Confounding

A popular approach, although not always recommended, is to use regression models to “adjust”

Here are the regression coefficients with a BB only model

(Intercept)          BB 
   326.8242      0.7126 

Note that the estimate for BB decreases

(Intercept)          BB          HR 
   287.7227      0.3897      1.5220 

Divide each team intro 10 strata, top 10%, second 20% etc… Then compute the correlation in each strata

• The more firemen are sent to a fire, the more damage is done.

• Children who get tutored get worse grades than children who do not get tutored

• In the early elementary school years, astrological sign is correlated with IQ, but this correlation weakens with age and disappears by adulthood.

From Peter Flom

• Admission data from Berkeley 1973 showed 44% men admitted compared to 30% women.

• All things being equal, the probability of this happening by chance is much less than 1 in a million.

        accepted rejected
males       1198     1493
females      557     1278

p-value= 1.056e-21

PJ Bickel, EA Hammel, and JW O'Connell. Science (1975)

• Closer inspection shows a paradoxical results.

• Here are the percent admissions by major:

  Major Male Female
1     A   62     82
2     B   63     68
3     C   37     34
4     D   33     35
5     E   28     24
6     F    6      7

• This is called Simpson's paradox

• Note there are “easy” majors and some confounding

The average difference by major is 3.5% higher for women.