Mosaic Plots

Mosaic plots were introduced by Hartigan and Kleiner as a means of visualizing contingency tables. As the name suggests, mosaic plots are pieced together from smaller rectangular tiles. Each tile corresponds to one cell of a contingency table. Its area is proportional to the size of the cell, and shape and location are determined during the construction process. We will explain the construction process using data from the Titanic (see Table 1 for the numbers). In this data set, age, gender, and passenger information is available for all 2,201 persons on board the MS Titanic on her fatal maiden voyage. Additionally, survival information is recorded for each person. We start with a single variable: Figure 1 shows a bar chart of Survival. The bars are colored according to the outcome. On the right, a spineplot is drawn. Spineplots are variations of bar charts, where the width instead of the height of each bar is proportional to the number of cases.

Additionally, the coloring shows survival within class. We can see that survival rates go down from left to right, that is, first class passengers had the highest rate of survival (about 62%), whereas third class passengers and crew members had the lowest survival rate (about 24%). The spineplot of Figure 1 is an example of a one-dimensional mosaic plot. Mosaic plots can show many variables and are limited only by practical issues, such as screen space and interpretability.

To make the mosaic of Figure 1 two-dimensional, we can include the information on age (classified as adult or child) and draw two separate mosaic plots on top of each other, as shown in Figure 2.

The top row in this mosaic plot shows survival rates of children within the classes. It becomes apparent that there were no children in the crew—obviously a structural zero. There also were no deaths in the first two passenger classes. We can now incorporate gender in the mosaic plot by placing the mosaic of Figure 2 for each gender separately side by side, as is shown in Figure 3.

Table 1 Titanic Data Set
			Child				Adult
Sex	Survived	1st	2nd	3rd	Crew	1st	2nd	3rd	Crew	Total
Male	No	0	0	35	0	118	154	387	670	1364
	Yes	5	11	13	0	57	14	75	192	367
Female	No	0	0	17	0	4	13	89	3	126
	Yes	1	13	14	0	140	80	76	20	344
	Total	6	24	79	0	319	261	627	885	2201

Survival rates by class, age, and gender are shown. Overall, a lot more men were on board than [Page 632]women. Survival rates for women are significantly higher than for men. The pattern within class also looks different for women than for men. Women have a strong class/survival association: With higher class, survival improves dramatically. This is not true for men. Survival rates of men in the second passenger class are curiously low and have led to many speculations.

The construction of mosaic plots is strictly hierarchical, which emphasizes the order of variables. Figure 4 shows the same data as the mosaic in Figure 3 with different order of the variables. The variables of class and gender are exchanged. This enables us to better compare the differences in survival rates between female and male persons on board.

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