SPSS - Crosstabulation Tables

Crosstabulation tables (contingency tables) display the relationship between two or more categorical (nominal or ordinal) variables. The size of the table is determined by the number of distinct values for each variable, with each cell in the table representing a unique combination of values. Numerous statistical tests are available to determine whether there is a relationship between the variables in a table. This tutor uses the file demo.sav. 

1. A Simple Crosstabulation
2. Counts vs. Percentages
3. Significance Testing for Crosstabulations
4. Adding a Layer Variable

A.A Simple Crosstabulation

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1) What factors affect the products that people buy? The most obvious is probably how much money people have to spend. In this example, we'll examine the relationship between income level and PDA (personal digital assistant) ownership.

1a) From the menus choose:

Analyze > Descriptive Statistics > Crosstabs

Note: This feature requires the Statistics Base option.

1b) Select Income category in thousands (inccat) as the row variable.

1c) Select Owns PDA (ownpda) as the column variable.

1d) Click OK to run the procedure.

2) The cells of the table show the count or number of cases for each joint combination of values. For example, 455 people in the income range $25,000–$49,000 own PDAs.

3) None of the numbers in this table, however, stand out in any obvious way, indicating any obvious relationship between the variables.

 

B.Counts vs. Percentages

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1) It is often difficult to analyze a crosstabulation simply by looking at the simple counts in each cell.

2) The fact that there are more than twice as many PDA owners in the $25,000–$49,000 income category than in the under $25,000 category may not mean much (or anything) since there are also more than twice as many people in that income category.

 

2a) Open the Crosstabs dialog box again. (The two variables should still be selected.)

2b) You can use the Dialog Recall button on the toolbar to quickly return to recently used procedures.

 

2c) Click Cells.

2d) Click (check) Row in the Percentages group.

2e) Click Continue and then click OK in the main dialog box to run the procedure.

3) A clearer picture now starts to emerge. The percentage of people who own PDAs rises as the income category rises.

C.Significance Testing for Crosstabulations

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1) The purpose of a crosstabulation is to show the relationship (or lack thereof) between two variables. 

2) Although there appears to be some relationship between the two variables, is there any reason to believe that the differences in PDA ownership between different income categories is anything more than random variation?

3) A number of tests are available to determine if the relationship between two crosstabulated variables is significant. One of the more common tests is chi-square. One of the advantages of chi-square is that it is appropriate for almost any kind of data.

3a) Open the Crosstabs dialog box again.

3b) Click Statistics.

3c) Click (check) Chi-square.

3d) Click Continue and then click OK in the main dialog box to run the procedure.

4) Pearson chi-square tests the hypothesis that the row and column variables are independent. The actual value of the statistic isn't very informative.

 5) The significance value (Asymp. Sig.) has the information we're looking for. The lower the significance value, the less likely it is that the two variables are independent (unrelated).

 

6) In this case, the significance value is so low that it is displayed as .000, which means that it would appear that the two variables are, indeed, related.

 

D.Adding a Layer Variable

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1) You can add a layer variable to create a three-way table in which categories of the row and column variables are further subdivided by categories of the layer variable.

2) This variable is sometimes referred to as the control variable because it may reveal how the relationship between the row and column variables changes when you "control" for the effects of the third variable.

2a) Open the Crosstabs dialog box again.

2b) Click Cells.

2c) Uncheck Row Percents.

2d) Click Continue.

2e) Select Level of Education (ed) as the layer variable.

2f) Click OK to run the procedure.

3) If you look at the crosstabulation table, it might appear that the only thing we have accomplished is to make the table larger and harder to interpret.

 

 

4) But if you look at the table of chi-square statistics, you can easily see that in all but one of the education categories, the apparent relationship between income and PDA ownership disappears (typically, a significance value less than 0.05 is considered "significant").

 

5) This suggests that the apparent relationship between income and PDA ownership is merely an artifact of the underlying relationship between education level and PDA ownership.

 

6) Since income tends to rise as education rises, apparent relationships between income and other variables may actually be the result of differences in education.