Graphics Reference
In-Depth Information
of a mosaicplot. his structure contains the meta-information of a set of categorical
variables:
the values that each variable can adopt and the order in which these values occur
(i.e., a tuple of the variable's categories)
the order and direction in which the variables appear in the hierarchy.
hroughout this chapter, we will assume that the default split direction in a mosaic-
plotishorizontal.Ifaverticalsplitisintended,wewillusethesuperscript
t
behindthe
variablename(denotingthe“transpose”ofthevariable).hemosaicplotsinFigs.
.
and
.
therefore have structures Class, Gender, Survival
t
and Gender, Class, Sur-
vival
t
, respectively. he concept of mosaicplot structure is discussed in more depth
in Hofmann (
).
he strictly hierarchical construction of mosaicplots enables us to interpret vari-
ous properties of mosaicplots, as we will discuss in the next section.
Interpreting Mosaic Plots
13.2
Mosaics arearea-based graphics: thearea ofeachtileisproportionaltothecellsizeof
the corresponding contingency table. However, the overall number of observations
isnotdisplayed inamosaicplot; multiplying eachcellbytendoesnotchange the plot
because the ratios between the cell counts are illustrated, not the cell counts them-
selves. It is therefore more relevant to discuss percentages or probabilities in relation
to mosaicplots rather than actual cell sizes. Tile sizes should always be interpreted
in relation to the sizes of other tiles. Ater mosaic construction, we will describe the
mathematical properties that we can retrieve from the plot, i.e., what we can reliably
“see from a mosaicplot.”
Probabilities in Mosaic Plots
13.2.1
Figure
.
shows a two-dimensional mosaicplot of the Titanic data. Class is plotted
versusSurvival. hefirstsplitisinthehorizontal direction; thewidthofatileisbased
on the number of persons in each class. he width is therefore an estimate of the
probability of P
.he number ofsurvivors
ineach of these tiles is then found,whichdetermines the heightof the final tiles. his
makes the height of the bottom let tile an estimate of the survival probability of the
first class passengers: P
Class
i
,withi
st,
nd,
rd, Crew
(
=
)
(
Survival = yes
Class =
st
)
, whereas the upper let tile's
height gives P
. Consequently, the area of a tile gives
the joint probability for Survival and Class, since
(
Survival = no
Class =
st
)
P
)
area
(
Survival=yes
Class=
st
=
=
)
height
P
(
Survival=yes
Class=
st
ċ
P
)
width
(
Class=
st
