Lord's Paradox Revisited - (Oh Lord! Kumbaya!)
Lord's Paradox Revisited - (Oh Lord! Kumbaya!)
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DOI：
10.1515/jci-2016-0021
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发表时间：
2016-09-01
影响因子：
1.4
通讯作者：
Pearl, Judea
中科院分区：
文献类型：
--
作者：
Pearl, Judea
在许多被善意的统计学家称为“悖论”的特性中，弗雷德里克·M·1967年，他获得了一个特殊的地位。虽然它可以被正式地看作是辛普森悖论的一个版本，但它的名声已经变得更糟了。与辛普森的逆转不同，洛德的逆转更容易陈述，更难理清，而且，出于某种原因，它在几种解释和重新解释下徘徊了近40年，并且在新的情况下不断出现，在新的光线下。最奇怪的是，虽然它的一些变体已经得到了令人满意的解决，但洛德提出的原始版本，据我所知，还没有得到适当的处理，更不用说解决了。本文的目的是追溯洛德悖论的原始表述，使用现代因果分析工具解决它，解释为什么它抵制了先前的解决尝试，最后，处理一般性方法问题，即在群组比较应用中是否有理由对先前存在的条件进行调整。
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, its reputation has gone much worse. Unlike Simpson's reversal, Lord's is easier to state, harder to disentangle and, for some reason, it has been lingering for almost four decades, under several interpretations and re-interpretations, and it keeps coming up in new situations and under new lights. Most peculiar yet, while some of its variants have received a satisfactory resolution, 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 preexisting conditions is justified in group comparison applications.