Warm Up I. Pilots or Senators: Which team has played better? vs. East vs. West vs. East vs. West WINSLOSSES PCT. WINS LOSSES PCT. WINSLOSSES PCT. WINS LOSSES PCT. PILOTS SENATORS __ ) 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 Gender 4 yr private 4 yr public Community Male579 Female ) Identify the row and column variables 2) Find the marginal distributions by percents 3) Find the conditional distribution of males and females going to a community college 4) Find the conditional distribution of community college attendees who are male and female.

Consider the following list of sixteen factors. Eight of the factors have a strong correlation (+ or -) with test scores; the other eight don’t 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 child has highly educated parents. The child’s family is intact. The child’s family is intact. The child’s parents have high socioeconomic status. The child’s parents have high socioeconomic status. The child’s parents recently moved into a better neighborhood. The child’s parents recently moved into a better neighborhood. The child’s mother was 30 or older at the time of the first child’s birth. The child’s mother was 30 or older at the time of the first child’s birth. The child’s mother didn’t work between birth and kindergarten. The child’s mother didn’t work between birth and kindergarten. The child had low birth weight. The child had low birth weight. The child attended Head Start. The child attended Head Start. The child’s parents speak English in the home. The child’s parents speak English in the home. The child’s parents regularly take him/her to museums. The child’s parents regularly take him/her to museums. The child is adopted. The child is adopted. The child is regularly spanked. The child is regularly spanked. The child’s parents are involved in the PTA. The child’s parents are involved in the PTA. The child frequently watches television. The child frequently watches television. The child has many books in his home. The child has many books in his home. The child’s parents read to him nearly every day. The child’s parents read to him nearly every day. Which ones correlate with test scores? Which ones correlate with test scores?

Lurking Variables Often the relationship between 2 variables is strongly influenced by one or more 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? 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?

4.3: Establishing Causation (Types of Associations) Causation: Changes in x cause changes in y Causation: Changes in x cause changes in y Common response: Both x and y respond to changes in some unobserved variable 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. Confounding: The effect of x on y is hopelessly mixed up with the effects of other variables.

Causation Examples of observed associations between x and y 1) x = mother’s body mass index y = daughter’s body mass index y = daughter’s body mass index 2) x = amount of artificial sweetener saccharin in a rat’sdiet y = count of tumors in a rat’s bladder

Careful: A strong association is not necessarily causation! An article in a woman’s mag reported that mother’s 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? An article in a woman’s mag reported that mother’s 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?

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

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 worker’s income Confounding

. 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). 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? YEARMinistersRum