1. The variables (number of people, average age, average value of consumer goods) describe villages. Because villages are the units of analysis, it is inappropriate to draw definitive conclusions about a relationship among individuals. To draw conclusions about individuals on the basis of data that pertain to social groupings is an ecological fallacy. One cannot tell from these data precisely who is buying the consumer goods. Perhaps villages with high proportions of children also have a high proportion of wealthy older people who are apt to purchase various consumer goods. Without specific information about which individuals are making the purchases, we cannot know if younger people are more likely than older people to be the buyers.

2. (a) unit of analysis: individuals (boys)
independent variable: whether a boy’s parents are divorced/separated or living together
dependent variable: number of behavioral problems

(b) unit of analysis: states
independent variable: number of (or dollar value of) sales of sexually explicit magazines
dependent variable: number of reported rapes

(c) unit of analysis: individuals
independent variable: rural or urban residence (i.e., whether the individual is a resident
of a rural or urban community)
dependent variable: level of tolerance of people holding controversial views

(d) unit of analysis: country
independent variable: level of economic development
dependent variable: level of human services provided

3. (a) A correlation of .23 indicates a relatively weak positive association between prior interracial contact and racial diversity of current friends: The greater the amount of contact with members of other races, the greater the diversity of one’s current circle of friends.

(b) This information indicates that the association is statistically significant; therefore, it is likely to exist among all students at the college from which a random sample of students were surveyed. More literally, “p < .01” means that the chances are less than 1 in 100 that you would get a correlation this large (r = .23) in the sample if there was no association in the population from which the sample was selected.

(c) Among whites, as contact with other races increases, the racial diversity of friends increases. (You also might add: Among blacks, there is no association between interracial contact and diversity of friends.)

4. Evidence of a statistically significant correlation meets only the first requirement for inferring a causal relationship: An association exists between exercise and depression. You cannot infer that lack of exercise is a cause of depression because you do not have evidence of direction of influence or nonspuriousness. One’s level of exercise may precede or follow the onset of depression; also, other variables may cause both a low level of exercise and depression. For example, women may be both less likely to exercise and more likely to become depressed than men.

5. (a) For any of the extraneous variables to create a spurious association it must simultaneously increase religious involvement and decrease the likelihood of partner violence. For example, age could create a spurious association if older people were both more religiously involved and less often engaged in domestic violence than younger people; employment status could create a spurious association if employed people were more religiously involved and less often engaged in domestic violence than the unemployed.

(b) The researchers are not hypothesizing that the relationship is spurious; rather, they are stating that religious involvement reduces the risk of abuse because it enhances social integration and support. Social integration is an intervening variable that explains how religious involvement lowers abuse.

6. Examples: (1) The higher one’s level of education, the less likely one is to believe in life after death. (2) Republicans are more likely to favor capital punishment than Democrats and Independents. (3) Men are more likely to believe in life after death than women.

7. Having expressed belief in life after death (a qualitative variable) as the likelihood of believing in life after death, the first hypothesis above is a continuous statement; the second and third hypotheses take the form of difference statements. Restating the second hypothesis above as a conditional, we have the following: If someone’s party affiliation is Republican, then he or she will favor capital punishment; if someone’s party affiliation is Democrat or Independent, then he or she will oppose capital punishment.