Simpson’s – the Paradox!
First Two Years
Player Hits
At bats
A
B
100
400
40
120
Second Two Years
Player Hits
At bats
A
B
400
100
80
10
Batting
average
Batting
average
First Two Years
Player Hits
At bats
Batting
average
A
B
100
400
.40
.30
40
120
Second Two Years
Player Hits
At bats
Batting
average
A
B
400
100
.20
.10
80
10
All Four Years
Player Hits
At bats
Batting
average
A
B
500
500
.24
.26
120
130
How does that happen?
Simpson’s – the Paradox!
Simpson’s paradox: occurs where a
comparison can be reversed when more
than one group is combined to form a
single group.
The effect of another variable,
sometimes called a lurking variable, is
masked when the groups are combined.

If a/b > c/d and p/q > r/s, then
◦ it is true that a/b + p/q > c/d + r/s.
◦ it is not necessarily true that
(a+p)/(b+q) > (c+r)/(d+s).

Text Problems –Simpson’s Paradox – Excel