Simpson's paradox

Simpson's paradox occurs when a relationship between two variables holds in each of several subgroups but reverses when the subgroups are aggregated into one. A treatment can appear to work better than an alternative within every individual patient subgroup, yet appear worse overall once the groups are pooled, because the groups differ in size or composition in a way that swamps the within-group pattern.

The paradox arises from a lurking or confounding variable, often group size or a demographic factor, that is unevenly distributed across the subgroups being compared. Aggregating hides that imbalance, making the combined correlation or comparison misleading even though each individual slice of the data tells a consistent, opposite story.

Simpson's paradox matters because it is a direct warning against trusting an aggregate number without checking whether it holds up when the data is broken down by relevant segments, such as region, device, or customer tier. It is closely related to selection bias and spurious correlation, and is a common cause of dashboards that seem to contradict what a deeper analysis shows. The practical safeguard is to always check whether a headline trend is consistent across the major subgroups that make up the total, not just present in the combined figure.