1. Categorical Data
National Opinion Research Center’s General Social Survey
In 2006 a sample of 1928 adults in the U.S. were asked the question “When is premarital sex wrong?” The participants were also asked with what religion they were affiliated.
The National Opinion Research Center’s General Social Survey is conducted every 2 years.

2. Who?/What? Who? What? A sample of 1928 adults.
Attitude towards premarital sex.
Religious affiliation.
Adults is the answer to the question who? The adult’s attitude towards premarital sex and his/her religious affiliation are the answers to the question what?

3. What? When is premarital sex wrong?
Categorical: Always Wrong, Almost Always Wrong, Sometimes Wrong, Not Wrong at All
What is your religious affiliation?
Categorical: Catholic, Jewish, Protestant, None, Other
Both the attitude towards premarital sex and the religious affiliation are categorical variables.

4. Data Table Adult Attitude Religion 1 Never Catholic 2 Always
Protestant 3
Jewish 4
Sometimes
None
The original data table would have 1928 rows for the 1928 adults participating in the survey. Each row of the data table would be a case (an adult). The columns of the data table would be the variables, the adult’s attitude towards premarital sex and the adult’s religion.

5. When is Premarital Sex Wrong?
Class
Count %
Always
506
26.25
Almost Always
166
8.61
Sometimes
376
19.50
Never
880
45.64
Total
1928
100
The original data table can be summarized by counting the number of adults in each category. For example, if we wanted to summarize the attitudes toward premarital sex we could simply count the number of adults in each category.

6. Bar Chart
A bar chart is a graphical representation of the number of adults in each category.

7. Bar Chart
If we scale the count by dividing by 1928, e.g. the relative frequency, or probability or percentage, we have the same graphical display but with a different scale. The largest percentage believe premarital sex is never wrong (44%)

8. Pie Chart
A pie chart displays the same information where the area of the slice is proportional to the relative frequency, percentage.

9. When is Premarital Sex Wrong?
Religion
Always Wrong
Almost Always Wrong
Sometimes Wrong
Not Wrong at All
Total
Catholic 83 47
105
249
484
Jewish 4 2 9 20 35
Protestant
364 97
190
341
992
None 27 12 52
219
310
Other 28 8 51
107
506
166
376
880
1928
We can cross classify the opinion and religious affiliation. In this case 62 adults were both Catholic and responded that premarital sex is always wrong, while 384 adults were both Protestant and responded that premarital sex is never wrong. Because there are different numbers of adults affiliated with each religion it is hard to compare across religions. Can create “row” percentages by dividing the number who fell in each premarital sex category by the number in that “row”, e.g. religion.

10. When is Premarital Sex Wrong?
Religion
Always
Almost Always
Sometimes
Never
Total
Catholic
17.2%
9.7%
21.7%
51.4%
100%
Jewish
11.4%
5.7%
25.7%
57.2%
Protestant
36.7%
9.8%
19.1%
34.4%
None
8.7%
3.9%
16.8%
70.6%
Other
26.2%
7.5%
18.7%
47.6%
With percentages it is easier to compare across religions. For example, 51% of Catholics said premarital sex is never wrong, while about 70% of adults with no religion said premarital sex is never wrong. Only about 1 in 3 Protestants said premarital sex is never wrong. So, it is twice as likely that an adult with no religion will say premarital sex is never wrong compared to a Protestant. Protestants are 2 times as likely to answer premarital sex is always wrong compared to Catholics.

11. Mosaic Plot
The table of “row” percentages can be displayed in a mosaic plot. Here each column is a bar chart with the bars stacked on top of each other. At the far right is the bar chart for the entire set. Compare this with the bar chart on slide 11. The width of columns in the mosaic plot is proportional to the number of cases in that category. For example, there are over twice as many Protestants as Catholics and very few Jewish adults in the sample. One can compare religions by comparing the heights of the similarly colored rectangles. For example, about the same proportion of each religion has the attitude that premarital sex is sometimes wrong. Jewish adults are almost twice as likely to have the attitude that premarital sex is never wrong compared to Protestants.

12. Separate Pie charts display similar information as the mosaic plot.