Chapter Five Exercises

In this chapter, we'll look at how SPSS for Windows can be used to create cross tabulations (crosstabs). A crosstab is sometimes called a "contingency table," because it helps us look at whether the value of one variable is "contingent" upon that of another. It is useful when each variable contains only a few categories. Usually, though not always, such variables will be nominal or ordinal. Some techniques for examining relationships among interval or ratio variables are presented in later chapters.

To illustrate the Crosstabs technique, we'll use the General Social Survey subset (GSS98A.SAV). (See Chapter 1 if you need to refresh your memory on how to start SPSS and load a data file.)

Let's compare the way in which people voted in the 1996 presidential election with the way the same people voted four years earlier. Click on "Analyze," "Descriptive Statistics," and "Crosstabs." This will open up the dialog box shown in Figure 5-1. You'll next need to choose the row (usually the dependent) and column (usually the independent) variables. In this case, "PRES96" measures how respondents voted in the 1996 presidential race, and "PRES92" measures how they voted in the 1992 contest. We'll look only at votes for Bill Clinton, for his Republican opponent (George Bush in 1992 and Bob Dole in 1996), and for Ross Perot. The very small number of voters who chose some other candidate has been classified as "missing data."

Figure 5-1

In the box on the left, drag the scroll bar or click and hold the down arrow until you find "PRES96." Click on "PRES96," then on the arrow key that is pointing to the right toward the box labeled "Row(s):." Now find "PRES92" in the box on the left. Click on it, and then click on the arrow pointing toward the box labeled "Column(s):."

The next step is to indicate what information you would like to have in each cell of the table. SPSS for Windows automatically provides a cell "count," that is, the number of cases actually occurring (observed) in each cell. To obtain additional information, click on "Cells." This opens up a new dialog box (Figure 5-2). Here you encounter a number of choices. For present purposes, we need to convert raw numbers into percentages. In a crosstab, one should always percentage so that each category of the independent variable totals to 100%.

Figure 5-2

In this example, we will (somewhat arbitrarily) treat the 1992 vote as the independent variable. Since we have placed "PRES92" in the columns, click on "Column," then on "Continue." You are returned to the Crosstabs dialog box. Click on "OK." SPSS for Windows has now opened up an output viewer that includes your table. Click on "Case Processing Summary" in the left frame to see Figure 5-3, which displays the numbers and percentages of cases that have missing values for one or both variables, and the number and percentages of valid cases.

Figure 5-3

Now click on "VOTE FOR CLINTON, DOLE . . . ." This should display the contingency table (Figure 5-4).

Figure 5-4

Notice a few interesting things about the figures in the table. Overall, voting patterns in the two elections were fairly similar. Clinton held on to 90% of those who had voted for him in 1992. Dole was somewhat less successful in this regard, retaining about three out of four of those who had supported his fellow Republican, George Bush, four years earlier. He was able to make up part of the difference by picking up more defectors from Perot than did Clinton.

We'd probably like to know the probability that the relationship found in the table occurred by chance, especially since a lot of respondents (1,348, or 47.6 % of the total) had missing values for one or both variables, reducing the number of cases on which the table is based from 2,832 (the total sample) to 1,484. We'd also probably like some measure of the strength of the relationship within the sample between the two variables.

To get this information, click again on "Analyze," "Descriptive Statistics," and "Crosstabs." Notice that all the information you provided last time has been retained. Now click on "Statistics." This opens up a new dialog box (Figure 5-5).

Figure 5-5

Click on "Chi-square" to obtain a measure of statistical significance, and on "phi and Cramer's V." Phi and Cramer's V are measures of the strength of association between two variables when one or both are at the nominal level of measurement. Phi is appropriate for tables with two rows and two columns, while Cramer's V is appropriate in other instances, including this example. Now click on "Continue," and on "OK." The output window now reappears. The table that we obtained earlier is repeated, but is now followed by additional information. Click on "Chi-Square Tests." The right window should now look like Figure 5-6. Several different versions of chi-square (Pearson's chi-square is probably the most familiar) all indicate that the relationship in our table would occur by chance less than one time in a thousand. (The significance level of .000 actually means less than .0005, since SPSS rounds to the nearest third decimal place.) The Cramer's V of .618 indicates that the relationship is a strong one.

Figure 5-6

Let's look at a somewhat different table. For many years, scholars have observed that, compared to other industrialized countries, social class has relatively little impact on political attitudes and behavior in the United States. Click on "Analyze," "Descriptive Statistics," and "Crosstabs." Click on "Reset" to get rid of what is already in the box. Now move to the box on the left and click on "POLVIEWS." Click on the arrow pointing right next to the "Row(s):" box. In the same way, add "INCOME98" to the "Column(s):" box. As you did before, click on "Cells," "Column," and "Continue" to percentage in the direction of the independent variable. Since both of these variables are ordinal, we'll want to obtain different statistics than we did before to measure their relationship. Click on "Statistics," on "Kendall's tau-c." (Tau-c is a measure of association that is appropriate when both variables are ordinal and do not have the same number of categories.) Click on "Continue," then on "OK." What do the results show?

Summary

This chapter explored ways of examining relationships between two variables when both contain just a few categories. In Chapter Six, we will look at procedures that can be used when the independent variable is categorical, but the dependent variable is continuous, and in Chapter Seven, we will look at ways to analyze relationships between variables that are bot continuous.

Exercises for Chapter Five

1. Suppose we measure class, not by income, but by what people perceive their social class to be (using the variable named "CLASS")? How closely is this measure related to a person's self-identified political views ("POLVIEWS")? Note: before running this crosstab, look at the frequency distribution for "CLASS." (See Chapter 4 on univariate statistics.) You may want to recode this variable before proceeding. (See Chapter 3 on transforming data.)
2. Consult the codebook in Appendix A describing this dataset. Other than income and self-perceived class, what background variables (such as region of country, age, marital status, religion, sex, race, or education) best explain a person's political views? (Here as well, you may need to recode some variables before proceeding.)
3. Is ideology a general characteristic, or is it issue-specific? That is, are people who are liberal (or conservative) on one issue (such as capital punishment) also liberal (or conservative) on other issues (such as gun control or legalizing marijuana)?
4. What background variables (such as those listed in exercise 2 above) best predict how a person voted in the 1996 presidential election? Did Perot supporters look more like Clinton supporters, or more like Dole supporters?
5. How closely were people's positions on issues associated with how they voted? Did Perot supporters think more like Clinton supporters, or more like Dole supporters?