Procedure Crosstabs

The CROSSTABS procedure creates tables showing the joint distribution of two or more categorical variables (e.g., cell counts, cell percentages, expected values, and residuals). Various measures of association can be obtained.

Example 1

Twenty married men and twenty married women were asked whether they would marry their current spouse if they had to do it all over again. 
 

Code Data

Binary Variables

1. Gender: Assign 0 for `married women` and 1 for `married men`.
2. Choice: Assign 0 for `Yes` and 1 for `No`.  

Four Combinations
 

	Yes (0)	No (1)
Women (0)	Women/Yes	Women/No
Men (1)	Men/Yes	Men/No

 

Data Set

Their responses can be shown below.  
 

Response Patterns: There are four binary response patterns: [0,0] [0,1] [1, 0] and [1,1] .

Frequency count of four binary response patterns.

Count the frequencies and fill in the four cells.  
 

	Yes (0)	No (1)
Women (0)	5 [0,0]	15 [0,1]
Men (1)	13 [1,0]	7 [1, 1]

 

Research Question

There are two categorical variables (gender and choice). A chi-square test of independence is called for. The null hypothesis is that the two variables (gender and choice) are unrelated (independent). The alternative hypothesis is that there is an association between gender and choice.

Conduct a two-way contingency table analysis to find out if gender and choice are related.

SPSS for Windows

A. Enter data values in the Data View window.


B. Define variable names, labels, and value labels in the Variable View window.
 

Click the Variable View tab to open the Variable View window.




The Name Column

To edit the variable name, double click on var00001. Delete var00001 and type in `gender` to replace the default one. Next, double click on var00002. Delete var00002 and type in `choice` to replace the default one.
 

 

The Values Column

Values: Assign descriptive labels to values.

gender

Double click on the textbox and a gray square will appear. Click on the gray square. a Value Label dialog box will appear.

            

(1) Enter the value: 0. 

(2) Enter the value label: Women. 

(3) Click on Add. The value label is added to the list. 

(4) Enter the next value: 1. Enter the corresponding value label: Men. Click on Add. Click on OK to end the input. 

choice

Value Labels: `Same` is coded as `0`. `Different` is coded as `1`.

B. Choose the Crosstabs procedure 

1. From the menus to choose: Analyze \ Descriptive Statistics \ Crosstabs 

2. Select the row variable `gender` and the column variable `choice`. 

3. Click on Statistics.

Click on the Chi-square check box. In the Nominal area, click on the `Phi and Creamer’s V` check box.  (To access the definition of the 'Phi and Cramer's V', right-click on the term.) Click on Continue. Return to the Crosstabs dialog box. 

4. Click on Cells. This opens the Crosstabs: Cell Display dialog box.

In the Counts area: In addition to the default observed count, select Expected. 

In the Percentages area, select Row. The researcher wanted to know the percentages who made the same or different choices within each gender.

In the Residuals area: Choose Unstandardized. Unstandardized residuals are the observed minus the expected frequencies. Click Continue. Click OK.

C. Data Visualization. Produce a clustered bar chart.  

From the SPSS Data Editor menus choose: Graphs \ Bar 

Type of Bar Chart: Select Clustered.

Data in Chart Are: Summaries for groups of cases. It is the default.

Click on Define to open a dialog box.

Bars Represent: Select % of cases.

Specify a category axis: Click on the variable 'gender'. Click on the right arrow button.

Define Clusters by: Select the variable 'choice'. Click OK. The bar chart will be displayed in the SPSS Viewer window.

SPSS Printout


The data can be expressed in a 2 (gender) by 2 (choice) table.   
 

• Gender by Choice Crosstabulation
   

   

Examine the obtained percentages.

Women & Choices

The percentage of women who chose to marry their current spouse (25%) was less than the percentage of women who chose not to (75%). 

Men & Choices

The percentage of men who chose to marry their current spouse (65%) was more than the percentage of men who chose not to (35%). 

Gender & Choices

Most women chose not to marry the same spouse while most men chose to marry the same spouse.

 

• Bar Chart: Gender by Choice
  
  

 

1. The percentage of men who chose to marry the same spouse is greater than the percentage of women in the same category.

2. The percentage of men who chose not  to marry the same spouse is less than the percentage of women in the same category.

Examine the above pattern. What do you observe?

 

• Were males more likely to choose to marry the same spouse than were females?

The statistical significance of the relationship between the two categorical variables, choice and gender, can be investigated using the test. The expected counts and residuals are used to compute the chi-square statistic.

Examine the expected counts.

The expected counts can be obtained from the row and column totals. 

(1) For the women-same cell, the expected count is computed as
 

number of women * number of same
total

(20*18) / 40 = 9

 

	Same (0)	Different (1)	Row Total
Women (0)	Count: 5  Expected Count: ?	Count: 15	20
Men (1)	Count: 13	Count: 7	Count: 20
Column Total	18	Count: 22	Count: 40

 

(2) For the women-different cell, the expected count is computed as
 

number of women * number of different
total

 

(20*22) / 40 = 11

 

	Same (0)	Different (1)	Row Total
Women (0)	5	Count: 15 Expected Count: ?	20
Men (1)	13	7	20
Column Total	18	22	40

 

(3) For the men-same cell, the expected count is computed as ___________

(20*18) / 40 = 9
 

(4) For the men-different cell, the expected count is computed as ___________

(20*22) / 40 = 11
 

Examine the Residuals.

A residual is the difference between an observed and an expected count. 

Women
 

	Same (0)	Different (1)
Women (0)	observed: 5 expected: 9  residual: ?	observed: 15 expected: 11  residual: ?

For the women-same cell, the residual is computed as 5-9= -4. For the women-different cell, the residual is computed as 15-11= 4.

Men
 

	Same (0)	Different (1)
men (1)	observed: 13 expected: 9  residual: ?	observed: 7 expected: 11  residual: ?

 

For the men-same cell, the residual is computed as _____. (13-9=4)
For the men-different cell, the residual is computed as _____. (7-11=-4)

 

• Chi Square Tests
   

The  can be calculated by summing over all cells the squared residuals divided by the expected frequencies:

 

 

 

Results

 

 

What do you conclude?

The value of the Pearson chi-square equals 6.465. Its probability is .011. The associated degree of freedom is computed as (2-1)(2-1)=1. The observed probability is less than .05.

There is a significant relationship between the two categorical variables. Women and men differ in their choices. Gender and choice are related.

(A problem arises when we do CROSSTABS with a small number of cases. Fisher's exact test is an alternative test for the 2 x 2 table. It is most useful when the total sample size and the expected values are small.)
 

• Phi Coefficient of Correlation

The results of a chi-square test of contingency merely indicate whether or not there is a statistically significant relationship between two categorical variables. It is desirable to include both a significance test and a measure of the strength of the relationship.

The phi coefficient equals -.402. Gender and choice are related, p < .05. About 16% of the variance in the variable Choice is accounted for by gender.

Ignore the sign of the phi coefficient. It depends on which levels in each variable get the one and which the zero.  
 

The phi coefficient can be calculated indirectly by using chi-square. The phi coefficient modifies the chi-square by dividing it by the sample size and taking the square root of the result.   
 

The phi coefficient of correlation is associated with the chi-square test of significance. Use phi coefficient to quantify the strength of the association between gender and choice. Phi = .402    
 

Example 2

Randomly selected American college graduates and high school graduates were asked how they kept up with the news. The observed frequencies of their responses were shown below.