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