Galton's Problem Research Articles

The diffusion possibility method: a more general and simpler solution to Galton's problem1

A new statistical technique permits detection of the influence of certain types of diffusion on the results of a cross‐cultural analysis. The key tool is a “diffusion possibility matrix” which shows the possibility of diffusion occuring between each pair of societies in the sample. With the aid of such a matrix, several different kinds of clustering tests are described and demonstrated. The method has the advantage of greater flexibility and simplicity than previous methods, as well as greater statistical power.

Galton's Problem in Cross-National Research

Galton's problem raises questions about the nature of explanation in cross-national research using aggregate data. When political units such as states interact, to what extent can correlations between two traits or behaviors, such as socioeconomic development and political stability, be explained in terms of functional relationships within political systems, and to what extent are they the result of diffusion or borrowing among them? This article explores the logic of Galton's problem and then evaluates several empirical solutions to it, using data drawn from three different types of crossnational samples. The solutions juxtapose explanations based on internal (functional) relationships and external (diffusion) patterns, and suggest that previous research which has ignored diffusion may have led to incomplete or incorrect conclusions.

On Critical Appraisal of Solutions to Galton's Problem

Previous articleNext article No AccessDiscussion and CriticismOn Critical Appraisal of Solutions to Galton's ProblemJules de Leeuwe, David J. Strauss, and Martin OransJules de Leeuwe Search for more articles by this author , David J. Strauss Search for more articles by this author , and Martin Orans Search for more articles by this author PDFPDF PLUS Add to favoritesDownload CitationTrack CitationsPermissionsReprints Share onFacebookTwitterLinkedInRedditEmail SectionsMoreDetailsFiguresReferencesCited by Current Anthropology Volume 17, Number 3Sep., 1976 Sponsored by the Wenner-Gren Foundation for Anthropological Research Article DOIhttps://doi.org/10.1086/201781 Views: 1Total views on this site Citations: 1Citations are reported from Crossref Copyright 1976 The Wenner-Gren Foundation for Anthropological ResearPDF download Crossref reports the following articles citing this article:David Strauss, Martin Orans Residence and Descent Is Hyperdiffusional?, Behavior Science Research 13, no.11 (Sep 2016): 1–23.https://doi.org/10.1177/106939717801300101

Murdock-White Interdependence Alignment of Ethnographic Atlas Culture Clusters

The Murdock-White sampling alignment, prepared for their Standard Cross-Cultural Sample, is the procedure of choice for solving Galton's problem, in place of any of Naroll's alignments. In order to use the Mur dock-White alignment for societies other than the 186 in their sample, it is necessary to take advantage of the Loftin-Hill concordance, which cov ers the 862 societies of the 1967 Ethnographic Atlas. However, Loftin and Hill's original concordance is ambiguous with respect to the placement of 32 societies, including such well-known ones as the Rwala, the Sanussi, the French, the Hupa, the Yurok, and the Karok. Loftin and Hill also did not classify the Tzeltal or any of the dozens of Overseas European soci eties. This paper claims to resolve these difficulties and thus to make the full 1967 Ethnographic Atlas list available for the Murdock-White align ment procedure. A revised concordance is presented as an appendix.

Galton's Problem and HRAFLIB

Two aspects of Galton's problem are considered here—the tendency for cultural diffusion to inflate coefficients of correlation and also its tendency to inflate the number of independent cases for significance tests. Spatial autocorrelation is seen as a generally useful tool for measuring and control ling the influence of diffusion. The Strauss-Orans cluster reduction method reduces spatial autocorrelation in 2 x 2 matrices. In special cases, cluster reduction may eliminate Galton's problem entirely by eliminating spatial autocorrelation of key variables. Wirsing's second order partials reduce in flated correlation coefficients. The Orcutt-James correction reduces inflated sample sizes. Where none of these approaches is useful, Zucker's cluster difference test may be helpful. HRAF plans to apply these methods to its HRAFLIB computer program library.

The Standardized Diffusion Test

An accurate and flexible method for measuring cultural diffusion is presented. When the diffusion of pairs of traits is measured, the method constitutes a solution to Galton's problem. Application of the method to data on the association of patrilocal residence with patrilineal descent indicates that the association is based on diffusion rather than function.

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

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.

