Graphics Reference
In-Depth Information
Deinition and Construction
13.1
Mosaic plots were introduced by Hartigan and Kleiner ( ) as a means of visu-
alizing contingency tables. More recent works on them include those of Hartigan
and Kleiner ( ), Friendly ( ), Friendly ( ), Friendly ( ), and Hofmann
( ).Asthe namesuggests,mosaicplots consist ofgroupsofrectangular tiles. Each
tile corresponds to one cell from a contingency table. Its area is proportional to the
size of the cell, and its shape and location are determined during the construction
process.
Table . provides a breakdown of people on board the Titanic according to their
class and gender, as reported in Dawson ( ).Figure . shows the corresponding
mosaicplot.
Mosaic plots are not restricted to two dimensions; in principle they can be ex-
tendedtoanarbitrarynumberofdimensions. Inpractice,however,spaceisalimiting
factor.
Construction of a p -dimensional mosaicplot:
Let us assume that we want to construct a mosaicplot for p categorical variables
X ,...,X p .Letc i be the number of categories of variable X i , i
,...,p.
. Start with one single rectangle r (of width w and height h ), and let i
=
.
. Cut rectangle r i into c i pieces: find all observations corresponding to rectan-
gle r i , and find the breakdown for each variable X i (i.e., count the number
of observations that fall into each of the categories). Split the width (height) of
=
Table . . Breakdown of Gender versus Class for those aboard the Titanic (Dawson, )
Class
1st
2nd
3rd
Crew
Totals
Sex
f
145
106
196
23
470
m
180
179
510
862
1731
Totals
325
285
706
885
2201
Figure . . Stepwise construction of a two-dimensional mosaicplot of Gender distribution across
different classes based on the data given in Table .
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