Simpson’s paradox describes a phenomenon, in which a trend in a set of “unaggregated” data is reversed in the “aggregated” data. It occurs occasionally in statistics of social sciences, medical sciences and many other settings. Its explanations are limited to a single special case, or statistical, or framed in terms of contingency tables. Here we provide a mathematical explanation in a general context, by converting it to a problem of determining the definiteness of a quadratic form.

Simpson’s paradox, quadratic form.