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Simpson's Paradox

Simpson’s paradox can be encountered in a contingency table analysis when comparing the results from the marginal table to the results from the conditional tables. If Simpson's Paradox is present, the odds ratio for the marginal table is opposite that of those for the conditional tables.
Simpson’s paradox is not a paradox in the strictest sense of the word. Instead, it is the
result of the researcher not having identified a variable (or variables) that have an effect on
the risk, or the outcome, of the experiment.

This is related to confounding, where an extraneous variable wholly or partially accounts for
an apparent effect, or that masks an underlying true association.
(See Agresti problem 3.1)