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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Example 1: Let's use odds ratio to find out!
Students Teachers Total
Drink n11 = 90 n21 = 20 n+1 = 110
Don't drink n12 = 10 n22 = 80 n+2 = 90
Total n1+ = 100 n2+ = 100 n = 200
Step 1: the odds of a student drinking beer is 90 to 10 or 9/1 and the odds of a teacher drinking beer is 20 to 80 or 1/4 = 0.25:1
Step 2: the probability of success for every cell is
11 = n11/n1+ = 90/100 = 0.9 21 = n21/n2+ = 20/100 = 0.2
12 = n12/n1+ = 10/100 = 0.1 22 = n22/n2+ = 80/100 = 0.8
Step 3: Odds Ratio () = 0.9 / 0.1 = 0.72 = 36
0.2 / 0.8 0.02
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11 22
Odds Ratio () =
21 12
Inference from odds ratio:
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If
Then
odds ratio = 1
the event is equally likely in both groups
odds ratio > 1
the event is more likely in Group 1
odds ratio < 1
the event is more likely in Group 2
the greater the number the stronger the association
is never a negative number
In example 1:
odds ratio = 36
students are much more likely to drink beer than teachers!
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