Simpson’s paradox refers to a phenomenon whereby the association between a pair of variables (X, Y ) reverses sign upon conditioning of a third variable, Z, regardless of the value taken by Z. If we partition the data into subpopulations, each representing a specific value of the third variable, the phenomenon appears as a sign reversal between the associations measured
in the disaggregated subpopulations relative to the aggregated data, which describes the population as a whole.