Chapter 7, page 159
dimensions. They also found that the many readers of Consumer Reports who owned a Volvo reported having
fewer mechanical problems than the many readers who were owners of Saabs. They were about to go and strike
a bargain with the Volvo dealer when Mr. Caldwell remembered that they had a friend who owned a Saab and
one who owned a Volvo. Mr. Caldwell called up the friends. The Saab owner reported having had a few
mechanical problems but nothing major. The Volvo owner exploded when asked how he liked this car. “First
that fancy fuel injection computer thing went out: 250 bucks. Next I started having trouble with the rear end.
Had to replace it. Then the transmission and the clutch. I finally sold it after 3 years for junk.”Given that the Caldwells are going to buy either a Volvo or a Saab today, which do you think they should
buy? Why? Good reasoners will realize that if the Caldwell’s goal is reliability, the Volvo is the better
choice. The experiences of many Volvo owners (reported in Consumer Reports) is a better predictor of
whether a new car will be reliable than one owner’s experience. It’s more helpful to look at the maintenance
records of thousands of Saabs and Volvos than of 1 Saab and 1 Volvo. But many people who read this
story do not reason in this way and instead recommend that the Caldwell’s choose the Saab, based on this
single vivid story. When making a decision then, students who understand the value of statistics will make
more informed choices.
These two examples (diets and choice of cars) illustrate the importance of considering sample size in
everyday decision making. The implication for teachers is that students should learn to give greater weight
to evidence based on larger rather than smaller samples. In later chapters, we will examine ways to help
students learn to reason about sample size as well as about other issues.
Figure 7.7: The SAT Problem
Does Doxymillin work?
Scientists have been trying to find out how nutrition affects learning. They studied 30 high school
juniors in a New Jersey school. The students agreed to eat a very healthy diet. They ate many
fewer fatty foods and junk foods. They cut way back on foods with processed sugar. Then they
checked on how the students did on tests that they took for college, such as the SAT test.
They found that the students got an average SAT score of 1195, which is much higher than the
average SAT score of students in New Jersey.
What should the scientists conclude from this study? Explain your answer as much as you can.
Considering comparison groups. Read the problem in Figure 7.7. How would you answer the
question posed in the figure? Nearly all middle school students as well as most high school students and
even many undergraduates respond that the scientists can conclude that those who eat healthy diets get high
SAT test scores, or a conclusion similar to this. However, there is a crucial piece of information missing
from this problem: The SAT scores of other students in the same high school who did not eat the very
healthy diet. Without this information, it is not possible to draw any conclusion about diet. Suppose that
this was a high school with very high SAT scores on average. In fact, suppose that if all juniors took the
SAT, their average test score would be 1197. Then an average SAT score of 1195 for students eating a
healthy diet would be just about at the average of the whole school. Without knowing the SAT scores of
other students in the same high school, no conclusion at all can be drawn from the study.
When effective reasoners see problems like the one in Figure 7.7, they notice that there is a need to
consider a relevant comparison group, in this case students in the same high school who ate a less healthy