# Introduction to (log) Odds Ratio - University of Groningen

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Introduction to (log) Odds Ratio

Statistics and Methodology Anna Lobanova: a.lobanova@ai.rug.nl

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?

Students Teachers Total

Drink 90 20 110

Don't drink 10 80 90

Total 100 100 200

Group 1 = students, group 2 = teachers

Event ? 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?

Terminology & Notation:

A Two-way Contingency Table

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Drink

Students n11

Teachers n21

Total

n+1

Don't drink

Total

n12

n1+

n22

n2+

n+2

n

Terminology & Notation:

A Two-way Contingency Table

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response variable

explanatory variable

Drink Don't drink

Total

Students Teachers Total

n11 = 90 n12 = 10 n21 = 20 n22 = 80 n+1 = 110 n+2 = 90

n1+ = 100 n2+ = 100 n = 200

joint distribution

marginal distributions

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