Simpson Paradox from Interactive Mathematics Miscellany and Puzzles

Cut the knot: learn to enjoy mathematics

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Simpson Paradox

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Vector algebra provides a simple explanation to the Simpson paradox.

With the help of the above applet, it is easy to find four vectors A_i = (x_ai, y_ai) and B_i = (x_bi, y_bi), i = 1, 2, such that:

y_bi/x_bi > y_ai/x_ai, i = 1, 2, whereas
(y_b1 + y_b2)/(x_b1 + x_b2) < (y_a1 + y_a2)/(x_a1 + x_a2).

1. means that Slope(B₁) > Slope(A₁) and Slope(B₂) > Slope(A₂). However, this does not imply the same inequality for the sums: Slope(B₁ + B₂) > Slope(A₁ + A₂) may not be true.

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