probability that A occurs given that B has occurred
E(Y|X)
cond. expected value
expected value of variable Ygiven that X takes a given value
E(Y) = a + bX
linear regression
if E(Y|X) is linear
the regression function is it
The Case of Berkeley (1973)
University of California, Berkeleywas sued for bias against women
who had applied for admissionto graduate schools there.
Men Women
Applicants Admitted Applicants Admitted
ALL 2590 46% 1835 30%
ALL 2590 46% 1835 30%
Men Women
Applicants Admitted Applicants Admitted
ALL 2590 46% 1835 30%
DepartmentMen Women
Applicants Admitted Applicants Admitted
A
B
C
D
E
F
ALL 2590 46% 1835 30%
DepartmentMen Women
Applicants Admitted Applicants Admitted
A 825 62% 108 82%
B 560 63% 25 68%
C 325 37% 593 34%
D 417 33% 375 35%
E 191 28% 393 24%
F 272 6% 341 7%
ALL 2590 46% 1835 30%
DepartmentMen Women
Applicants Admitted Applicants Admitted
A 825 62% 108 82%
B 560 63% 25 68%
C 325 37% 593 34%
D 417 33% 375 35%
E 191 28% 393 24%
F 272 6% 341 7%
ALL 2590 46% 1835 30%
xkcd.com/552
Mr. Allen, the candidate for politicalParty A will run against Mr. Baker of Party B for office. Past races betweenthese parties for this office werealways close, and it seems that thisone will be no exception – Party A candidates always have gottenbetween 40% and 60% of the vote and have won about half of the elections.
Carl Morris (1987)
QUESTION
Mr. Allen needs to know whether he is going to win the election, so he ordersa poll. Which of three outcomes wouldbe the most encouraging for him?