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Statistical Paradoxes and Fallacies

This session focusses on some paradoxes and fallacies that have been encountered in statistical research. In particular I would like to consider two: Simpson’s paradox and the regression fallacy. (also known as Galton's fallacy)

Simpson’s paradox (or Yule-Simpson effect). How every component of a statistical aggregate can move in the opposite direction from the aggregate. Simpson’s paradox happens quite frequently in applied work, but is often missed. Real world examples have occurred in: education results; voting (eg the vote on the Civil Rights bill in US Congress in 1964); the effect of smoking on low birth weight; .

The Regression Fallacy (Galton’s fallacy). The regression fallacy is a basic property of a bivariate distribution. If the two variables are at different points in time, regression results can lead to highly misleading inferences about processes occurring over time. This fallacy is associated with the name of Francis Galton who thought he had detected evidence of a process of convergence towards the mean, what he called ‘regression to mediocrity’. When he observed this in human populations

Real world examples include: Galton’s example of regression towards mediocrity in stature (mid-parent height and children’s height); the hypothesis of economic convergence of countries based on international cross-sectional regressions.

Illustrative Reading:

Galton, Francis (1886), “Family Likeness in Stature”, Proceedings of the Royal Society of London, 1886, 42-72.

Quah, Danny, (1993), "Galton's Fallacy and Tests of the Convergence Hypothesis", The Scandinavian Journal of Economics 95 (4): 427–433.

Friedman, Milton, (1992) “Do old fallacies ever die?”, Journal of Economic Perspectives, 30 (4): 2129–2132.

Wodon, Quentin and Shlomo Yitzhaki (2006), “Convergence forward and backward?”, Economics Letters, 92(1), 47-51.