Graphics Reference
In-Depth Information
Exploratory Visualization Techniques
12.4.1
Asanexample, consider thewell-known UCBadmissions data (Bickeletal.,
)on
applicants, classified byadmissionandgender,tograduateschoolattheUniversity of
California in Berkeleyfor the six largest departments in
.he“flattened” contin-
gency table, which associates departments with columns and admissions - nested by
gender-withrows,isshownasTable
.
.Aggregated overalldepartments, thetable
gives a false impression of gender bias, i.e., higher admission rates for male students.
A first step in the exploratory analysis of more complex tables is to get a quick
overview of the data. For this, all basic plots can be combined in pairwise displays,
arranged in a matrix similar to scatterplots in a pairs plot. he diagonal cells con-
tainthevariable names,optionally withunivariate statistics, whereastheoff-diagonal
cellsfeature plots whosevariables are implicitly specified bythe cells'positions inthe
matrix. InFig.
.
,thediagonal cellsshowbar plotsforthe distributions ofthevari-
ables, and the off-diagonal cells mosaicplots for the corresponding pairs of variables.
he plots suggest that admission differs between male and female students, and be-
tween the departments, and that the proportion of male and female students varies
across the departments. In particular, departments A and B have higher proportions
of male students and lower rejection rates than the other departments.
he next step is to investigate three-way interactions among the variables. In this
example,wehaveabinaryvariableofinterest(admission)thatneedstobe“explained”
by the others. A natural way of representing such a three-way table is to use a mo-
saic display, which first involves splitting by the explanatory variables department
andgenderand then highlighting the resulting mosaic with respecttothedependent
variable admissions. Here, we use vertical splits for both explanatory variables, re-
sulting in the doubledecker plot in Fig.
.
. From the widths of the tiles, it is clear
that students apply to the six departments in unequal numbers (with a particularly
small number of females in departments A and B),and fromthe highlighting we can
also see that the admission rates differ among the departments (roughly speaking,
the admission rate is high for A and B, low for F, and in-between for C to E). he
rates are equal for male and female students, except for department A where more
female than male students are admitted.
Table
.
.
he UCB admissions data, in flat representation
Department
Gender
Admission
A
B
C
D
E
F
Male
Admitted
512
353
120
138
53
22
Rejected
313
207
205
279
138
351
Female
Admitted
89
17
202
131
94
24
Rejected
19
8
391
244
299
317
