Strange Expectations: A Dickens of a Problem

Pooling different data sets can produce artificial results that apply to neither of the original sets. We know this from Simpson’s paradox. But other paradoxes can arise as well, including ones that appear to show the probability of an event may be larger or smaller than each of its mutually exclusive and exhaustive component conditional probabilities. Of course, this cannot be. On the surface, however, the problematic scenarios presented in this column appear to suggest otherwise. The seeming paradoxes discussed in this column have real-world applications that merit recognition and discussion in the literature and the classroom.

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