Part One
1. On a radio show, an official reported that people who have more children get divorced less often. Because of this, the official argued that people should have more kids to help strengthen their marriage.
A. Name three possible causal statements you could make about this bivariate correlation.
B. Name one possible third variable that might account for this correlation.
C. Design a regression study that will test whether this third variable accounts for the correlation between number of children and divorce.
1. What are the independent and dependent variables in your model?
2. There are at least two possible results (when controlling for the third variable, the number of children no longer predicts divorce, or when controlling for the third variable, the number of children still predicts divorce). Draw each one, using circles to represent each variable.
3. Estimate some betas that you would expect to find if each of the two patterns turns out to be the case.
4. Write a sentence that represents each of the three possible results using the words “controlling for.”
2. Gillen, Lefkowitz, & Shearer (2006) studied the relationship between body image and risky sexual behaviors among college students. They studied three kinds of risky sexual behaviors: having unprotected sex, having a high number of sexual partners, and using alcohol before or during sex.
They found a positive correlation between positive evaluations of one’s appearance (appearance evaluation) and sexual risk-taking such that students with better body images were more likely to engage in riskier sexual behaviors.
They also found a positive correlation between importance of and investment in appearance (appearance orientation) and having engaged in risky sexual behaviors. Both appearance evaluation and appearance orientation are components of body image.
However, they felt that several other variables might account for this correlation, including gender, age, and body mass index (BMI). They included these variables in a regression model predicting whether people had engaged in each of the risky sexual behaviors. For good measure, they included ethnicity and body dissatisfaction as control variables as well.
A. Given the correlation between body image and risky sexual behaviors, name the three possible causal statements (two representing temporal precedence, and one representing a third variable problem).
B. Explain how gender, age, or BMI could be third variables in this correlation.
C. What are the independent and dependent variables in their model?
D. Interpret the betas presented in the regression model in the table below. What are the results for each of the three dependent variables?
E. According to the results, does body image appear to have an effect on adolescents’ risky sexual behaviors?
F. Challenge question: Who is more likely in this sample to have used alcohol during/before sex—European American/Latino students or African American students?
Standardized Regression Coefficients in Regression Models Predicting Risky Sexual Behavior from Body Image
Variable
Number of lifetime partners (N = 242)
Lifetime unprotected sex (N = 232)
Lifetime alcohol use during/before sex (N = 241)
Gender (1 = male, 2 = female)
−0.05
−0.04
−0.04
Ethnicity (0 = European American or Latino, 1 = African American)
0.07
−0.06
−0.13*
Age
0.04
0.00
0.12t
BMI
0.20**
0.07
0.19*
Appearance orientation (high score = more time on appearance)
0.09
−0.01
−0.01
Appearance evaluation (high score = more positive view of appearance)
−0.21**
−0.01
−0.12
Body dissatisfaction
0.04
−0.04
−0.03
** p = 0.01; * p = 0.05; tp = 0.10.
Source: Adapted from Gillen et al. (2006), Table 1.
REFERENCE
Gillen, M. M., Lefkowitz, E. S., & Shearer, C. L. (2006). Does body image play a role in risky sexual attitudes and behaviors? Journal of Youth and Adolescence, 35, 243–255.
PART TWO
Multiple Regression Activity
A magazine, The Atlantic, provides a clearly written summary of a recent longitudinal study. The headline reads:
Math Skills at Age 7 Predict How Much Money You’ll Make (https://www.theatlantic.com/health/archive/2013/05/study-math-skills-at-age-7-predict-how-much-money-youll-make/275690/)
According to the summary, the researchers measured kids’ IQ, math skills, reading skills, and SES (Socioeconomic status) at age seven, and then measured their income at age 42. They found that:
“How much money the people made at midlife was predicted by math ability at age seven. The other factors may have helped them on the path to success, but even when those were controlled for, the association between basic math and reading skills and future socioeconomic status remained, and remained significant . . .”
Do you notice how this description uses the key phrase, “even when those were controlled for”? This should signal to you that the researchers used multiple regression in their design.
What might the regression table have looked like in the study? What would the DV have been? What would the predictor variables have been? Estimate what you think the beta might have been for the predictor, “Math skills at age 7″—that is, is it positive or negative? Significant or not?
Suppose a critic reads this article and says, “I don’t think that it’s math skills—I think it’s IQ. Smarter people just earn more money and they did better at math as kids, that’s all.” What should you say in response? In this study, is IQ a potential third variable that could explain the association between math skills and future income?
Now suppose that a critic suggests that school quality might be a third variable. Kids who go to higher-quality schools had better math skills and also made more money. In this study, is school quality a potential third variable that could have explained the association between math skills and future income?