11. Correlational data slows scientific progress (compared to experimental data free of correlations) because

12. Which of the following statements attempt to infer causation from correlation: Mark only those answers in which a correlation is present, and in which the statement infers causation from the correlation.

13. Which of the following constitutes an example of inferring causation from correlation? Base your answer only on the information provided.

14. Which of the following statements constitute an example of inferring causation from correlation?

15. In some cases, there is wide agreement among scientists that they understand the cause of a phenomenon. Mark all of the following statements that are true. That is, mark all statements in which scientists generally agree that they understand causation.

16. to 19. You gather data showing that among all grammar school students in Austin, there is a tendency for children who spend more time watching television to receive poorer grades than average. After thinking about the problem, you realize that there are several models that could conceivably account for this correlation. These models are labeled (A) through (D):

(A) Model: Certain television programs (such as "The Simpsons") downgrade the importance of an education. Such programs cause the children who watch them to pay less attention in class. Children who do not pay attention in class tend to receive poorer grades than average.

(B) Model: Children who watch a lot of television tend to come from poorer families, and children from poor families do not do as well in school as children from more well-to-do families.

(C) Model: There is a negative correlation between the amount of television a child watches, and the amount of formal education that that child's parents have. Parents with less formal education discourage their children from succeeding in school. These children do poorly because they are discouraged.

(D) Model: Children who watch more television spend less time doing homework than children who watch less television. There is a causal relation between doing homework, and school grades.

The following are data sets that you might gather to investigate whether the models above are correct. For each data set, circle any model that the data could conceivably refute (i.e. do not circle a model if there is no conceivable way that the given data could show it wrong). Do not assume more than is stated.

16. Data showing the relation between family income and the amount of television the children watch.

17. Data on the correlation between family income and the amount of formal education that the parents have.

18. Data on the correlations between i) family income and the amount of formal education that the parents have, and between ii) amount of time spent viewing television versus the amount of time spent doing homework.

19. Data on the relation between the amount of time a child spends doing homework, and their grades.

20. to 23. You gather data showing that people who live near an EPA superfund site (i.e. a toxic waste site) tend have higher rates of leukemia than the general population. After thinking about the problem, you realize that there are several alternative models that could account for this correlation:

(A) The increased cancer incidence is caused by toxic wastes released from site.

(B) People who live near the superfund site tend to have lower incomes. Furthermore, people with low incomes tend to smoke more frequently than the general population, and smoking causes cancer.

(C) People who live near the superfund site tend to be retired, and hence older than the general population. Older people get cancer more frequently than young people.

The following data sets are ones that you might gather to investigate which of the above models is correct. For each data set, circle any model that the data could conceivably refute (i.e. do not circle a model if there is no conceivable way that the given data could show it wrong).

20. Data showing the income of people living near the site, and the average income in the city that the site is located in.

21. Data showing the average age of people living near the site, and the average age of everyone in the city that the site is located in.

22. Data showing the correlations between age and cancer incidence, between income and smoking, and between smoking and cancer incidence.

23. Data on the correlation between income and age.

 
Table of contents Chapter 11. Correlations are hard to interpret
Problems 1-10
Problems 24-30
Problems 31-35
Copyright 1996, 1997 Craig M. Pease and James J. Bull. All rights reserved.
301C@bull.zo.utexas.edu