We know firemen are always present at fires.
Does that mean that firemen cause fires?
AP Statistics – 4.3 Establishing Causation – Notes
I.
Explaining Association: Causation
a. Causation – a direct cause-and-effect relationship between two variables
i. Mother’s body mass index and daughter’s body mass index.
b. Even when direct causation is present, it is rarely a complete explanation of an association
between two variables.
c. Even well established casual relations may not generalize to other settings.
d. ASSOCIATION DOES NOT MEAN CAUSATION!!
II.
Explaining Association: Common Response
a. Lurking Variable – a variable that is not among the explanatory or response variables (not
measured in the study) in a study and yet may influence the interpretation of relationships
among those variables.
b. Common Response – when a lurking variable affects (changes) both the explanatory (x) and
response (y) variables.
i. GPA and ACT score.
c. Extraneous Variables – are those variables whose potential impact are small, but could have
been explicitly measured.
III.
Explaining Association: Confounding
a. Confounding Variable – one whose effects on the response variable cannot be separated
from another possible explanatory variable.
i. Attending religious services and living longer.
b. Confounding variables can be either explanatory variables or lurking variables.
i. Year’s of education and worker’s income.
IV.
Establishing Causation
a. Experiments (with randomization) are the best way to establish cause-and-effect
relationships!
b. Sometimes you can not use experiments to establish cause-and-effect relationships.
i. Does praying make you live longer?
ii. Does smoking cause lung cancer?
c. Just because there is a lack of evidence does not necessarily mean there is no cause-andeffect relationship.
d. Criteria for establishing Causation (with out experiments)
i. The association is strong
ii. The association is consistent
iii. Larger values of the response variable are associated with stronger responses.
iv. The alleged cause precedes the effect in time.
v. The alleged cause is plausible.
vi. Careful examination of lurking variables.
Examples: Causation (partial), Lurking Variables, Common Response, & Confounding
1. Causation: The amount of alcohol consumed and the blood alcohol level.
2. Common Response: Student’s SAT score and college GPA are highly correlated. However,
there is a lurking variable present that is affecting both the SAT and GPA. Students who are
smart and who have learned a lot tend to have both high SAT scores and high college grades.
3. Common Response: The number of ministers in Massachusetts and the price of rum in
Havana are highly correlated. Lurking Variables: inflation, income increase, economy, etc.
The lurking variable is affecting both the explanatory and response variables.
4. Confounding: Level of education and amount of income. It is likely that more education is a
cause of higher income – many highly paid professions required advanced education.
However, confounding is also present. People who have high ability and come from
prosperous homes are more likely to get many years of education than people who are less
able or poorer. Of course, people who start out able and rich are more likely to have high
earnings even without much education. We can’t say how much of the higher income of
well-educated people is actually caused by their education. You can not separate (or take
away) someone’s education.
Activity: Consider the following list of sixteen factors. Eight of the factors show strong correlation
(positive or negative) with test scores. The other eight don’t seem to matter. Feel free to guess which
are which.
1. The child has highly educated parents.
2. The child’s family is intact.
3. The child’s parents have high socioeconomic status.
4. The child’s parents recently moved into a better neighborhood.
5. The child’s mother was thirty or older at the time of the first child’s birth.
6. The child’s mother didn’t work between birth and kindergarten.
7. The child had low birth weight.
8. The child attended Head Start.
9. The child’s parents speak English in the home.
10. The child’s parents regularly take him to museums.
11. The child is adopted.
12. The child is regularly spanked.
13. The child’s parents are involved in the PTA.
14. The child frequently watches television.
15. The child has many books in his home.
16. The child’s parents read to him nearly every day.
“A Fair Shake” – Better Homes and Gardens (p. 224-229), Sept 2011
"Skeptics point out that sodium doesn't act alone. In addition to eating more salt, Americans are eating
more food, contributing to unhealthy weight gain. Lack of exercise also raises risks for disease. Plus, most
studies purporting to link high sodium intake with poor health were observational, meaning volunteers
simply were tracked as they went about their usual lives. Such studies can't establish for sure why some
people develop health problems and others don't. For instance, some cases of hypertension might have
arisen from a genetic predisposition, not necessarily a salty diet.
To really measure the effects of sodium, a group of volunteers would have to be randomly assigned to a
high-salt diet and monitored closely against a control group. Cappuccio says this will never happen.
'There's now so much evidence to support the correlation between high sodium intake and poor health
outcomes that such a trial would be unethical,' he says."