Does Association Imply Causation

1
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
  income
• This figure (Moore McCabe) gives three possible
  scenarios explaining a found association between
  a response variable y and an explanatory variable
  x

2

• 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)

3
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
  relationship.
• What is the lurking variable in these two
  examples?

• 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.

4
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.
5
Lurking vs. confounding, association
vs.causation

• 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
  causation.
• Only careful experimentation can show causation -
  but see the next example

6
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?