How to measure what we speak about

NASA satellites have been measuring lower troposphere global temperatures since 1979. At that time I went around the world at a snail’s pace. Lord Kelvin’s thoughts about how to measure what we speak about were much on my mind in those days. I thought a lot of metrology in general, and of sampling and statistics in detail. I was to visit all of Cominco’s operations around the world. My task was to assess the sampling and weighing of a wide range of materials. Of course, it couldn’t possibly have crossed my mind that I would look in 2008 at the statistics for 30 years of lower troposphere global temperatures.

My job with Cominco did have its perks. When I was at the Black Angel mine in Greenland, I saw Wegener’s sledge on a glacier above the Banana ore zone. I knew how geologists had struggled with Wegener’s continental drift, and how they slowed it down to plate techtonics.

Southeast Coast of Greenland

I knew geologists were struggling with Matheron’s new science of geostatistics. I travelled around the world with a bag of red and white beans, a HP41 calculator and a little printer to make the Central Limit Theorem come alive during workshops on sampling and statistics. I lost my bag of beans because it was confiscated at customs in Australia.

On-stream analyzers that measure metal grades of slurry flows at mineral processing plants ranked high on my list of tools to work with. The fact that the printed list of measured values was just peeled of the printer at the end of a shift rubbed me the wrong way. I got into the habit of asking who did what with measured values. It was not much at that time because on-stream analyzers were as rare as weather satellites. Daily sheets made up a monthly pile, and that was the end of it. I entered the odd set in my HP41 to derive the arithmetic mean and its confidence limits for a single shift. But that was too tedious a task. That’s why spreadsheet software ranked high on my list of stuff to work with.

I met a metallurgist who tried to put to work Box and Jenkins 1976 Time series analysis. So, he did have a few questions. I explained what Visman’s sampling theory had taught me. First of all, the variance terms of an ordered set of measured values give a sampling variogram. Secondly, the lag of a sampling variogram shows where orderliness in a sample space or a sampling unit dissipates into randomness. The problem is that Time series analysis doesn’t work with sampling variograms. So, the metallurgist got rid of his Box and Jenkins and I took his Time series analysis. Box and Jenkins referred to M S Bartlett, R A Fisher, A Hald, and J W Tukey but not to F P Agterberg or G Matheron. Box and Jenkins provide interesting data sets. I’ve got to look at the statistics for Wölfer’s Yearly Sunspot Numbers for the period from 1770 to 1869.

Sunspots

Visman’s sampling theory did come alive while I was working with Cominco. So much so that I decided to put together Sampling and Weighing of Bulk Solids. The interleaved sampling protocol plays a key role in deriving confidence limits for the mass of metal contained in a concentrate shipment. So, I was pleased that ISO Technical Committee 183 approved ISO/DIS 13543–Determination of Mass of Contained Metal in the Lot. I was already thinking about measuring the mass of metal contained in an ore deposit! But CIM’s geostatistical thinkers had different thoughts. For example, CIM’s Geological Society rejected Precision Estimates for Ore Reserves. In contrast, CIM’s Metallurgical Society approved Simulation Models for Mineral Processing Plants.

In other words, testing for spatial dependence is acceptable when applied to an ordered set of metal grades in a slurry flow. Testing for spatial dependence is unacceptable when applied to metal grades of ordered rounds in a drift. So I talked to Dr W D Sinclair, Editor, CIM Bulletin. He was but one of a few who would listen to my objection against such ambiguity. In fact, I put together a technical brief and called it Abuse of Statistics. I mailed it on July 2, 1992, and asked it be reviewed by a statistician. A few weeks later Sinclair called and said Dr F P Agterberg, his Associate Editor, was on the line with a question. What Agterberg wanted to know is when and where Wells did praise statistical thinking. That was all!

H G Wells

I didn’t know when or where Wells said it! I didn’t even know whether he said it or not! What I did know was that Darrell Huff thought he had said it. In fact, he did quote it in How to Lie with Statistics. I didn’t know much about Agterberg in 1992. What I did know then was that David in his 1977 Geostatistical Ore Reserve Estimation referred to Agterberg’s 1974 Geomathematics. And I found out that Agterberg didn’t trust statisticians when he reviewed Abuse of Statistics.

F P Agterberg

Agterberg , CIM Bulletin’s Associate Editor in 1992, was a leading scholar with the Geological Survey of Canada. Yet, he didn’t know that functions do have variances. It does explain why he fumbled the variance of his own distance-weighted average zero-dimensional point grade first in 1970, and again in 1974. He could have told me in 1992 that this variance was gone but chose not to. Agterberg was the President of the International Association for Mathematical Geology when it was recreated as the International Association for Mathematical Geosciences. He is presently IAMG’s Past President. He still denies that his zero-dimensional distance-weighted average point grade does have a variance. Agterberg was wrong in 1970, in 1974, and in 1992. And he is still wrong in 2009. That's bad news for geoscientists!