The Question of
Causation
YMS3e 4.3:Establishing Causation
AP Statistics
Lurking Variable:
A variable that is not among the
explanatory or response
variable in a study and yet may
influence the interpretation of
relationships among those
variables
Lurking Variable:
A dentist found a strong
correlation between the number
of cavities his patients had in a
year and the number of apples
eaten….What is the lurking
variable?
Confounding Variable:
•May be a lurking variable
•One whose effects on the
response variable cannot be
separated from another possible
explanatory variable.
(Example will be
come later)
Beware the post-hoc fallacy
“To avoid falling for the post-hoc
fallacy, assuming that an observed
correlation is due to causation, you
must put any statement of
relationship through sharp
inspection.
Causation can not be established
“after the fact.” It can only be
established through well-designed
experiments.
Explaining Association
Strong Associations can generally be explained by
one of three relationships.
Causation:
x causes y
Common Response:
x and y are reacting to
a lurking variable z
Confounding:
x may cause y, but y may instead be
caused by a confounding variable z
Causation
Causation is not easily established.
The best evidence for causation comes from
experiments that change x while holding all other
factors fixed.
Even when direct causation is present, it is
rarely a complete explanation of an association
between two variables.
Even well established causal relations may not
generalize to other settings.
Common Response
“Beware the Lurking Variable”
The observed association between two variables may be
due to a third variable (z).
Both x and y may be changing in response to changes in z.
Consider the “Ice cream sales and Drowning”
example...does ice cream actually cause people to
drown? The common response was temperature
Confounding
Two variables are confounded when their
effects on a response variable cannot be
distinguished from each other.
The confounded variables may be either
explanatory variables or lurking variables.
Confounding
Confounding prevents us from drawing
conclusions about causation.
We can help reduce the chances of
confounding by designing a wellcontrolled experiment.
Causation, Confounding or
Common Response?
x=whether a person regularly attends religious
y=how long the person lives
Confounding
x=whether a person regularly attends religious
y=how long the person lives
Many studies have found that people who are
active in their religion live longer than nonreligious
people. But people who attend church or mosque
or synagogue also take better care of themselves
than nonattenders. They are less likely to smoke,
more likely to exercise, and less likely to be
overweight. The effects of these good habits are
confounded with the direct effects of attending
religious services.
Causation, Confounding or
Common Response?
x = mother’s body mass index
y = daughter’s body mass index
Causation
x = mother’s body mass index
y = daughter’s body mass index
A study of Mexican American girls aged 9 – 12
years recorded body mass index (BMI), a
measure of weight relative to height, for both the
girls and their mothers. People with high BMI are
overweight or obese.
Causation
x = mother’s body mass index
y = daughter’s body mass index
The study also measured hours of television,
minutes of physical activity, and intake of several
kids of food. The strongest correlation (r = 0.506)
was between the BMI of daughters and the BMI
of their mothers.
Causation
x = mother’s body mass index
y = daughter’s body mass index
Body type is in part determined by heredity.
Daughters inherit half their genes from their mothers.
As a result, there is a direct causal link between the
BMI of mothers and daughters. Yet the mother’s
BMIs explain only 25.6% (that is r2 again) of the variation
among the daughters’ BMIs. Other factors, such as diet and
exercise, also influence BMI. Even when direct causation is
present, it is rarely a complete explanation of an association
between two variables.
Causation, Confounding or
Common Response?
x = a high school senior’s SAT score
y = the student’s first-year college grade point
average
Common Response
x = a high school senior’s SAT score
y = the student’s first-year college grade
point average
Student who are smart and who have learned a lot tend
to have both high SAT scores and high college grades.
The positive correlation is explained by the common
response to students’ ability and knowledge.
Exercises
4.41: There is a high positive correlation: nations with
many TV sets have higher life expectancies. Could we
lengthen the life of people in Rwanda by shipping them
TVs?
4.42: People who use artificial sweeteners in place of
sugar tend to be heavier than people who use sugar.
Does artificial sweetener use cause weight gain?
4.43: Women who work in the production of computer
chips have abnormally high numbers of miscarriages.
The union claimed chemicals cause the miscarriages.
Another explanation may be the fact these workers
spend a lot of time on their feet.
Exercises-con’t
4.44: People with two cars tend to live longer than
people who own only one car. Owning three cars is even
better, and so on. What might explain the association?
4.45: Children who watch many hours of TV get lower
grades on average than those who watch less TV. Why
does this fact not show that watching TV causes low
grades?
Exercises-con’t
4.46: Data show that married men (and men who are
divorced or widowed) earn more than men who have
never been married. If you want to make more money,
should you get married?
4.47: High school students who take the SAT, enroll in an
SAT coaching course, and take the SAT again raise their
mathematics score from an average of 521 to 561. Can
this increase be attributed entirely to taking the course?