Chapter Five: Cross Tabulations

In this chapter, we'll look at how SPSS for Windows can be used to create contingency tables, sometimes called cross tabulations (or crosstabs), bivariate, or two-variable tables. A contingency table helps us look at whether the value of one variable is associated with, or “contigent” upon, that of another. It is most 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 make it easier to follow the instructions in this chapter, we recommend that you set certain options in SPSS in the same way that we have.  First, click on 'Edit" in the menu bar, then on "Options," and "General."  Under "Variable List," click on "Display names," and "Alphabetical."  These choices will ensure that the variables in dialog boxes will look like they do in our examples (see Figure 5-1).

Figure 5-1

Now click on "Pivot Tables."  SPSS offers a number of different "looks" for contingency tables.  You might want to experiment with the different choices.  For now, however, click on "Academic.tlo" under "TableLook," and on "Labels and data" under "Adjust Column Widths" (see Figure 5-2). Then click on OK.

Figure 5-2

To illustrate the Crosstabs technique, we'll use the General Social Survey subset (GSS00A.sav). Open this file following the instructions in chapter 1 under "Getting a Data File."

Crosstabs are particularly useful in hypothesis testing. Let’s see if there is any difference between men and women in their attitudes towards abortion. To create a contingency table (crosstabs), from the menu choose “Analyze,” “Descriptive Statistics,” and “Crosstabs” to open the dialog box shown in Figure 5-3.

Figure 5-3

You then choose the row (usually the dependent) variable and column (usually the independent) variable. In Appendix A, you will see that there are seven variables that deal with opinions about abortion. Let’s choose “ABANY” (Abortion if a woman wants one for any reason) for our row variable and “SEX” (Respondent’s sex) for column variable. To do this, select the variable you want from the list and click on it to highlight it, then use the arrow keys to the right of the list box to move the variable into either the row or the column box (for now, ignore the bottom box – more about it in Chapter 8). If you’ve done everything correctly, your screen will look like Figure 5-4. Don’t click OK yet!

Figure 5-4

Note the buttons at the bottom of the Crosstabs dialog box. Click on “Cells..” first. Here you have a number of choices for the information you would like to have in each cell of your table. The “Observed” box should already be selected – it shows the actual number of cases in each cell. You will also want to see percentages as well as raw numbers so that you can easily compare groupings of different sizes. You should always make sure that each category of the independent variable totals 100%; our general rule is to have the dependent variables be the rows and the independent variables the columns. So choose “Columns” for the percentages as in Figure 5-5.

Figure 5-5

Now click on “Continue” to get back to the Crosstabs dialog box. Once you are back there, click OK. SPSS will now open the Output Viewer window which will show you your table (see Fig 5-6).

Figure 5-6

The Case Processing Summary shows the Valid, Missing, and Total cases. The high percent of missing cases here reflects the people who were not asked this particular question in the survey. The Valid N (number of cases) is used in the table.

The Crosstabs shows the 1,768 valid cases arranged in a table that shows what percent of men and women said either Yes or No to the “ABANY question. Note that 39.9% of the men and 39.8% of the women said Yes, a percentage point difference of only .1. If you round off the numbers to eliminate the decimal points, there’s no difference at all between men and women on this question – 40% say Yes (and 60% say No).

Your initial conclusion here might be that on abortion issues, there’s no difference between men and women in their responses. Is this correct, or did you stop your analysis a little too soon? Let’s look at a different abortion question. Repeat the steps above, but use “ABRAPE” as your dependent variable this time. Your results should look like Figure 5-7.

Figure 5-7

Now we see that 84% of the men and 78% of the women said Yes to “Abortion if a woman is pregnant as the result of rape.” The most important thing we discover when we compare Figure 5-6 with Figure 5-7 is the large difference between total Yes answers (40% compared with 81%), which indicates that “abortion” as an issue needs to be broken down into specific conditions if you want to study it in depth. We also see that there is now a difference between men and women on this particular question. But is it a significant difference? To answer that, we will need to do some statistical analysis.

For our next Cross Tabulation, again go to the menu and choose “Analyze,” “Descriptive Statistics,” and “Crosstabs”. In the Crosstabs dialog box place “ABRAPE” as the row variable and “SEX” as the column variable. Now click on the “Statistics..” button, then “Chi-square” to obtain a measure of statistical significance, and on “Phi and Cramer’s V,” which 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 otherwise. Your dialog box should look like Figure 5-8.

Figure 5-8

Click on “Continue,” then “OK.” The table in Figure 5-7 re-appears, but with some additional information (you might have to scroll down to see it) – look for “Chi-Square Tests” (Figure 5-9).

Figure 5-9

Several different versions of chi-square (Pearson’s 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 Cramer’s V of .080 in Figure 5-10 (Symmetric Measures), however, indicates that the relationship is not a strong one.

Figure 5-10

Let's look at a somewhat different table.  For many years, scholars have observed that in the U.S., compared to other industrialized countries, social class has relatively little impact on political attitudes and behavior.  To find this out, click on "Analyze," "Descriptive Statistics," and "Crosstabs." If the variables you used before are still there, click on the “Reset” button, then move "POLVIEWS" to the “Row(s):” box and “INCCAT98” to the "Column(s):" box. Since both of these variables are ordinal, we'll want to obtain different statistics to measure their relationship. Click on "Statistics" and then 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?

Chapter Five Exercises
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) might help explain a person's views?  (Here as well, you may need to recode some variables before proceeding.)
3. Is trust related to race? Run the crosstabs for “TRUST” (Can people be trusted?) with “RACE” and see what you find.

4. 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)?