Graphics Reference
In-Depth Information
fewer of the people that do not recall being punished do not approve of punishment
than expectedfor(conditional) independence.Forthe groupofpeopleagedbetween
and
, the lighter shading indicates that the association is only significant at the
% level.
he advantage of the exploratory view is its ability to visualize the joint distribu-
tions ofallvariables. Ontheotherhand,thisvisualization maybestronglyinfluenced
bythe marginal distribution ofeducation overage(inparticular thelarge proportion
of
+ people with elementary education), which is not relevant to the conditional
independenceproblem.hepartialmosaicplotsuppressesthiseffectbycomplement-
ing the conditioning in the model with conditioning in the visualization.
Summary
12.4.4
Mosaic, association, and sieve plots can be used to visualize multiway tables by con-
verting them into flat representations. Mosaic plots are particularly useful for ex-
ploratory analysis, whereas the other two require that a particular model of inde-
pendence be specified from which deviations can be examined. In addition, spe-
cialized plot “flavours” can leverage exploratory analyses (pairs plots, highlighting,
doubledecker plots) or model-based analyses (residual-based shadings, conditional
plots).
Conclusion
12.5
his chapter reviews several alternatives for the visualization of multiway contin-
gency tables. For two-way tables, mosaic, sieve, and association plots are suitable for
thevisualization ofobserved andexpectedvalues andPearsonresiduals, respectively.
hese basic methods can be enhanced by using residual-based shadings, preferably
based on perceptual color palettes such as those derived from HCL space. Residual-
based shadings can be used to visualize the signs and sizes of the residuals, as well as
thesignificanceofteststatisticssuchas χ
orthemaximumteststatistic.helatterhas
theadvantagethatitdetectsresidualsthatcausethehypothesisofindependencetobe
rejected. he methods extend directly to the multiway case by using “flat” represen-
tations of the multiway tables, andspecialized displaysforconditional independence
such as trellis layouts of partial tables and pairs plots.
References
Agresti, A. (
). Categorical Data Analysis.Wiley,Hoboken,NJ,
ndedn.
Andersen,E.B.(
).he Statistical Analysis of Categorical Data. Springer, Berlin,
nd edn.
Bickel,P.J.,Hammel,E.A.andO'Connell,J.W.(
).Sexbiasingraduateadmissions:
Data from Berkeley. Science,
:
-
.
