1. SIMPSON’S PARADOX

2. Simpson’s Paradox A and B represent two treatments for a terrible disease. In the following study 26 people with this disease were treated. Some chose treatment A, others chose B. The following data was collected.
1 man treated with A recovered.
4 men treated with A did not recover.
4 women treated with A recovered.
5 women treated with A did not recover.
3 men treated with B recovered.
7 men treated with B did not recover.
1 woman treated with B recovered.
1 woman treated with B did not recover.

3. Treatment A
Treatment B
Cure rate=3/10=30%
Cure rate = 1/5=20%
Cure rate=1/2=50%
Cure rate=4/9=44%
Treatment B has a higher cure rate
for men AND
for women.

4. But A has a higher cure rate overall !
Treatment A
Treatment B
Cure rate=3/10=30%
Cure rate = 1/5=20%
B has a higher cure rate
for men
Cure rate=1/2=50%
Cure rate=4/9=44%
B has a higher cure rate
for women
5 of the total number of 14 people
treated with A survived.
Cure rate=5/14=36%
4 of the total number of 12 people
treated with B survived.
Cure rate=4/12=33%
But A has a higher cure rate overall !

5. A MOST INGENIOUS PARADOX