Warm Up

1
Warm Up

• I. Pilots or Senators Which team has played
  better?
• vs. East vs. West
• WINS LOSSES PCT. WINS LOSSES
  PCT.
• PILOTS 4 1 .800 3 7 .300
• SENATORS 7 3 .700__ 1 4 .200
• 1) Make a new table of the teams overall
  performance (wins/losses/pct.)
• 2) Which team had a better winning percentage
  when divvied up by East/West division?
• 3) Which team had a better overall winning
  percentage?
• 4) What happened? What is this called?
• 5) What do you notice about team records that
  might cause this?
• II. Consider the following two-way table
• Type of college

2
Consider the following list of sixteen factors.
Eight of the factors have a strong correlation (
or -) with test scores the other eight dont
seem to matter. Its taken from the 2005 best
selling book Freakanomics. Try to guess which are
which

• The child has highly educated parents.
• The childs family is intact.
• The childs parents have high socioeconomic
  status.
• The childs parents recently moved into a better
  neighborhood.
• The childs mother was 30 or older at the time of
  the first childs birth.
• The childs mother didnt work between birth and
  kindergarten.
• The child had low birth weight.
• The child attended Head Start.
• The childs parents speak English in the home.
• The childs parents regularly take him/her to
  museums.
• The child is adopted.
• The child is regularly spanked.
• The childs parents are involved in the PTA.
• The child frequently watches television.
• The child has many books in his home.
• The childs parents read to him nearly every day.
• Which ones correlate with test scores?

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Lurking Variables

• Often the relationship between 2 variables is
  strongly influenced by one or more lurking
  variables.
• Ex Studies show that men who complain of chest
  pain are more likely to get detailed tests and
  aggressive treatment such as bypass surgery than
  are women with similar complaints. Is this
  association between gender and treatment due to
  discrimination?

4
4.3 Establishing Causation(Types of
Associations)

• Causation Changes in x cause changes in y
• Common response Both x and y respond to changes
  in some unobserved variable
• Confounding The effect of x on y is hopelessly
  mixed up with the effects of other variables.

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CausationExamples of observed associations
between x and y

• 1) x mothers body mass index
• y daughters body mass index
• 2) x amount of artificial sweetener saccharin
  in a rats diet
• y count of tumors in a rats bladder

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Careful A strong association is not necessarily
causation!

• An article in a womans mag reported that
  mothers who nurse their babies feel more
  receptive toward their infants than mothers who
  bottle-feed. The author concluded that
  breast-feeding (x) led to a more positive
  attitude (y) toward the child. Problems with this?

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Common Response

• 1) x Ice Cream Sales
• y of shark attacks in swimmers
• 2) x Skirt Length
• y Stock Prices
• 3) x of cavities in elementary school kids
• y vocabulary knowledge
• 4) x a high school seniors SAT score
• y the students first-year college grade
  point
• average
• 5) x monthly flow of money into stock market
  funds
• y monthly rate of return for the stock
  market

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Confounding

• CONFOUNDING ONLY EXISTS if there is CONFUSION
  about whether changes in the confounding variable
  on the explanatory variable are leading to
  observed changes in the response variable.
• 1) x whether a person regularly attends
  religious services
• y how long the person lives
• 2) x the number of years a worker has
• y the workers income

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.

• Example of a (spurious) correlation between the
  number of Methodist ministers in New England and
  the amount of Cuban rum imported to Boston over
  the years (by of barrels).
• 1) Calculate r
• 2) Is the increasing number of ministers causing
  people to drink more? What could be the lurking
  variable?
• 3) What type of association is this?