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SPSS® for Windows®: Comparing proportions of two groups in different categories of polytomous response variables

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Question

I have two groups of cases who responded to a series of questions.The responses fall into several different categories. I know how to use the SPSS CROSSTABS procedure to obtain an omnibus Chi-square test for whether the groups differ in their distributions of responses across the categories, but I want to get a test for each response category, comparing the groups on the proportions responding in that category as opposed to any other category. I don't see a way to do this without recoding all my response questions into two category variables, and I would have to do that several times for each response variable, making that impossibly time consuming. Is there an easier way to do this?

Answer

In a table with only two levels of one variable, the values of the adjusted residuals (or adjusted standardized residuals) will be equal in magnitude and opposite in sign for each pair of values at the same level on the other variable. In other words, with two groups and response categories, the adjusted residuals for each response category will be equal in magnitude and opposite in sign for the two groups. This means that they provide the same information about the mis-fit of a model that assumes that these two groups have equal proportions of responses in that category. The adjusted residuals are the square roots of the single degree of Pearson Chi-square statistic you would get if you ran 2x2 crosstabulations involving recoded response variables. These values are thus Z-values, which can be referred to a standard normal distribution to compute p-values, or squared and referred to a Chi-square distribution with one degree of freedom.

For example: If you have a series of items named question_1 to question_k, the grouping variable is named "group" and the labels for your grouping variable are "Group 1" and "Group 2," you could use the following set of commands:

OMS
/SELECT TABLES
/IF COMMANDS = ["Crosstabs"]
SUBTYPES = ["Crosstabulation"]
/DESTINATION FORMAT = SAV NUMBERED = TableNumber_
OUTFILE = "C:\temp\OMS.sav".
CROSSTABS
/TABLES=question_1 TO question_k BY group
/CELLS= ASRESID.
OMSEND.
GET FILE='C:\temp\OMS.sav'.
COMPUTE p=SIG.CHISQ(Group1**2,1).
RENAME VARIABLES Var1=Item Var2=Category.
SPLIT FILE BY Item.
SUMMARIZE
/TABLES=Category p
/FORMAT=LIST NOCASENUM NOTOTAL
/TITLE='Group comparisons for response categories'
/MISSING=VARIABLE
/CELLS=NONE.

This produces a table listing items, categories, and p-values. The p-values are in the data file OMS.sav and are thus available for further processing, if desired.

Adjusted residuals file.
Figure 1: The adjusted residuals file.
Click image to enlarge.

Crosstabulation for question_1.
Figure 2: Crosstabulation for question_1.
Click image to enlarge.

Crosstabulation for question_2.
Figure 3: Crosstabulation for question_2.
Click image to enlarge.

The Case processing summary.
Figure 4: The case processing summary.
Click image to enlarge.

Group comparisons for response categories.
Figure 5: Group comparisons for response categories.
Click image to enlarge.

The OMS.save file.
Figure 6: The OMS.save file.
Click image to enlarge.

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