Goofing with Gy's sampling errors

Searching for sound sampling practices always deserves praise. Sampling experts in South Africa have tried to put into plain words what sound sampling practices are all about. What a shame that they took a shine to Pierre Gy’s sampling errors. So much so that they have decided to put together a study of Gy’s sampling errors. Gy had grasped but little of what he had come to call “sampling errors”. What a pity that sampling experts in South Africa, too, have failed to come to grips with Gy’s sampling errors as much as had Gy himself.

What irked me is that sampling experts in South Africa praised Gy’s unpublished tale on “Minimum mass of a sample needed to represent a mineral lot”. Gy didn’t refer to it in his 1979 Sampling of Particulate Materials. But why didn’t he refer to Visman’s 1947 PhD Thesis anymore? And why did he take to praising David’s 1977 Geostatistical Ore Reserve Estimation? Famous French sampling scholars such as Professor Dr G Matheron, Dr P M Gy and Professor Dr M David have left no doubt that the properties of variances were far beyond their shared grasp. That’s why they never were familiar with one-to-one correspondence between functions and variances. And that’s why degrees of freedom have become such a burden!

Part 1 and Part 2 of this 2007 review of Pierre Gy’s sampling errors were strung together by R C A Minnitt, P M Rice and C Spangenbergs. All that is necessary to get goofy statistics is to pay no attention to those who do grasp applied statistics. I have sent an email to Professors F Cawood and R Minnitt. I spelled out why mining students ought not to be taught to assume spatial dependence between measured values in ordered sets, to interpolate by kriging, and to ignore the rules of applied statistics with impunity. Added to my email was a link to pre-read copies of Volk’s textbook on Applied Statistics for Engineers for the benefit of those who are studying mining engineering at the Witwatersrand University.

It feels at times as if I grew up with Volk’s Applied Statistics for Engineers under my pillow. I bought my first copy when a friend told me he liked it a lot. I did so before moving to Canada in 1969. Volk’s Chapter Seven Analysis of Variance deals in rich detail with all of the properties of variances. Section 7.3 Confidence range of variances shows how to derive lower and upper confidence limits for an observed variance as a function of the number of degrees of freedom. The odd inquisitive student may wonder why statisticians do count degrees of freedom. Those who are against counting degrees of freedom are bound to score passing grades wherever Gy’s sampling errors are taught.

Volk’s 1980 reprint is still as sound as was his 1958 work. I have lost two copies while I was teaching sampling and statistics around the world. Initially, I taught coal sampling for the McGraw-Hill Seminar Center. After Trans Tech Publications had published Sampling and Weighing of Bulk Solids in 1985 I drifted into mineral exploration and mining. Showing why geostatistics is a scientific fraud ranks high on my list of things to do on this planet. Volk’s tattered 1958 textbook remains my favorite. I would have written a Wiki page about William Volk and his work if I had known him as well as I did Dr Jan Visman. But Wiki is not what it used to be when those who assume, krige and smooth, do rig the rules of applied statistics.

The above table gives arithmetic mean assay results (g/t Au) for each of four (4) sets of samples. The variances in the second line would be obtained if infinite sets of test portions were selected and assayed. However, this sampling tree experiment was based on selecting and assaying finite sets of thirty (30) test portions which give 29 degrees of freedom. Excel’s FINV function has been applied to derive lower and upper limits of 95% confidence ranges in (g/t)².