Lord's Paradox Revisited - (On Lord! Kumbaya!)
CALIFORNIA UNIV LOS ANGELES DEPT OF COMPUTER SCIENCE
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Among the many peculiarities that were dubbed paradoxes by well meaning statisticians, the one reported by Frederic M. Lord in 1967 has earned a special status. Although it can be viewed, formally, as a version of Simpsons paradox Arah, 2008 Tu et al., 2008 Pearl, 2014 its reputation has gone much worse. Unlike Simpsons reversal, Lords is easier to state, harder to disentangle Wainer and Brown, 2007 and, for some reason, it has been lingering for almost four decades, under several interpretations and re-interpretations Holland and Rubin, 1983, and it keeps coming up in new situations and under new lights van Breukelen, 2013 Senn, 2006 Eriksson and Haggstrom, 2014. Most peculiar yet, while some of its variants has received a satisfactory resolution Glymour, 2006 Hernandez-Diaz et al., 2006, the original version presented by Lord, to the best of my knowledge, has not been given a proper treatment, not to mention a resolution. The purpose of this paper is to trace back Lords paradox from its original formulation, resolve it using modern tools of causal analysis, explain why it resisted prior attempts at resolution and, Finally, address the general methodological issue of whether adjustments for pre-existing conditions is justified in group comparison applications.
- Statistics and Probability