Mosaic Plot

A mosaic plot (also referred as a Marimekko diagram) is a graphical way for visually representing data from two or more qualitative variables. It is a multidimensional version of spineplots, which graphically represent the same data for only one variable. It provides a summary of the data and allows for the identification of correlations between distinct variables. For example, independence is demonstrated when all of the boxes in the same category have the same areas. Hartigan and Kleiner proposed mosaic plots in 1981, and Friendly elaborated on them in 1994. Because of its similarity to a Marimekko chart, mosaic plots are often known as Mekko charts. The area of the tiles, which is also called the bin size, is related to the number of observations inside that category, as with bar charts and spineplots.

EXAMPLE

A typical example of a mosaic plot incorporates data from Titanic passengers. This example’s data set has 2201 observations and three variables. The variables are as follows:

• the individual’s gender (male / female)
• the class (first, second, and third class, or crew) 
• did this person escape the sinking (yes / no)?

The observations were gathered into the following table:

Construction: 

The categorical variables are initially arranged in alphabetical order. The variables are then allocated to an axis. This data set’s sequence and categorization are shown in the table to the right. Another ordering will produce a different mosaic plot, indicating that the order of the variables is important in all multivariate plots.

We initially display “Gender” at the left edge of the first variable, which means we divide the data vertically into two blocks: the bottom (much smaller) one relates to females, while the top (much bigger) one refers to males. One can readily tell that around one-quarter of the passengers were female, with the remaining three-quarters being male.

The top edge is then given the second variable “Class.” As a result, the four vertical columns represent the four values of that variable (1st, 2nd, 3rd, and crew). Because column width shows the proportional fraction of the relevant value on the population, these columns are varied in thickness. The crew is clearly the most male-dominated category, whereas third-class passengers are the most female-dominated group. The number of female crew members is likewise said to be small.

Finally, the third variable (“Survived”) is applied, this time along the left side, with the outcome underlined by shade: dark grey rectangles represent those who did not survive the calamity, whereas light grey rectangles represent people who did. Women in the first class are quickly shown to have had the best chance of surviving. Females appear to have had a higher survival probability than men (marginalized over all classes). Similarly, a gender marginalization identifies first-class passengers as the most likely to survive. In all, approximately one-third of all persons survived (proportion of light grey areas).