Sociology 3151: Elaboration
I. Elaboration (continued)
A. Babbie uses Glock's theory about religion (that people who are denied status gratification in secular life are more likely to be strongly religious) to illustrate the use of cross-tabulation (contingency tables). (see p. 358, "Data Analysis"). Women, he suggests, are still treated as second-class citizens; according to Glock's theory, women should therefore be more religious than men.
Church Attendance Reported by Men and Women in 1996
| Men | Women | |
| Weekly | 25% | 34% |
| Less often | 75% | 66% |
| 100%(901) | 100%(1134) |
(This, by the way, is a good table to illustrate the main features of proper table construction.)
These results, says Babbie, "confirm this reasoning." How could we use elaboration to check this out further?
B. Let's look at Glock's theory again, this time using SPSS and substituting race for gender. We'll do the crosstabs between race and church attendance, and then as a possible measure of status deprivation, we'll control for income (in one of its ordinal versions).
II. Elaboration (using cross-tabulation to look at the relationship between two variables, controlling for a third variable). In part I, we looked at how sociologists try to establiship causal relationships among variables. For nominal/ordinal variables, this whole process ordinarily involves cross-tabulation, in which separate tables (called partial tables) are calculated for each category of a control variable. Several patterns typically emerge:
A. Direct relationship. Controlling for a third variable has no effect on the original relationship between two variables.
Example: Imagine we have done a study of parents' attitudes toward disciplining their children in relation to their education levels. We've come up with a way to measure each variable, probably using a survey, and we get the following results:
Parenting Style by Education, Hypothetical
| Parenting style | High Education | Low education |
| Permissive | 80% | 10% |
| Authoritarian | 20% | 90% |
| 100%(50) | 100%(100) |
In real world data, we'd almost never get such a strong pattern, but here 80% of the parents with high education follow a permissive discipline style, which only 10% of low education parents follow such a style.
But we find ourselves wondering whether it's really education that makes the difference; perhaps it just that upper and upper-middle class parents pass along this style to their children, regardless of how much education they get. To find out, we control for education, by running separate, partial tables, for each social class group:
1. People with upper class parents
| Parenting style | High Education | Low education |
| Permissive | 80% | 10% |
| Authoritarian | 20% | 90% |
| 100% | 100% |
2. People with middle class parents
| Parenting style | High Education | Low education |
| Permissive | 80% | 10% |
| Authoritarian | 20% | 90% |
| 100% | 100% |
3. People with lower class parents
| Parenting style | High Education | Low education |
| Permissive | 80% | 10% |
| Authoritarian | 20% | 90% |
| 100% | 100% |
As you can see, the original pattern remains the same, regardless of the social class of people's parents. Whether I grew up in poverty or riches, these partial tables say that the variable that mainly affects my parenting style is my level of education. This is called a direct relationship between education level and parenting style.
B. Spurious variables.
We talked in part I about the spurious relationship between shoe size and reading ability among grade school children. Let's look at another example, this time including the cross tabulations.
How can we understand the strong positive relationship between the number of firefighters who come to a fire and the amount of damage done? Is it possible that firefighters really do more hamr than good? Here's the original pattern (again, just hypothetical):
| Amount of damage | Few firefighters | Many firefighters |
| Low | 70% | 30% |
| High | 30% | 70% |
| 100% | 100% |
Of course it isn't really the firefighter's doing the damage. Let's control for the size of the fire:
1. Small fires
| Amount of damage | Few firefighters | Many firefighters |
| Low | 88% | 100% |
| High | 12% | 0% |
| 100% | 100% |
2. Large fires
| Amount of damage | Few firefighters | Many firefighters |
| Low | 0% | 12% |
| High | 100% | 88% |
| 100% | 100% |
As we can see from these tables, the original relationship was spurious. When we control for fire size, we find that it reduces damage to have more firefighters, as we would have expected.
C. Intervening variables. We also learned in part I that it helps understand causality if we can establish an intervening variable by which the original independent variable has its effect on a dependent variable. How are we to understand the positive relationship between gender and GPA?
| GPA | Male | Female |
| High | 50% | 65% |
| Low | 50% | 35% |
| 100% | 100% |
It could be, of course, that women are genetically superior in intelligence to men, but it might also involve study habits. Let's control for hours of study:
1. High hours of study
| GPA | Male | Female |
| High | 80% | 80% |
| Low | 20% | 20% |
| 100% | 100% |
2. Medium hours of study
| GPA | Male | Female |
| High | 50% | 50% |
| Low | 50% | 50% |
| 100% | 100% |
3. Low hours of study
| GPA | Male | Female |
| High | 20% | 20% |
| Low | 80% | 80% |
| 100% | 100% |
The relationship between gender and GPA disappears when we control for hours of study. Of course, with real data, the results would rarely if ever be so neat and decisive. But this is the general pattern we expect to find when our control variable is really an intervening variable.
Notice that for both spurious and intervening relationships, controlling for a third variable makes the original relationship disappear (or at least get weaker). How can we tell whether it's a spurious relationship or whether our control variable is an intervening variable? It depends upon time order and upon our original theoretical model.
Now lets look at an even more complicated pattern that sometimes emerges from using cross-tabulation to control for third variables.
D. Interactive relationships.
In general I think we'd find a positive relationship between education and trust in the police. Maybe the results would be something like this.
| Trust police | Low education | Medium educ | High educ |
| No | 50% | 40% | 30% |
| Yes | 50% | 60% | 70% |
| 100% | 100% | 100% |
But does education have the same effect on trust for police
among minorities as among whites?
Let's do the partial tables.
1. Whites only
| Trust police | Low education | Medium educ | High educ |
| No | 40% | 20% | 10% |
| Yes | 60% | 80% | 90% |
| 100% | 100% | 100% |
2. Minorities
| Trust police | Low education | Medium educ | High educ |
| No | 80% | 80% | 80% |
| Yes | 20% | 20% | 20% |
| 100% | 100% | 100% |
Notice that among whites only, the relationship between education and trust if pretty strong; among minorities, the relationship disappears. Where the relationship disappears or even reverses direction among one category of the control variable, we have an interactive relationship.