AP Statistics Section 4.3

Establishing Causation

When we study the relationship between two variables, we often hope to show that changes in the

explanatory variable cause changes in the response variable.

However, a strong association between two variables is not

enough to draw conclusions about cause and effect.

What ties between two variables (and others lurking in the

background) can explain an observed association?

What constitutes good evidence for causation?

There are 3 associations to consider:

In the following diagrams, variables X and Y show a strong association

(dashed line). This association may be the result of any of several

causal relationships (solid arrow).

Causation

Changes in x cause changes in y.

Common Response

Changes in both X and Y are caused by changes in a lurking variable Z.

Confounding

The effect (if any) of X on Y is confounded with the effect of the lurking variable Z.

The best evidence for causation comes from an experiment in

which the researcher controls the explanatory variable(s).

CAUTION: Even well-established causal relationships may not generalize to other settings.

For example, experiments have shown that large amounts of

saccharin in the diet cause bladder tumors in rats.

BUT, humans are not rats!!!!!!!

At least most aren’t.

We cannot experiment with humans, but studies with humans

who consume different amounts of saccharin show little association between saccharin and bladder

tumors.

On the AP Exam, be very careful anytime the question asks, “does

one thing cause another?”

In the following examples, state whether the relationship between

the two variables involves causation, common response or confounding. When applicable,

identify possible lurking variables.

1. There is a negative correlation between the number of flu cases reported each week

throughout the year and the amount of ice cream sold in that particular week.

Temperature during the week affects both the number of flu cases and the amount of ice cream sold

Common Response

Many colleges offer versions of courses that are also taught in the classroom. It often happens that students who enroll in the online version do better than the classroom students on the course exams. Does this show that online instruction

is more effective than classroom teaching?

Older people with jobs more likely to take online courses and more likely to take their studies seriously. People with greater computer knowledge more likely to take online courses and perhaps this causes an increase in exam scores

Confounding