Abuse of Statistics

My take on Abuse of Statistics was put in print in March 1992. It didn’t end up in CIM Bulletin but in CIM Forum. That’s where “Articles of a controversial nature” tend to end up. Merks and Merks in 1991 had shown how to test for spatial dependence by applying Fisher’s F-test to gold grades of ordered rounds mined from a drift. What a pity that geostatisticians in the 1990s didn’t test for spatial dependence between measured values in ordered sets. It is imperative in mineral exploration, mining and mineral processing that degrees of freedom be counted. On-stream analyzers measure and monitor metal grades of mill feed and tailing! That’s why confidence intervals and ranges for metal contents and grades are easy to derive.

So it came about that CIM Bulletin had decided to print in CIM Forum a technical brief on Abuse of Statistics in 1992. But why then had Armstrong and Champigny’s “A study on kriging small blocks” seen the light in CIM Bulletin of March 1989. Why was Abuse of Statistics published in CIM Forum? Why was placing distance-weighted averages AKA kriged estimates between measured values deemed sound science in CIM Bulletin? Why do geostatisticians not test for spatial dependence between measured values in ordered sets? Why are degrees of freedom ignored? Simple questions but still no answers! 

Dr W D Sinclair, Editor CIM Bulletin, brought up CIM Forum in his letter of September 21, 1992. He was aware that I have served on various standard committees since 1974. Dr F P Agterberg was his Associate Editor in those days. Both were scholars with the Geological Survey of Canada. They agreed that CIM Forum was a fitting format but that my article should pass rigorous scrutiny. Dr Agterberg wanted to know when H G Wells had said: “Statistical thinking will one day be as necessary as the ability to read and write”. Surely, one cannot be rigorous enough when entrusted with peer review for CIM Forum. Was it Agterberg who had approved Armstrong and Champigny’s study in 1989? Or was it perhaps David himself?

It was in Darrell Huff’s 1954 How to Lie with Statistics where H G Wells’s quote was printed ad verbatim. Huff had also referred to Disraeli’s famous lament: “There are three kinds of lies: lies, damned lies, and statistics”. But where had Huff found so much praise for statistical thinking? I had been reading Sherborne’s Another Kind of Life. I tried to contact Dr Sherborne and was pleased he did respond. He attributed Wells’s quote to Samuel Wilks’s 1954 presidential address to the American Statistical Association. It does have an extensive website. Wilks had strung together a rather rambling train of thought whereas Wells was much more frugal with words.

Dr Michael Sherborne has tracked Wells’s train of thought to page 204 of Wells’s book Mankind in the Making: “The great body of physical science, a great deal of the essential fact of financial science, and endless social and political problems are only accessible and only thinkable to those who have had a sound training in mathematical analysis, and the time may not be very remote when it will be understood that for complete initiation as an efficient citizen of one of great new complex world-wide Stats that are now developing, it is necessary to be able to compute, to think in averages and maxima, as it is now to be able to read and write.”

H G Wells

At the same time a budding geologist in Algiers did not know how to derive length-weighted average lead and silver grades determined in core samples of variable length. In fact, he even thought he was working with applied statistics. In time Professor Dr Georges Matheron stripped the variance off the distance-weighted average, called what was left a kriged estimate to honor D G Krige. Next, he praised what he had cooked up and decided to call it the new science of geostatistics. It is a fact that Matheron’s new science is as doomed as the dodo once was!

Asking McGill's Brass

Here's an emessage that was transmitted to McGill University on Thursday, August 12th, 2005. Why is it that not a single response has been received? Geostatistical software converted Bre-X's bogus grades and Busang's barren rock into a massive phantom gold resource. McGill Office of Academic Integrity ought to assess whether or not the variance can be stripped off the distance-weighted average AKA kriged estimate. Not a single response has ever been received!


When Sir Ronald A Fisher was knighted in 1953 each weighted average had its own variance. When geostatistics was hailed as a new science in the 1960s the distance-weighted average was reborn as an honorific kriged estimate but lost its variance. Statistically dysfunctional geologists and mining engineers were as ecstatic as nascent geostatisticians simply because any set of measured values, determined in samples selected at positions with different coordinates, defines an infinite set of distance-weighted averages-cum-kriged estimates. It is beyond comprehension that the infinite set of variances was replaced with the kriging variance of a subset of the infinite set of kriged estimates.

Professor Dr Michel David, who taught at McGill University in the 1970s, wrote the first textbook on geostatistics, in which he cautioned, "This is not a book for professional statisticians" and predicted, "... statisticians will find many unqualified statements..." Dr David was a dedicated defender of geostatistical doctrine until he passed away.

Google "bre-x bogus barren" to find out how the junk science of interpolation without justification converted $30,000 worth of placer gold into the world's largest phantom gold resource. Look under "Documentation/Book reviews" and read what I wrote about David's textbook and a few others. Geostatisticians assume spatial dependence, interpolate by kriging, smooth to perfection and rig the rules of mathematical statistics. In contrast, mathematical statisticians at McGill University accept the following inviolable rules:

1 One-to-one correspondence between weighted averages and variances is sine qua non,
2 Each and every distance-weighted average-cum-kriged estimate has its own variance,
3 Kriging variances of subsets of infinite sets of kriged estimates are invalid.
   
Surely, scientific integrity and fair play demand that McGill's students not be taught stochastic modeling with pseudo variances.

Yours truly,
J W Merks

This emessage was sent to the following Officers, Faculty and Staff:

    Mr Richard W Pound, Chancellor
    Dr Heather Monroe-Blum, Principal & Vice-Chancellor
    Professor Dr David Wolfson, Chair, Mathematics and Statistics
    Department Members, Mathematics and Statistics
    Dr Ferri Hassani, Webster Chair Professor and Director of the Mining Program
    Academic Staff, Mining Engineering
    McGill Office of Academic Integrity
    McGill Reporter