The Question of Causation

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The Question of Causation

• YMS3e 4.3Establishing CausationAP Statistics

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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
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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?
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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)
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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.

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Explaining Association

• Strong Associations can generally be explained by
  one of three relationships.

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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.

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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

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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.

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Confounding

• Confounding prevents us from drawing conclusions
  about causation.
• We can help reduce the chances of confounding by
  designing a well-controlled experiment.

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Causation, Confounding or Common Response?

• xwhether a person regularly attends religious
  yhow long the person lives

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Confounding

• xwhether a person regularly attends religious
  yhow 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.
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Causation, Confounding or Common Response?

• x mothers body mass index
  y daughters body mass
  index

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Causation

• x mothers body mass index
  y daughters 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.
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Causation

• x mothers body mass index
  y daughters 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.
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Causation

• x mothers body mass index
  y daughters 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 mothers 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.
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Causation, Confounding or Common Response?

• x a high school seniors SAT score
  y the students
  first-year college grade point average

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Common Response

• x a high school seniors SAT score
  y the students
  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.
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Exercises

• 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?
• 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?
• 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.

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Exercises-cont

• 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?
• 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?

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Exercises-cont

• 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?
• 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?