session#5 Divényi János @divenyi.janos

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CASE STUDYelection poll

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)

QUESTIONMr. Allen needs to know whether he is going to win the election, so he ordersa poll. Which of the 3 outcomes wouldbe the most encouraging for him?(a) Y = 15, n = 20(b) Y = 115, n = 200(c) Y = 1046, n = 2000

Carl Morris (1987)

How to find answersto relevant questions

using data

QUESTION

DATA

ANALYSIS

PRESENTATION

QUESTION

DATA

ANALYSIS

P(A|B)conditional probability

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

”A statistician can have his head

in an oven and his feet in ice, and he will say that on the

average he feels fine.

17,9%

0,0%

10,0%

20,0%

30,0%

40,0%

50,0%

60,0%

70,0%

80,0%

90,0%

100,0%

average bottom 99% top 1%

Income real growthUSA 1993-2012

Source: Saez (2013)

17,9%

0,0%

10,0%

20,0%

30,0%

40,0%

50,0%

60,0%

70,0%

80,0%

90,0%

100,0%

average bottom 99% top 1%

Income real growthUSA 1993-2012

Source: Saez (2013)

17,9%

6,6%

86,1%

0,0%

10,0%

20,0%

30,0%

40,0%

50,0%

60,0%

70,0%

80,0%

90,0%

100,0%

average bottom 99% top 1%

Income real growthUSA 1993-2012

Source: Saez (2013)

E(Y|X) = a + bXlinear regression

if E(Y|X) is linearthe regression function is it

REGRESSIONGIVES COMPARISON

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%