Elaboration

Elaboration is a crosstab adding a control variable (CV).

The control variable must be categorical, with at least two categories, and ideally no more than five categories.  The independent and dependent variables must be categorical, with at least two categories and ideally no more than five categories. 

With elaboration you get a separate crosstab for every category of your control variable, including a chi-square and p value for each crosstab.  This allows you to isolate the effect of the IV on the DV for every value of the CV. 

You perform and interpret the hypothesis test the same as for a bivariate crosstab, but you must do it for each of the values of the control variable. The hypotheses are:

Ho: There is no relationship between IV and DV, controlling for CV.  Chi-square = 0

H1: There is a relationship between IV and DV, controlling for CV.  Chi-square ≠ 0 

We will not be doing elaboration by hand because it will take too long! Although you could. It is not difficult. Just do a bivariate crosstab for each value of the CV.  

Example 1:  Does race influence people's attitudes about legalizing marijuana when you control for political ideology?

Dependent Variable = attitude about marijuana legalization; measured as should be legal or  should not be legal

Independent Variable = race; measured as white or black

Control Variable (CV) = political ideology measured as liberal, moderate, conservative

All variables are categorical, so analysis = elaboration. 

Hypotheses:

Null: There is no relationship between race and attitudes about legalizing marijuana, controlling for political ideology.  Chi-square = 0.

Research: There is a relationship between race and attitudes about legalizing marijuana, controlling for political ideology.  Chi-square  ≠ 0.

Based on the above chi-squares and probabilities, we would accept the null hypothesis for conservative and moderates and state that there is no relationship between race and attitudes about legalizing marijuana for people with conservative and moderate political ideologies.  For moderates and conservatives similarly high percentages of Whites and Blacks oppose legalizing marijuana (74% and 71%, and 79% and 80%, respectively).

However, for liberals we would reject the null hypothesis.  There is a relationship between race and attitudes about legalizing marijuana for people with liberal ideologies.  More liberal Whites support legalizing marijuana (44%) than do liberal Blacks (25%) (chi-square = 8.17, p = .004).

Example 2:  Does race influence people' s attitudes about gun permits when controlling for educational degree?

DV = whether people oppose or favor requiring gun owners to have a permit (gunlaw)

IV = race

CV = educational degree (degree) measured as less than HS, HS, some college, college degree, graduate degree 

All variables are categorical.  So analysis  = elaboration

Hypotheses:

Null: There is not a relationship between race and attitudes about gun permits, controlling for educational degree.  Chi-square = 0.

Research: There is a relationship between race and attitudes about gun permits, controlling for educational degree.  Chi-square  ≠ 0.

Do this on the computer using SPSS:

Less than HS: p = .41, accept null
HS: p = .005, reject null
Some college: p = .52, accept null
College degree: p = .33, accept null
Graduate degree: p=.38, accept null

See SPSS output for %'s.

Interpretation:

For people with a high school degree, race does influence attitudes about gun permits.  Most Whites, Blacks and people of other races who ended their education with a high school degree favor requiring gun permits.  However, among these people, more Whites (21%) oppose gun permits than do Blacks (12%) or people of other races (8%). 

For people with less than a high school degree, some college, a college degree, or a graduate degree, there is no difference between Whites, Blacks and people of other races on whether they favor or oppose gun permits.  Most people in all of these groups favor requiring gun permits.

Example 3: In Class Exercise

Does gender influence whether Eastern North Carolinians think homosexuals should be barred from the U.S. military controlling for race?   (This study is a telephone survey of people residing in eastern NC.)

DV = whether people think homosexuals should be barred from the U.S. military (measured as yes/no) 

IV = gender (measured as male/female) 

CV = race (measured as white/black/other) 

Null: There is not a relationship between gender and attitudes about barring homosexuals from the military, controlling for race.  Chi-square = 0.

Research: There is a relationship between gender and attitudes about barring homosexuals from the military, controlling for race. Chi-square  ≠ 0.

White: p = .000, reject null 
Black: p = .000, reject null 
Hispanic:  p = .34, accept null
Native American: p = .39, accept null
Asian: not computable, not enough cases or variation
Other: p = .46, accept null

Interpretation:

For Whites and Blacks gender does influence people's attitudes about barring homosexuals from the military.  More White women (81%)  oppose barring homosexuals from the military than do White men (64%).  Similarly, more Black women (86%) oppose barring homosexuals from the military than do Black men (67%). 

For Asians, the statistical test could not be performed because of a low number of cases (n=3) and lack of variation among those cases.

For Hispanics, Native Americans, and people of Other races gender does not influence people's attitudes about barring homosexuals from the military.     The sample sizes on these groups are relatively small, so generalizations are limited, but it looks like most men and women in these groups, with the exception of Native American men, oppose barring homosexuals from the military.

Because of these small sample sizes, I did the analysis again combining Hispanics, Asians, Native Americans, and people of Other races together and got the following results.

White: p = .000 
Black: p = .000 
Other:  p = .47 

Ho:  There is no relationship between gender and whether people think homosexuals should be barred from the U.S. military when we control for race? Chi-square = 0 

H1: There is a relationship between gender and whether people think homosexuals should be barred from the U.S. military when we control for race? Chi-square ≠ 0

White: p = .000  Reject null.
Black: p = .000  Reject null.
Other:  p = .47  Accept null.

Interpretation:

Most men and women of all races think homosexuals should not be barred from the U.S. military.  However, for whites and blacks, higher percentages of women think this than do men.

For Whites, 81% of the women think homosexuals should not be barred from the U.S. military, whereas only 64% of the men think this.

Similarly, for Blacks, 86% of the women think homosexuals should not be barred from the U.S. military, whereas only 67% of the men think this.

For people of other races, about 74% of men and women think homosexuals should not be barred from the U.S. military.

Example 4: In Class Exercise

Do men and women differ in whether they think a book written by a homosexual should be allowed (yes or no) in public libraries, controlling for the region of the country in which they live? 

1.  Determine DV, IV, CV, level of measurement, and analysis

2. Write Hypotheses

3. Conduct Test on the computer: Variable Names = sex, libhomo, region

4. Interpret findings

Answers:

1. Analysis = elaboration, the DV, IV and CV are all categorical

2.  Hypotheses

Ho: Men and women do not differ in whether they think a book written by a homosexual should be allowed in public libraries, controlling for the region of the country in which they live.  Chi-square = 0

H1:  Men and women differ in whether they think a book written by a homosexual should be allowed in public libraries, controlling for the region of the country in which they live.  Chi-square ≠ 0

3.  Chi-Square Tests, from SPSS

4. Interpretation

In all areas of the country besides the South Atlantic, men and women do not differ in their attitudes about whether books written by homosexuals should be allowed in public libraries. In all of these areas, besides the South Atlantic, most men and women favor allowing these books in the libraries.

In the South Atlantic, men and women do differ in their attitudes about whether books written by homosexuals should be allowed in public libraries.  More women in the South Atlantic (38%) want books written by homosexuals to be removed from public libraries than do men (21%).