Introduction to (log) Odds Ratio

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Introduction to (log) Odds Ratio

Statistics and Methodology

Anna Lobanova: a.lobanova@ai.rug.nl

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Who is more likely to drink beer

on Queen¡¯s Day - students or

teachers?

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Example: Who is more likely to drink beer on Queen¡¯s Day students or teachers?

Drink

Don¡¯t drink

Total

Students

90

10

100

Teachers

20

80

100

Total

110

90

200

Group 1 = students, group 2 = teachers

Event ¨C drinking beer at Queen¡¯s Day

Question: Is one group more likely to drink beer on

Queen¡¯s Day than the other group? Or is this event

independent of professional status?

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Terminology & Notation:

A Two-way Contingency Table

Drink

Don¡¯t drink

Total

Students

n11

n12

n1+

Teachers

n21

n22

n2+

Total

n+1

n+2

n

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Terminology & Notation:

A Two-way Contingency Table

explanatory

variable

response variable

Drink

Don¡¯t drink

Students

n11 = 90

n12 = 10

n1+ = 100

Teachers

n21 = 20

n22 = 80

n2+ = 100

Total

n+1 = 110

n+2 = 90

n = 200

joint distribution

Total

marginal distributions

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