Confoundle · a reasoning trap
Simpson's paradox
One choice can win in every single group, yet lose the moment you lump all the groups together. It sounds impossible, but it's real. It happens when the groups aren't a fair comparison: one side quietly got the easy cases, the other got the hard ones. So the big combined number says one thing while the group-by-group numbers say the opposite, and it's the big number that fools you.
The rule
An overall trend can reverse once you account for a lurking variable that's split unevenly between the groups.
What it looks like
Why it works
The 'combined' score isn't a fresh measurement; it's the group scores blended together, and bigger groups count for more. When one side is packed with easy cases and the other with hard ones, that blend pulls their combined scores in opposite directions. So one option can lead in the easy group and in the hard group, yet still trail overall, because it handled most of the hard cases, and its blended score sits closer to that lower number. The cure is a fair split: give both sides the same mix of easy and hard cases (exactly what a randomised trial does), and the reversal can't happen.
Source
See if it fools you
This page gives the answer away. The puzzle version shows you the same figures first and asks you to commit before the reveal.
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