Simpson’s Paradox

A paradox in probability and statistics, in which a trend appears in different groups of data but disappears or reverses when these groups are combined.

You have two groups of related data that show similar correlations. But you combine these two data sets and — the correlation reverses! What the hell is going on?

The likely culprit is that you didn’t consider or underestimated the impact of a variable in the data set. Let’s look at an example.

You are a sales manager and have two salesmen. These guys are your closers and one of their KPIs is win rate. So let’s have a look at the data:

Salesman A:

• 50 deals closed
• 40 deals won

Salesman B:

• 25 deals closed
• 15 deals won

Who has the better win rate? Salesman A has a win rate of 90% and Salesman B has a win rate of 60%. According to the data, Salesman A is a 30% better salesman than Salesman B.

You dig deeper and discover that the win rates lump together enterprise and mid-market deals. Enterprise deals are critical to company success so you decide to unpack the data.

Salesman A:

• 10 enterprise deals closed
• 2 enterprise deals won
• 40 mid-market deals closed
• 38 mid-market deals won

Salesman B:

• 10 enterprise deals closed
• 5 enterprise deals won
• 15 mid-market deals closed
• 5 mid-market deals won

In a combined view of the data, Salesman A is the better salesman by 30%. In an unbundled view of the data, Salesman B is the better salesman by 30%. The lurking variable affecting the correlation here is the deal type.

All this probably makes sense to you. You have unbundled variables in your work to make better decisions. Then why is this important?

It’s important because Simpson’s Paradox provides a label to this phenomenon. By giving it a name, you increase your ability to identify and effectively act on the phenomenon. It serves as a reminder to check your analysis before jumping to a conclusion. A name also makes it easier to share the phenomenon with others, like I am sharing it with you!