Graphics Reference
In-Depth Information
Figure
.
.
Mosaic plot for the arthritis data, using the χ
test and fixed cut-off points for the shading
ple the maximum of the absolute values of the Pearson residuals (Meyer et al.,
),
instead of the sum of squares:
M
=
max
i, j
r
ij
(
.
)
Given a critical value c
α
for this test statistic, all residuals whose absolute values ex-
ceed c
α
violate the hypothesis of independence at level α (Mazanec and Strasser,
,Chap.
).hus,theinterestingcellsthatprovideevidencefortherejectionofthe
independencehypothesiscaneasilybeidentified.Asexplainedabove,theconditional
distribution of this test statistic underthe null hypothesis can beobtained bysimula-
tion, by sampling tables with the same row and column sums n
i
+
and n
+
j
using, e.g.,
the Patefield algorithm (Patefield,
) and computing the maximum statistic for
each of these tables. In Fig.
.
,we again visualize the arthritis data, this time using
the maximum test statistic and its
% and
% critical values as cut-off points. Now
the tile shading clearly shows that the treatment is effective: significantly more pa-
tients in the treatment group exhibit marked improvements than would be expected
for independence.
Summary
12.3.4
Uniform colors and color palettes should always be used to visualize areas, and the
HCL color space provides a convenient way to do this. Shadings can be used to add
information to the basic plots and to support the analysis. Tile highlighting can sup-
