The American Society for Testing and Materials fell for geostatistics in the 1990s. It came about when statistically challenged soil and rock experts had cooked up ASTM D5549-Standard Guide for Reporting Geostatistical Site Investigations. I had brought my case against what Professor Dr Georges Matheron himself had come to call a new science to the attention of Mr James A Thomas, President of the American Society for Testing and Materials. I had done so by snail mail on April 19, 1994.
ASTM has yet to sort out why and when geostatistocrats have made such a mess of applied statistics. Matheron and his disciples brought geostatistics all the way to North America in the 1970s. The problem is not that distance-weighted average point grades morphed into kriged estimates to honor D G Krige. The real problem is that variances of distance-weighted average point grades AKA kriged estimates didn’t morph along but got lost. Kriged estimates and kriging variances are the heart and soul of geostatistics. David’s 1977 Geostatistical Ore Reserve Estimation and Journel’s 1978 Mining Geostatistics reject the fact that every kriged estimate has its own variance. Clark’s 1979 Practical Geostatistics, unlike David in 1977 and Journel in 1978, derived not only the distance-weighted average point grade but also its true variance. But here’s the cinch!
Having a PhD in geostatistics seems a must when assuming spatial dependence between measured values in ordered sets. Yet, it’s so simple to apply Fisher’s F-test to the variance of a set of measured values and the first variance term of the ordered set. It puts on view whether or not orderliness in sampling units or sample spaces dissipates into randomness. Who wouldn’t want to know? Geostatisticians would have known if they ever got around to counting degrees of freedom. Those who scored a passing grade on Statistics 101 are bound to grasp the properties of variances. Some may even know that one-to-one correspondence between functions and variances is sine qua non in applied statistics.
ASTM itself got on track so to speak in 1898. At that time engineers and chemists of the Pennsylvania Railroad needed standard methods. It made me nostalgic to read such an account of courage and vision. At that time there were no degrees of freedom to count. Geostatistocrats have never stooped to count stuff what can neither be seen nor touched. Once upon a time I was in charge with sampling shipments of Pennsylvania anthracite in the Port of Rotterdam. ASTM Standard Methods for coal were specified in contracts between trading partners. It would be a long while before ISO Standards for coal caught up with ASTM Standard Methods. Now I wish’s why I put together a false test for bias in a previous blog. I wouldn’t want ASTM Committee D05 to dictate how ISO TC27 is to test for bias. But it may well do so!
Those who had master minded ASTM Standard Methods for Soil and Rock must have been smitten silly with geostatistics. My son and I had found out in 1989 why geostatistics is an invalid variant of applied statistics. My work for Barrick Gold in 1997 proved that geostatistical software converted Bre-X’s bogus grades and Busang’s barren rock into a massive phantom gold resource. Student’s t-test proved that crushed core samples had been salted with placer gold. Bre-X’s duplicates for every tenth test sample proved the intrinsic variance of gold at Busang to be statistically identical to zero. That’s the very reason why I’ll always work with applied statistics.
Read what I did point out in April 1994. Either fundamental requirements of probability theory and applied statistics are no longer valid or geostatistical theory and practice are fatally flawed. ASTM’s President wrote on May 13, 1994 that he had asked Mr Bob Morgan, Director of Technical Committee Operations, about the role of Committee E11 Quality and Statistics. What I wanted to study but never got was a copy of D5549-94e1 Standard Guide for Reporting Geostatistical Site Investigations. Robert J Morgan, ASTM’s Director Technical Operations, asked me in February 1995 to direct my input to R Mohan Srivastava.
Teaching Mo all I know about sampling and statistics tops my list of things to never do. It would take more than a few blogs to show what Mohan could have done had he grasped in June 1993 what was wrong with David’s 1977 textbook. That’s when Mo and his coauthor went to McGill University. As a matter of fact, that’s where the united geostatocracy went to praise David’s 1977 Geostatistical Ore Reserve Estimation. For crying out loud!
Testing for bias plays a key role in science and engineering. Student’s t-test is the par excellence test for bias. The t-test for paired data has always played a key role in my work. A bias between test results at loading and discharge is a constant cause of conflict between trading partners. The question is then whose test results are biased. A matter of concern in 1967 was dry ash contents of anthracite shipments from the mines in Pennsylvania to the port of Rotterdam. I went to the USA and determined that loss of dust during sample preparation was the most probable cause of bias between dry ash contents. I had done time at TUDelft. So, I knew that carbonaceous shale is softer than anthracite, and that hammer mills tend to crush and grind autogenously. That’s why I thought loss of fine dust during preparation of primary samples at loading would cause test samples to show lower dry ash contents at discharge in the Port of Rotterdam.
