Once proper adjustments are made that deal with external dependencies, then the axioms of probability theory concerning statistical independence will apply.
By the early 20th century unilineal evolutionism was abandoned and along with it the drawing of direct inferences from correlations to evolutionary sequences.
Statistician William S. Gosset in 1914 developed methods of eliminating spurious correlation due to how position in time or space affects similarities.
Methods developed by geographers that measure and control for spatial autocorrelation[7][8] do far more than reduce the effective n for tests of significance of a correlation.
"The results suggest that ... it would be prudent to test for spatial and phylogenetic autoccorrelation when conducting regression analyses with the Standard Cross-Cultural Sample.
"[11] The use of autocorrelation tests in exploratory data analysis is illustrated, showing how all variables in a given study can be evaluated for nonindependence of cases in terms of distance, language, and cultural complexity.
This lagged dependent variable is endogenous, and estimation requires either two-stage least squares or maximum likelihood methods.
[12] A public server, if used externally at http://SocSciCompute.ss.uci.edu Archived 2016-02-20 at the Wayback Machine, offers ethnographic data, variables and tools for inference with R scripts by Dow (2007) and Eff and Dow (2009) in an NSF supported Galaxy (http://getgalaxy.org) framework (https://www.xsede.org) for instructors, students and researchers to do "CoSSci Galaxy" cross-cultural research modeling Archived 2016-02-20 at the Wayback Machine with controls for Galton's problem using Standard Cross-Cultural Sample variables at https://web.archive.org/web/20160402201432/https://dl.dropboxusercontent.com/u/9256203/SCCScodebook.txt.
Researchers now use longitudinal, cross-cultural, and regional variation analysis routinely to analyze all the competing hypotheses: functional relationships, diffusion, common historical origin, multilineal evolution, co-adaptation with environment, and complex social interaction dynamics.
Expert investigation of this question shows results that "strongly suggest that the extensive reporting of naïve chi-square independence tests using cross-cultural data sets over the past several decades has led to incorrect rejection of null hypotheses at levels much higher than the expected 5% rate.
Since this critique was published in 1993, and others like it, more authors have begun to adopt corrections for Galton's problem, but the majority in the cross-cultural field have not.
Second, if there are clusters of similar and related societies in the sample, measures of variance will be underestimated, leading to spurious statistical conclusions.