Simpson’s Paradox

Simpson’s Paradox

 

Simpson’s Paradox

 

A family member can go to one of two local hospitals for heart surgery.
Checking the history for the past year, you find that each of the two hospitals has performed cardiac surgery on 1000 patients. In hospital A 710 patients survived (71%). In hospital B 540 (54%) survived.
Based on the numbers presented, which hospital do you think is superior in cardiac surgery?

Surely hospital A is better, right?

Now, let’s look at more data. The below chart summarizes three categories of patients (those entering in fair, serious and critical condition) and the survival rate from surgery (in percent) for the two local hospitals.

Patient Entering Condition

Hospital A

Hospital B

Survivors from A (# and percent)

Survivors from B (# and percent)

Fair

700

100

600 or 86%

90 or 90%

Serious

200

200

100 or 50%

150 or 75%

Critical

100

700

10 or 10%

300 or 43%

Total

1000

1000

710 or 71%

540 or 54%

Looking at the data broken down in this way, we see that Hospital B has a higher success rate in all three categories of patients but when averaged all together, Hospital A has the higher overall survival rate. Based on the numbers presented, which hospital do you think is superior in cardiac surgery and why? Must be at least 75 words