Holmes hammer mill
SGS’s coal testing laboratory in Rotterdam, too, had a Holmes hammer mill. It was similar to the one at loading but ours was run with its spring-loaded container closed. Settlements between buyer and seller were based on test results determined at discharge. So, we couldn’t afford to mess up primary samples by running our hammer mill ajar. What we did do was prepare test samples for analysis in the usual manner. We would then pass the reject of each primary sample through the hammer mill with its container left slightly ajar. We collected dust on sheets of paper placed at 0.5 m and 1.5 m from the hammer mill. Dust that had settled at 0.5 m weighed 26.2 grams and contained 14.6% dry ash. Dust that had settled at 1.5 m weighed 12.1 g and contained 16.5% dry ash. The settlement sample showed 10.40% ash on dry basis whereas our messed-up sample showed 10.26% ash on dry basis. With but one degree of freedom our experiment was not much of a true test for bias. But it did prove the integrity of our settlement samples passed scrutiny. We didn’t determine dry ash in dust collected on our coveralls and face masks. I had a fine team to work with. But I wanted more than a team! I wanted SGS to build a new laboratory as far away as possible from where we were. But SGS was not ready yet. What SGS did do was ask me to set up a laboratory in Vancouver. Now guess what?
When I met Greg Gould for the first time at Rotterdam in 1967 he did already chair ASTM Committee D05 on coal and coke. Greg praised Volk’s Applied Statistics for Engineers so I bought my first copy. He told me about Dr Jan Visman, his work at the Dutch State Mines during the war, his 1947 PhD thesis, and his input in ASTM. I was pleased to meet him in person after we had moved to Canada in October 1969. Dr Jan Visman was an independent thinker. He was as much a true a scientist as Greg Gould was a professional engineer. And a true PEng he was! I treasure my copy of Visman’s PhD thesis and our correspondence. With fondness I remember our talks. We talked about the composition and segregation components of his sampling variance. I pointed out the term “segregation” suggests that a sampling unit may have been more homogeneous in the past. That’s why the distribution variance and the composition variance added up to the sampling variance. It happened when two Dutchmen talked about sampling in a foreign language. But unlike French sampling experts we did grasp the properties of variances.
The odd reader of my blogs may think I’m a pack rat. I do plead guilty! I want to get back to testing for bias with Student’s t-test. But I need to tell one more tale before talking about false bias testing. Once upon a time Matheron’s new science of geostatistics somehow slipped into bias testing. It came about after ASTM awarded me in 1996 a plaque for 25 years of services. Greg Gould had asked ASTM’s Board of Directors to recognize Dr Jan Visman and his work. ASTM did so but misspelled Jan’s first name as Jane! It was the same year that Barrick Gold signed me on to figure out what kind of gold resource Bre-X Minerals had cooked up in the Kalimantan jungle. It was the time when Greg Gould sent me bias test data that Charles Rose had enhanced by kriging. Rose had taken to liking to geostatistics. So much so that one of his papers was approved for David’s 1993 bash at McGill University. Rose talked about A Fractal Correlation Function for Sampling Problems. But one of his many problems was that Mohan Srivastava lent him a helping hand. I met Rose for the first time in Colombia many years ago. He joined SGS after I had left in 1979. ASTM awarded Rose in 2004 the R A Glen Award. He represents the USA on ISO/TC27 on coal. He talked about his take on bias testing during the meeting at Vancouver in 2009. What a waste of time! SGS announced on April 24, 2008 the strategic acquisition of Geostat Systems International, Montreal, Canada. For crying out loud!
False test for bias
That’s why I decided to show how to apply a false bias test. Firstly, I got the set of paired dry ash contents determined in eleven (11) shipments of Pennsylvanian anthracite at loading and at discharge. Next, I played the kriging game by inserting a kriged estimate between each pair of measured values. Take a look at what I cooked up! The variance of differences between paired data dropped from var(Δx)=0.1078 for a set of eleven (11) measured values to var(Δx)=0.0396 for a set of eleven (11) measured values which was enriched with a set of ten (10) kriged estimates. So much for kriging when testing for bias. Stay tuned for a true test for bias.