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.