Mighty Sifts: A Critical Appraisal of Solutions to Galton's Problem and a Partial Solution [and Comments and Replies]

• Published in: Current anthropology 1975-12, Vol.16 (4), p.573-594
• Main Authors: Strauss, David J., Orans, Martin, Barnes, J. A., Chaney, Richard Paul, de Leeuwe, J., Ember, Melvin, Greebaum, Lenora, Kawamata, Noboru, McCarthy, F. D., McNett, Charles W., Naroll, Raoul, Rehak, Jan, Jan ?ehák, Rohner, Ronald P., Sakata, Masaaki, Schweizer, Thomas, Tschohl, Peter
• Format: Article
• Language: English
• Subjects: Applied statistics; Correlation coefficients; Correlations; Cross cultural studies; Cultural anthropology; Cultural studies; Ethnography; Neighborhoods; Null hypothesis; Statistics
• ISSN: 0011-3204; 1537-5382
• DOI: 10.1086/201620

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.