Frequency Distribution Graphs (Visualizations)
for Category Variables

Bar Graphs

A Bar Graph is used to portray the (grouped) frequency distribution of a variable at the Nominal level of measurement. Such variables are called Category Variables in ViSta. It consists of vertical bars drawn above categories such that

1. The height of the bar corresponds to the frequency
2. The bars are separated by empty space since the nominal level of measurement has separate, discrete categories.

Example: Consider the information given in the following table about the percent of those in the age group 25-34 who have completed various amounts of education (from Moore and McCabe, p. 186):

These percentages can be represented by the following bar graph:

This bar graph shows us right away that the educational level of most of those in the 25-34 age group is the completion of high-school.

Stacked (Segmented) Bar Graphs

While a bar graph represents the frequencies of categories of one variable, a stacked (segmented) bar graph represents the frequencies of combinations of categories of two variables.

In a stacked (or segmented) bar graph:

1. The horizontal axis still represents one variable, with each bar representing one of the catgories of the variable.
2. Each bar is segmented according to the categories of the second variable. Alternatively, each bar can be seen as being made up of smaller bars stacked on top of each other.

Example: Consider the entire set of data about educational level given by Moore and McCabe:

Here is the stacked bar graph:

Mosaic Plots

A mosaic plot presents the same information as is presented by a stacked bar-graph: The frequencies of combinations of categories of two variables. Furthermore, it represents the information in a similar, but slightly different fashion:

1. A mosaic plot consists of rectangles laid out in a mosaic. The rectangles are like the sub-bars in a stacked bar-graph.
2. In a mosaic plot, each column of rectangles represents a category of the variable on the horizontal axis.
3. In a stacked bar-graph, each bar represents the overall frequency of a category of the variable plotted on the horizontal axis. In a mosaic, the several column of tiles are all the same height, representing 100%.
4. Whereas a stacked bar-graph's sub-bars representing the joint frequency of a category of each of the two variables, in a mosaic plot each rectangle represents the joint probability of a category of each of the two variables.

Here is the mosaic plot for the data shown above:

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