Simpson's paradox is when a trend that appears in every subgroup reverses when the groups are combined, because group sizes and base rates differ. A classic case is a treatment that performs better in both mild and severe patient groups yet looks worse overall because it was given disproportionately to severe cases. The fix is to segment on the confounding variable rather than trusting the aggregate.
Why interviewers ask this
It is a direct test of whether you interrogate aggregates. Interviewers use it because business dashboards are aggregates by default, and an analyst who never segments will eventually report a reversed conclusion with total confidence. A real example from your own work is worth far more than the textbook admissions case.
How to structure your answer
- Define the reversal clearly with the mechanism, not just the name.
- Give one concrete example with the confounding mix.
- Explain the practical defense: segment before concluding.
- Say how you decide which variable to segment on.
- Note that the segmented view is not automatically the right one either.
Example answer
It is when each subgroup shows one direction and the pooled data shows the opposite, driven by uneven group sizes. I ran into a version of this comparing two acquisition channels. Channel A had a worse overall conversion rate, so the obvious move was to cut its budget. When I split by device, channel A converted better on both mobile and desktop. The reason the aggregate flipped was that channel A sent overwhelmingly mobile traffic, and mobile converts worse for everyone, so the channel was being penalized for its mix rather than its quality. Cutting it would have been the wrong call. Since then my default is to check the aggregate against two or three obvious segments before I present anything, usually device, geography, and new versus returning. I would add that segmenting is not automatically correct either. If you slice far enough you can find a story in noise, so I decide which variables to segment on based on what plausibly causes the outcome, not by hunting for the split that agrees with me.
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See how it worksFollow-up questions to expect
- How do you decide which variables to segment by?
- How do you avoid finding false patterns when slicing many ways?
- When is the aggregate number the right one to report?
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