AP Statistics

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AP Statistics

• Causation
• Relations in Categorical Data

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HW Questions???
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Causation

• The old adage, Correlation does not necessarily
  imply causation.
• Many times in statistics we can find a
  connection or a correlation or an association
  between two variables, it is more difficult to
  prove that the explanatory actually causes the
  response variable to respond.

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Examples

• X number of complete passes a quarterback
  throws
• Y passing yardage for the quarterback
• Its reasonable to assume that the more complete
  passes he throws, the more yards hell rack up.

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Example 2

• Xthe number of ounces of alcohol consumed
• YFine motor skills abilities
• Again, its reasonable to assume the x is
  actually causing y to respond.

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Common Response

• Two variables show a strong association because a
  third variable is causing both of them to
  respond.
• XA students ACT score
• Y A students SAT score
• Its fair to assume that ones intelligence, or
  lack of it, will cause high, or low, scores on
  both tests. Having a high ACT score doesnt
  cause the SAT score to be high.

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Confounding

• Two variables are confounded when their effect on
  a response variable cannot be distinguished from
  each other.
• It looks like x is causing y, but another
  variable z is also acting on y, and its hard to
  sort out who is doing what.

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Example 1

• X of mentos dropped into the soda bottle
• Y height of soda spray
• One might think that x causes y to respond, more
  mentos higher spray, but Z the temperature of
  the soda is also changing, and now you cant tell
  what did what.

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Example 2

• X latitude at which a person lives
• Y lifespan
• The variables are associated, but its hard to
  know if living at a higher latitude causes you to
  live longer, or if, it just happens that poorer
  countries tend to be in the tropics and its the
  poverty that is reducing the life span.

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How to establish causation???

• You need a controlled experiment, where the
  effects of lurking variables are controlled and
  minimized. See chapter 5!!

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Relations in Categorical Data

• What if we want to see if there is an association
  among categorical data? Obviously we cant make
  a scatterplot and compute the correlation, do a
  regression, etc.
• We make a two way table.

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Example 1 College Students
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Conditional and Marginal Distribution

• The Marginal Distribution is the distribution of
  one variable alone, that is a column total out of
  the total total. Ex. of males in college.
• The Conditional Distribution is the distribution
  of one variable across another variable.
  Example, of Women among 15 17 year olds.

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Looking for association

• If age does not have any effect on gender in
  college, then wed expect the conditional
  percentages to be roughly equal. If there is a
  big disparity, then we might conclude that age
  and gender in college are connected.
• Compute the conditional distributions for gender
  on age.

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Do Medical Helicopters Save Lives?

• A businessman is trying to cut costs to a
  hospital and knows that the helicopter program is
  quite expensive. He gets some data on whether or
  not the program is effective.
• ____________Helicopter Road
• Victim died 64 260
• Victim survived 136 840
• Total 200 1100

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Doesnt look good

• The conditional distributions for death on
  vehicle type is 64/200 32 on the helicopter,
  and 260/1100 24 on the road.
• As the hospital statistician, what might you do
  to try and save the helicopter program?? i.e.
  what lurking variables are out there?

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Statistics to the Rescue

• Since helicopters are more likely to respond to
  serious accidents
• Serious Accidents Less Serious
• Helicopter Road Helicopter Road
• Died 48 60 16 200
• Survived 52 40 84
  800
• Total 100 100 100
  1000

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Simpsons Paradox

• The reversal of the direction of a comparison or
  association when data from several groups are
  combined to form a single group.
• I.E. when you have data that isnt parsed out for
  various lurking variables, it might not be the
  true reprsentation.

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Homework

• 4.33, 4.36, 4.37 4.52 54, 4.60