Lord's Paradox Revisited - (On Lord! Kumbaya!)
Abstract
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 Simpson's paradox (Arah, 2008; Tu et al., 2008; Pearl, 2014) its reputation has gone much worse. Unlike Simpson's reversal, Lord's 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 Lord's 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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Oct 03, 2014
- Accession Number
- ADA615058
Entities
People
- Judea Pearl
Organizations
- University of California, Los Angeles