22.6 Everyday Application: Non-Random “Selection” Is Everywhere: The problem in our initial discussion of A-grade insurance markets was that adverse selection led to non-randomness in the insurance pool: Although almost everyone was willing to pay the insurance premium that would have made zero expected profit for insurance companies with a randomly selected insurance pool, no one was willing to pay as higher cost students adversely selected into the pool. This kind of non-random selection is, however, not confined to insurance markets but lies at the heart of much that we see around us.13 (Both part A and part B of this exercise can be done without having done Section B in the chapter.)

A. Consider the following examples and describe the non-random selection that can cause observers to reach the wrong conclusion just as insurance companies would charge the “wrong” premiums if they did not take into account the effect of non-random selection.

a. Suppose I want to know the average weight of fish in a lake. So you take out a boat and fish with a net that has 1-inch holes. You fish all day, weigh the fish, take the average, and report back to me.

b. A TV report tells us the following: A recent study revealed that people who eat broccoli twice a week live an average of 6 years longer than people who do not. The reporter concludes that eating broccoli increases life expectancy.

c. A cigarette company commissions a study on the impact of smoking on fitness. To compare the average fitness of smokers to that of nonsmokers, they recruit smokers and nonsmokers at a fitness center. In particular, they recruit smokers from the aerobics program and they recruit nonsmokers from a weight-loss class. They find the “surprising result” that smokers are more fit than nonsmokers.

d. “Four out of five dentists” recommend a particular toothbrush, from a sample of dentists that are provided free dental products by the company that makes the toothbrushes.

e. When surveyed after one year of buying and using a facial cream, 95% of women attest to its effectiveness at making their skin look younger.

f. Children in private schools perform better than children in public schools. Thus, concludes an observer, private schools are better than public schools. (Careful: The selection bias may go in either direction!)