Use and misuse of statistics

“Statistical thinking will one day be as necessary for

efficient citizenship as the ability to read and write.”

H G Wells (1866-1946)

Wells was a prolific writer with a keen sense of rights and wrongs in his life and time. What had inspired him to praise statistical thinking were the works of Karl Pearson (1857-1936), and of Sir Ronald Aylmer Fisher (1890-1962). Pearson worked with large data sets whereas Fisher worked with small data sets. That was what inspired Fisher to add degrees of freedom to Pearson’s chi-square distribution. Thus was born a feud between giants of statistics. Degrees of freedom converted probability theory into applied statistics, and sampling theory into sampling practice. Fisher and Pearson were both outstanding statisticians. They inspired H G Wells and scores of statisticians. Applied statistics shall stand the test of time until our sun bloats into a red giant and Van Gogh’s Sun Flowers burn to a crisp.

Why did geoscientists get into geostatistical thinking? All it took was a young French geologist who went to work at a mine in Algeria in 1954. He measured associative dependence between lead and silver grades of drill-core samples. But he did not count degrees of freedom. So, he did not know whether his correlation coefficient was significant at 95%, 99% or 99.9% probability. What is more, his drill-core samples varied in length. As a result, the number of degrees of freedom is a positive irrational rather than a positive integer. He did not know how to test for spatial dependence by applying Fisher’s F-test to the variance of the set of measured values and the first variance term of the ordered set. His first paper was not peer reviewed. Nobody asked him to report primary data and give references. As luck would have it, he was without peers. Professor Dr Georges Matheron and his magnum opus were accepted on face value. His students thought of him as “creator of geostatistics”. Dr Frederik P Agterberg in his eulogy called him “founder of spatial statistics”. Yet, between 1954 and 2000 Professor Dr Georges Matheron did not teach his disciples how to test for spatial dependence and how to count degrees of freedom.

My son and I wrote Precision Estimates for Ore Reserves. It was based on applied statistics as it had been developed by Fisher and Pearson and was praised by Wells. We did test for spatial dependence by applying Fisher’s F-test to the variance of a set of measured values and the first variance term of the ordered set. We had studied David’s 1977 Geostatistical Ore Reserve Estimation. Professor Dr Michel David did not show how to test for spatial dependence and how to count degrees of freedom. Our paper was submitted to CIM Bulletin on September 28, 1989. We did not criticize geostatistics nor did we refer to it. CIM Bulletin rejected it but Erzmetall praised and published it in October 1991.

Bre-X Minerals was selling stock and getting ready to drill at Busang. The internet would not be ready for a while. The mining industry liked unbiased confidence limits for masses of metals contained in mined ores and mineral concentrates. What it did not like in the 1990s and still does not like in 2013 are unbiased confidence limits for masses of metals contained in reserves. I had sent to CIM Bulletin on September 21, 1992, an article on Abuse of Statistics. The Editor advised that articles of a controversial nature can be published in CIM Forum. I was asked to cite a specific reference for the quotation in which H G Wells spoke so highly about statistical thinking. I had found it long ago in Darrell Huff’s How to lie with statistics. Penguin Books published the first edition in 1954 when young Matheron was working with statistics in Algeria. Matheron and Agterberg would have been pleased had Wells praised geostatistical thinking.

Geostatistics messed up the study of climate change. Spatial dependence in our sample space of time may or may not dissipate into randomness. Sampling variogram shows whether, where and when it does. High school students ought to be taught how to construct sampling variograms. It would have made H G Wells smile.