Galton's Problem, Autocorrelation, and Diffusion Coefficients

The linked pair solution to Galton's problem is examined from the per spective of the autocorrelation problem in economics. The estimated de grees of freedom, but not the correlations, are shown to be inflated due to diffusional and historical associations. An alternate form of the linked pair method is derived from the Orcutt-James solution to the autocorrelation problem. This technique permits unrestricted sampling of societies along a diffusion or geographic arc, and then provides a formula for calculating the effective number of nonredundant cases for statistical tests. The advantages and disadvantages of the method are discussed.

Partial Correlation as an Adjustment Procedure for Galton's Problem

This paper provides a critical evaluation of the procedure that Naroll has suggested for using partial correlation to control for the effects of diffusion on estimates of functional relationships. An examination of par tial correlation and Naroll's formula shows that they are not consistent. Hypothetical data are used to demonstrate that Naroll's formula does not provide good estimates of the true functional relationships.

Dominant Epistemological Presuppositions in the Use of the Cross-Cultural Survey Method [and Comments and Reply

This article subjects to critical analysis the epistemological conceptions which have dominated the way cross-cultural survey research has been carried out and propagated within the anthropological discipline. These conceptions may be characterized as inductivist and empiricist. This orientation is critized primarily from the point of view of Popper's concept of science. In this context, problems of concept formation and theory construction as well as Galton's problem are discussed.

Testing Some Assumptions of the Cross-Cultural Survey Method Regarding Sampling and Galton's Problem

Testing Some Assumptions of the Cross-Cultural Survey Method Regarding Sampling and Galton's Problem

Galton's Problem in a New Holocultural Study of Drunkenness

Galton's Problem in a New Holocultural Study of Drunkenness

Statistical Probabilities, Functional Relationships, and Galton's Problem

Statistical Probabilities, Functional Relationships, and Galton's Problem

A Comparison of Alignment Procedures for Tests of Galton's Problem

A Comparison of Alignment Procedures for Tests of Galton's Problem

Galton's Problem as Spatial Autocorrelation: Comments on Ember's Empirical Test

Galton's Problem as Spatial Autocorrelation: Comments on Ember's Empirical Test

Sampling Methods, Functional Associations, and Galton's Problem: A Replicative Assessament 1

Sixteen independent tests of the relationship between technological adap tation and settlement patterns provided material for testing sample methods and the interdependence of cases or Galton's problem. Our hypothesis that societies dependent upon agriculture tend to have fixed settlement patterns was strongly confirmed. Linked pair tests for Galton's problem indicated that sample neighbor scores were frequently similar, and we con cluded that these traits were hyperdiffusionally associated. A test for differences between sampling methods showed no significance, suggesting that sampling strategies (simple or stratified) do not significantly alter correlations. An attempt was made to test Galton's problem. Correlation magnitude differences between linked pair alignment strips of different widths were used. No significant differences were noted. Finally, an ap pendix provides sixteen samples arranged in linked pair alignments for future research(ers).

A Comment on "Sampling methods, functional associations, and Galton's problem: a replicative assessment," by James M. Schaefer et al

A Comment on "Sampling methods, functional associations, and Galton's problem: a replicative assessment," by James M. Schaefer et al

An Empirical Test of Galton's Problem

An Empirical Test of Galton's Problem

Stratified Sampling and Galton's Problem (A Comment on "Evaluation of a Stratified versus an Unstratified Universe of Cultures in Comparative Research," by Lenora Greenbaum)

Stratified Sampling and Galton's Problem (A Comment on "Evaluation of a Stratified versus an Unstratified Universe of Cultures in Comparative Research," by Lenora Greenbaum)

Population Pressure and the Social Evolution of Agriculturalists

Growth of population pressure is postulated to be a major determinant of human social evolution through the mechanism of competition for increasingly scarce subsistence resources. In terms of a model for societies practicing agriculture, inter- and intra-group competition for such natural resources is seen as leading to the evolution of more competitively successful cooperative units in descent (in classless societies) and in political structure, and to the evolution of class stratification. A scale for measuring population pressure in agricultural societies is proposed, and the prediction is made that a positive correlation should occur between the postulated population pressure scale and social forms in accordance with the theory. Tests are undertaken, in view of a reappraisal of Galton's problem, using all societies for which appropriate data are adequate in a universe of 1170 cultures. The results of the tests, presented as scatterplots, are consistent with the predictions based upon the theoretical model. The resource scarcity-competition model is successful in predicting evolution in descent as well as in political organization and class stratification.