Mighty Sifts: A Critical Appraisal of Solutions to Galton's Problem and a Partial Solution [and Comments and Replies]
Mighty Sifts: A Critical Appraisal of Solutions to Galton's Problem and a Partial Solution [and Comments and Replies]
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Mighty Sifts：对高尔顿问题的解决方案和部分解决方案的批判性评估[以及评论和回复]
作者：
David Strauss;M. Orans;J. A. Barnes;R. P. Chaney;J. de Leeuwe;M. Ember;Lenora Greebaum;Noboru Kawamata;F. D. Mccarthy;Charles W. Mcnett;R. Naroll;J. Rehak;R. Rohner;Masaaki Sakata;T. Schweizer;P. Tschohl
高尔顿的问题源于社会之间的历史联系，这使得统计独立性的准则不适用。由此产生的样本量的不确定性使得统计显著性的标准检验也不适用。此外，重复可能会影响结果。高尔顿问题的七个解决方案以前已经提供，我们发现他们都是无效的。他们中的三个人患有我们所说的“系统筛选谬误”。“我们所说的系统性筛选，是指通过每隔n个社会或使用固定的距离间隔，将一份按邻近和/或“文化相互联系”顺序排列的社会名单细化，从而产生一个社会样本。我们证明，这样的筛选只产生一个公正的表示，它是从原来的列表。另一个主要的错误是没有认识到随机的“历史”复制对相关性没有系统性的影响。此外，虽然一个正确的合法理论的“命中”（正确的预测）可能被“历史”复制过度复制，但这本身就是纯粹由历史联系产生的正相关性的情况。因此，合法的相关性和历史上产生的，但完全合法的虚假相关性之间没有分离，通过测试过度复制是可能的。另一个主要的错误是部分相关性的误用，在这种情况下，无聊的社会之间的“扩散相似性”被错误地视为与每个社会中观察到的变量相比较的部分决定因素。还注意到其他技术统计缺陷。作为一个积极的贡献，我们已经开发了一个部分解决高尔顿的问题，集群减少方法。这种方法进行了解释和实证结果检查。
Galton's problem arises from historical connection between societies, which makes the canon of statistical independence inapplicable. The resulting indeterminacy of sample size renders standard tests of statistical significance also inapplicable. In addition, replication might bias results. Seven solutions to Galton's problem have been previously offered, and we have found all of them invalid. Three of them suffer from what we have termed the "systematic-sift fallacy." By a systematic sift we mean a sample of societies produced by thinning down a list of societies arranged in order of propinquity and/or "cultural interconnection" by taking every nth society or by using a fixed distance interval. We demonstrate that such a sift yields only an unbiased representation of the original list from which it is drawn. Another major error is the failure to recognize that random "historical" replication has no systematic effect on correlations. Furthermore, though "hits" (correct predictions) for a correct lawful theory may be overreplicated by "historical" replication, this is ipso facto the case for positive correlations arising purely from historical connection. Therefore no separation between lawful correlations and historically produced, but law-fully spurious, correlations is possible by testing for over-replication. An additional major error is the misuse of partial correlations in which "diffusional resemblance" between neigh-boring societies is mistakenly treated as a partial determinant comparable to a variable observed in each society. Other technical statistical flaws are noted. As a positive contribution, we have developed a partial solution to Galton's problem, the cluster-reduction method. This method is explained and empirical results examined.