Welcome back to Numberholic! I’m your host, Sejari, and it’s always a pleasure to have you here. Today, we’re diving into the seventeenth episode of Proven Yet Hard to Believe.
Last time, I talked about Aristotle’s paradox. But I started to wonder—if we only focus on paradoxes that are too theoretical or full of sophistry, people might dismiss them as nothing more than clever wordplay with no real connection to everyday life. So today, I’d like to introduce a modern paradox instead.
It’s known in statistics as Simpson’s Paradox.
Let me explain with a simple example. Suppose two friends are considering getting a nose job.
One of them, Emma, shows the following data about two doctors:
| / | Dr. Taylor | Dr. Morgan |
|---|---|---|
| Surgeries Performed | 700 | 700 |
| Successful Surgeries | 625 | 635 |
| Success Rate | 89.2% | 90.7% |
Which doctor should you choose? Obviously, Dr. Morgan, right?
Then the other friend, Lily, presents this set of data:
| Patient Type | Dr. Adams | Dr. Bennett |
|---|---|---|
| First-Time Patients | 200 (100% success) | 500 (95% success) |
| Revision Patients | 500 (85% success) | 200 (80% success) |
Now which doctor would you choose? Looking at both first-time and revision patients, Dr. Adams appears to have the better success rate in each category. So, should we go with Dr. Adams?
But here’s the twist: Dr. Adams is actually Dr. Taylor, and Dr. Bennett is Dr. Morgan. Dr. Adams, a.k.a. Dr. Taylor, handled a much larger number of revision surgeries, which are more difficult, and that’s why their overall success rate appears lower.
Surprising, right? Even in situations that seem mathematically clear-cut, unexpected problems or contradictions can arise. This is the essence of Simpson’s Paradox.
That’s all for today’s episode of Proven Yet Hard to Believe! Until next time, keep exploring, keep questioning, and stay Numberholic!