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Mosaic plots

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Abstract Mosaic plots are a recursive generalization of barcharts to visualize multivariate categorical data. Mosaic plots were first introduced by Hartigan and Kleiner and are the de‐facto standard for advanced visualizations of categorical data. This review explains the general construction and the successful application of mosaic plots. Recent implementations of mosaic plots offer various generalizations which can effectively cope with almost any kind of categorical data. Besides plotting expected values of a proposed model, these variations include the doubledecker plot, the empty bin display and fluctuation diagrams. Within an interactive graphical analysis tool, subgroups reflecting a certain property can easily be linked into mosaic plots to effectively visualize the relationship between this property and the categorical variables in the plot. Mosaic plots are most powerful when investigating associations between categorical variables, conditioned by other categorical variables. This is illustrated along with an explanation of how Simpson's Paradox for categorical data can be explained using mosaic plots. WIREs Comput Stat 2012, 4:191–198. doi: 10.1002/wics.1192 This article is categorized under: Statistical and Graphical Methods of Data Analysis > Statistical Graphics and Visualization

Construction of a Mosaic plot using the Titanic passenger dataset. Starting from a one‐dimensional barchart, the plot is hierarchically build up by recursively subdividing the categories.

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While the association between ‘Gender’ and ‘Admission’ suggests a discrimination of female students (upper left), the mosaic plot at the bottom—showing this association conditioned by ‘Department’—reveals independence or even admission in favor of female students.

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The multiple barchart (top) and multiple spineplot (bottom) for the Titanic lifeboat data. The plot shows the occupancy of lifeboats in launch sequence by ‘Class’, with ‘Gender’ highlighted.

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Variations of a classical mosaic plot (top left). The same binsize view (lower left) equalizes all bins, the fluctuation diagram (lower right) uses a regular grid but proportional cell sizes. The expected values' display (upper right) shows the plot of the expected values of an underlying model, here the model of mutual independence.

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A doubledecker plot featuring the variables ‘Gender’ and ‘Class’, showing the survival rate for each crossing of gender and class side by side.

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