Simpson's Paradox

In 1973, UC Berkeley was accused of gender discrimination. The data looked like an ironclad case: overall admission rate — men 44%, women 35%.

But when statistician Peter Bickel broke it down by department, he found that in 85 departments, most departments actually favored admitting women. Where did the gap come from? Women tended to apply to departments with lower admission rates (humanities, social sciences), while men tended to apply to departments with higher admission rates (engineering, physics).

The aggregate numbers showed men had an advantage. The grouped numbers showed no discrimination. The two conclusions were completely opposite.

This is Simpson's Paradox: **aggregate data shows one trend, but when broken into groups, each group shows the opposite trend.**

This paradox isn't an academic curiosity. It happens every day in the real data of the restaurant and hospitality industries. And every time you make decisions based on the "overall rating," you might be falling into the same trap.

Your 4.5 → 4.2 is the same. The overall score is declining. But if you separate lunch and dinner service, dinner ratings are actually rising — climbing from 4.5 to 4.7, because you brought in a new head chef last month and dinner quality noticeably improved. It's the influx of new lunch customers dragging down the overall average — and the increase in lunch traffic is exactly why your revenue grew 22%.

The aggregate numbers tell you "decline." The grouped numbers tell you "growth." You've been looking at the wrong one.

This isn't your fault. The human brain naturally gravitates toward looking at aggregate numbers — it's more efficient from an evolutionary standpoint. But the value of data analysis lies precisely in overcoming intuition and asking a counterintuitive question: "If I break this apart, is the story still the same?"