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Does Association Imply Causation


of saccharin in a rat's diet, y=# of tumors in rat's bladder. x=student's SAT score as a HS senior, y=1st ... x=whether a person attends religious services, ... – PowerPoint PPT presentation

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Title: Does Association Imply Causation

Does Association Imply Causation?
  • Sometimes, but not always! What about
  • xmother's BMI, ydaughter's BMI
  • xamt. of saccharin in a rat's diet, y of
    tumors in rat's bladder
  • xstudent's SAT score as a HS senior, y1st year
    GPA in college
  • xwhether a person attends religious services,
    ylength of life
  • x years education a workder has, yworker's
  • This figure (Moore McCabe) gives three possible
    scenarios explaining a found association between
    a response variable y and an explanatory variable

  • Association between x and y can certainly be
    because changes in x cause y to change - but
    even when causation is present, there are still
    other variables possibly involved in the
    relationship. (first ex. above)
  • Be careful of applying a causal relationship
    between x and y in one setting to a different
    setting (second example shows a causal
    relationship in rats - does it extend to humans?)
  • Common response is an example of how a "lurking
    variable" can influence both x and y, creating
    the association between them (see third example
    on SAT/GPA)
  • Confounding between two variables arises when
    their effects on the response cannot be
    distinguished from each other - the confounding
    variables can either be explanatory or lurking
    (see the last two examples above)

Lurking variables
  • A lurking variable is a variable not included in
    the study design that does have an effect on the
    variables studied.
  • Lurking variables can falsely suggest a
  • What is the lurking variable in these two
  • Strong positive association between number of
    firefighters at a fire site and the amount of
    damage a fire does.
  • Negative association between moderate amounts
    of wine drinking and death rates from heart
    disease in developed nations.

There is quite some variation in BAC for the same
number of beers drunk. A persons blood volume is
a factor in the equation that we have overlooked.
The scatter is much smaller now. Ones weight
was indeed influencing the response variable
blood alcohol content.
Lurking vs. confounding, association
  • A lurking variable is a variable that is not
    among the explanatory or response variables in a
    study and yet may influence the interpretation of
    relationships among those variables.
  • 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. But you often see the terms lurking
    and confounding used interchangeably
  • Association and causation
  • Association, however strong, does NOT imply
  • Only careful experimentation can show causation -
    but see the next example

Establishing causation It appears that lung
cancer is associated with smoking. How do we
know that both of these variables are not being
affected by an unobserved third (lurking)
variable? For instance, what if there is a
genetic predisposition that causes people to both
get lung cancer and become addicted to smoking,
but the smoking itself doesnt CAUSE lung cancer?