4'3 Establishing Causation

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4.3 Establishing Causation
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Causation

• We would like to think that the change in the
  explanatory variable causes a change in the
  response variable.

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3 ways to explain association

• 1st way to explain association
• CAUSATION- when there is an association ( or -)
  between two variables, and it is direct
  cause-and-effect relationship.
• Ex calories consumed/weight

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The dashed line shows the association. The solid
line shows the direct link between x and y.
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Example of Causation

• A study showed that there is a strong correlation
  (r.505) between mothers BMI and their
  daughters BMI.
• Other variables were controlled like hrs. of TV,
  physical activity, etc.

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Example of Causation

• In this BMI experiment, the mothers BMI only
  explained 25.6 of the variability among the
  daughters BMI.
• Even when direct causation is present, it is
  rarely a complete explanation of an association
  between 2 variables!

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Example of Causation

• If we hold all other factors fixed, and just
  change the x-variable, if the y-variable changes,
  then we have good reason to think x caused a
  change in y!

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Example of Causation

• A study gave rats different amount of saccharin
  and larger amounts caused tumors in the rats
  bladders.
• Though we dont experiment on humans, a study
  of human consumption of different amounts of
  saccharin showed little association between
  saccharin and tumors
• Even well-established casual relations may not
  generalize into other settings!

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3 ways of explaining association

• 2nd way Common Response
• Common response is when a lurking variable is
  present and the association between x and y is
  explained by some lurking variable, z.

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Changes in both x and y are caused by changes in
a lurking variable, z. They are both influenced
by z so an association is present.

• There actually may be NO DIRECT LINK between x
  and y, but z makes it appear that there is!
• If there is an association between x and y,
  lurking variable z makes it appear stronger!

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Example of Common Response
No direct link between SAT scores and grades in
college

• X students SAT scores
• Y high grades in college
• Z students ability and knowledge (lurking
  variable)

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Example of Common Response