chi-squared-testcontingency tablesdata visualizationresiduals
This is a mosaic plot of contingency table dataset HairEyeColor described here.
How do I interpret the colors representing residuals? What is the difference between high and positive Pearson's residuals (shown in blue) versus low and negative ones shown in red?
The book you described sounds like, 'Visualizing Categorical Data,' Michael Friendly. The plot described in the 1st chapter that seems to match your request was described as a type of conceptual model for visualizing contingency table data (loosely described by the author as a dynamic pressure model with observational density), and can be seen in the google preview for Ch 1. The book is geared towards SAS users.
A paper on the topic is referenced here: www.datavis.ca/papers/koln/kolnpapr.pdf
'Conceptual Models for Visualizing Contingency Table Data,' Michael Friendly .
*incidentally, the author is also listed as one of the authors of the vcd package (as it was specifically inspired by his book mentioned above) -- maybe you could ask him directly if there's a simple modification to one of the built in functions that's not readily apparent.
** The coloring scheme seems to relate the color blue with positive deviations from independence, and red for negative deviations. Although the red scheme makes sense in that context, maybe it would have been more apt to have used green to represent positive deviations.
In the mosaic plot you see that the first split is wrt gender with about 2/3 female and about 1/3 male. The second split is wrt to alcohol (conditional on gender) showing that only about 1/6 of females drink alcohol while it is about 3/4 of the males. The final split is wrt to cigarettes (conditional on gender and alcohol) showing a clear association that persons who drink tend to smoke and vice versa.
The shadings are made based on the Pearson residuals of an independence model - by default complete independence of all factors but can also be changed to other independence models. The cutoffs of 2 and 4 are based on certain heuristics and are meant to bring out patterns in the Pearson residuals. Here, the default cutoffs do not work very well and you could consider changing them.
The association plot shows the Pearson residuals directly, highlighting in which cells there are more or less observations than expected.
For further details on the methods, I would recommend to read the references listed in ?mosaic. A starting point could be Michael Friendly's 1994 JASA paper or our JSS and JCGS papers on the vcd package and its shadings.
Best Answer
The colors represent the level of the residual for that cell / combination of levels. The legend is presented at the plot's right. More specifically, blue means there are more observations in that cell than would be expected under the null model (independence). Red means there are fewer observations than would have been expected. You can read this as showing you which cells are contributing to the significance of the chi-squared test result. For more information, it may help to read the Residual-based Shadings in vcd vignette (pdf) from the vcd package.