datas(ceil(end/4)+1:floor(end*3/4),:);
[n1 n2]=size(datainbox);
figure(1);clf
boxplot(data); hold on
plot(ones(n1,1)*[1 2 3],datainbox,'k.')
%%
% All datapoints coincide now horizontally. Consider adding a little random
% horizontal play to make them not coincide:
figure(2);clf
boxplot(data); hold on
plot(ones(n1,1)*[1 2 3]+.4*(rand(n1,n2)-.5),datainbox,'k.')
%%
% If you want to add all data between boxes and outliers too, do something like:
dataoutbox=datas([1:ceil(end/4) floor(end*3/4)+1:end],:);
n3=size(dataoutbox,1);
% calculate quartiles
dataq=quantile(data,[.25 .5 .75]);
% calculate range between box and outliers = between 1.5*IQR from quartiles
dataiqr=iqr(data);
datar=[dataq(1,:)-dataiqr*1.5;dataq(3,:)+dataiqr*1.5];
dataoutbox(dataoutbox<ones(n3,1)*datar(1,:)|dataoutbox>ones(n3,1)*datar(2,:))=nan;
figure(3);clf
boxplot(data); hold on
plot(ones(n1,1)*[1 2 3]+.4*(rand(n1,n2)-.5),datainbox,'k.')
plot(ones(n3,1)*[1 2 3]+.4*(rand(n3,n2)-.5),dataoutbox,'.','color',[1 1 1]*.5)

Answer 2

found a simple solution:
I edited the signature of the 'boxplot' function so it will return 'groupIndexByPoint' in addition to 'h':
function [h,groupIndexByPoint] = boxplot(varargin)
groupIndexByPoint is an internal variable used by 'boxplot'.
and now simply add 4 lines to the original code:
N = 1000;
% measurements values: they represent some kind of an
% electrical characteristic of a cable.
y = randn(N,1);
% each cable being measured can be of length 1m, 2m, or 3m:
x1 = randi(3,N,1);
% each cable being measured have a gauge of 1awg or 2awg:
x2 = randi(2,N,1);
% each cable can be produced by a different vendor. for instance: 'SONY' or
% 'YAMAHA'
x3 = cell(N,1);
for ii = 1:N
if mod(ii,3) == 0
x3{ii} = 'SONY';
else
x3{ii} = 'YAMAHA';
end
end
figure(1);
hold on;
[h,groups] = boxplot(y,{x1,x2,x3});
scattering_factor = 0.3;
scaterring_vector = (rand(N,1)-0.5)*scattering_factor;
groups_scattered = groups + scaterring_vector;
plot(groups_scattered,y,'.g');