 Simpson’s Paradox can occur for various types of data, but classically, it is formulated with respect to \(2\times2\) contingency tables. Let \(D_i = (a_i, b_i, c_i, d_i)\) be a four-dimensional vector of real numbers representing the \(2\times2\) contingency table for treatment and success in the i-th subpopulation, and let 