AI-GEOSTATS: Skewed distributions

[JW]

Hello Subscribers,   Our Webmaster has posted under http://www.ai-geostats.org/documents/ an Excel spreadsheet template that shows how to derive confidence limits for a large set of gold assays that departs significantly from the normal distribution. ISO/DIS 5479-Statistical interpretation of data, describes several tests for departure from the normal distribution but does not show how to compute stats for skewed sets. This template shows how to partition a large set of gold assays into subsets and compute count-weighted averages and confidence limits.  More subsets give more degrees of freedom, a lower tabulated t-value and a higher degree of precision for the count-weighted average. In this case, too, degrees of freedom are no longer positive integers but become positive irrationals.   Subscribers to ai-geostats.org may remember that the formula for the variance of a set of samples with variable weights was discussed in October 2005. The accepted formula did have the correct sum of terms in the numerator but the incorrect degrees of freedom in the denominator. At that time, a template with hypothetical uranium data set proved heuristically that the variance of the central value (the distance-weighted average at selected coordinates) converges on the Central Limit Theorem (the variance of the arithmetic mean!) when all of the weighting factors converge on 1/n. Analysis of variance (ANOVA) is applied in the same template to prove that this set does not display a significant degree of spatial dependence.   Popular Science freelance writer Laura Allen once wrote, "Scientists don't assume but test how the world works". Why do geostatisticians assume spatial dependence, interpolate by kriging, select the least biased subset of some infinite set of degrees-of- freedom-deprived, functionally dependent kriged estimates, smooth its pseudo kriging variance to perfection, and rig the fundamental rules of mathematical statistics with impunity. Surely, first generation geostatisticians can neither accept nor admit that each distance-weighted average-cum-kriged estimate has its own variance. Would future generations want to be wrong?   In mathematical statistics, one-to-one correspondence between weighted averages and variances is sine qua non. Who replaced the variance of the distance-weighted average with the pseudo kriging variance of a subset of an infinite set of kriged estimates? Why? When? The questions are simple but the geostatocracy remains silent!   Kind regards, Jan W Merks