Simpson Paradox

---

This applet requires Sun's Java VM 2 which your browser may perceive as a popup. Which it is not. If you want to see the applet work, visit Sun's website at http://www.java.com/en/download/index.jsp, download and install Java VM and enjoy the applet.

---

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:

1. y_bi/x_bi > y_ai/x_ai, i = 1, 2, whereas

2. (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.

Ratchet Effect

|Activities| |Contact| |Front page| |Contents| |Algebra| |Store|

Copyright © 1996-2012 Alexander Bogomolny