TABLE 9-2 Cross-Tabulation of Participants by Two Categorical Variables

Health Insurance Type

Commercial Public Military Other Total

Urban-Rural Classification of Residence Rural

60

60

34

42

196

Urban 68

81

36

41

226

Total

128

141

70

83

422

After looking at the frequencies in Table 9-2, you may be curious about the percentages, which would

make these numbers more comparable. But a cross-tab can get very cluttered if you try to include them,

as there are different types: the column percentage, the row percentage, and the total percentage. For

example, the 60 rural residents with commercial health insurance in Table 9-2 comprise 46.9 percent

of all participants with commercial health insurance, because 60 divided by the total number with

commercial health insurance, which is 128 (the column total), equals 46.9 percent.

Groups are often compared across columns, and if that is the intention, column percentages should be

displayed. But if you divide these same 60 rural residents with commercial insurance by their row

total of 169 rural residents, you find they make up 30.6 percent of all rural residents, which is a row

percentage. And if you go on to divide these 60 participants by the total sample size of the study, which

is 422, you find that they make up 14.2 percent of all participants in the study.

Categorical data are typically displayed graphically as frequency bar charts and as pie charts:

Frequency bar charts: Displaying the spread of participants across the different categories of a

variable is commonly done by a bar chart (see Figure 9-1a). Generally, statistical programs are

used to make bar charts. To create a bar chart manually from a tally of participants in each

category, you draw a graph containing one vertical bar for each category, making the height

proportional to the number of participants in that category.

Pie charts: Pie charts indicate the relative number of participants in each category by the angle of

a circular wedge, which can also be considered more deliciously as a piece of the pie. To create a

pie chart manually, you multiply the percentage of participants in each category by 360, which is

the number of degrees of arc in a full circle, and then divide by 100. By doing that, you are

essentially figuring out what proportion of the circle to devote to that pie piece. Next, you draw a

circle with a compass, and then split it up into wedges using a protractor — remember from high

school math? Trust us, it’s easier to use statistical software.

Most scientific writers recommend the usage of bar charts over pie charts. They express more

information in a smaller space, and allow for more accurate visual comparisons.