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It was a computer with geostatistical software that created a phantom gold resource out of bogus grades and barren rock. What geostatistical software cannot possibly create is a single degree of freedom. Geostatisticians deem degrees of freedom as redundant as the variance of the distance-weighted average. Agterberg made this variance vanish but the concept of degrees of freedom is more resilient to tampering.

Click here to find out how geostatisticians fumbled degrees of freedom. Peruse tables in textbooks on mathematical statistics where all sort of values are listed as a function of degrees of freedom and figure out why they went missing in textbooks on geostatistics. Just remember that degrees of freedom are awarded to measured values but not to functionally dependent (calculated!) values. Degrees of freedom are positive integers for sets of measured values with equal weights but positive irrationals for sets of measured values with variable weights.

Spreadsheet software is a powerful tool to compute statistics for a wide range of applications in mineral exploration, mining, processing, smelting and refining. Spreadsheet templates are simple to set up and easy to modify to suit either smaller or larger sets of primary data. Only three types of templates were required to compute 95% confidence limits for content and grade of a gold reserve defined by more than 300 boreholes.

H G Wells predicted that statistical thinking would become as important as the ability to read and write. Would Wells have embraced the nouveau pseudo science of interpolation without justification with the same unbridled passion as the world's mining industry did? After all, Wells was familiar with Fisher's work long before Fisher became Sir Ronald A Fisher in 1952.

Some caution is in order! Knowledge of mathematical statistics is empowering but addictive. Studying mathematical statistics and playing with spreadsheet templates may be the beginning of an irreversible process!

False and true tests for bias
A test program for bias between ash contents of Pennsylvania anthracite shipments to the Port of Rotterdam shows that interpolation between measured values makes no sense.

Bre-X and the kriging game
Start step-out drilling to create phantom ore, compute three lines of kriged boreholes between two lines of salted boreholes, get an illusion of spatial dependence between kriged boreholes in barren rock, and apply analysis of variance to show that salted boreholes do not even display spatial dependence.

Bre-X and the bonanza borehole
Bre-X's salters worked overtime on core samples from Borehole SEZ198 but Fisher's forbidden F-test proved that Bre-X's glory hole was as barren as Busang's gold phantom resource.

Clark and the kriging game
Play with Clark's coordinates, find out what would happen if each distance-weighted average-cum-kriged estimate were to have its own variance, figure out how missing variances of distance-weighted averages could possibly converge on the Central Limit Theorem but don't waste too much time while trying to enter the infinite set of all possible coordinates.

Platinum Palladium Concentrate
Interleaved sampling protocols make it possible to compute confidence limits for PGM contents and grades of concentrate production at the smelter of Stillwater Mining Company.

Uncorrected sampling variogram
Corrected sampling variogram
A 2000-Year Global Temperature Reconstruction Based on Non-Treering Series, Loehle, C, Energy & Environment, Vol 18, Nov 2007.

Cerattepe bulk sampling program for gold
Cerattepe bulk sampling program for silve
r
Cerattepe correlation-regression statistics
A paper on this project was submitted at the request of and rejected by JMG's Editor-in-Chief simply because he wanted his degrees of freedom in my paper. So I suggested that he should review the applicable ISO standard method.

Test for spatial dependence
Testing ordered sets of standard uniform random numbers for spatial dependence is an exercise in futility but counting degrees of freedom is not. This information was sent to MG's Editor-in-Chief in 1998.

Confidence limits for central value of skewed gold assays
Although this large set of gold assays departs significantly from the normal distribution, its is possible to compute confidence limits for its central value.

Single ore zone of borehole in massive sulfide
Set of fifty ore zones of boreholes in massive sulfide

Confidence limits for density- and length-weighted average grades of core samples from a single ore zone and from a set of fifty (50) ore zones in the same massive sulfide.

First borehole
Second borehole
A paper entitled 'Borehole Statistics with Spreadsheet Software' explains how to obtain a unique 'fingerprint' for each borehole. The stats for DDH9801 and DDH9802 show that not all core samples have the same length.

Matheron's 1954 correction
Matheron derived the weighted average lead and silver grades of core samples with variable lengths. He didn't derive the variances of his weighted averages. Neither did I because he didn't report primary data. Find out what I did with Matheron's variances of metal grades and his central values.

Matheron's 1967 Thesis
Matheron showed two (2) sets of eleven (11) data each but he did not apply Fisher's F-test to the variance of each set and the first variance terms of the ordered sets. He did not test for spatial dependence or count degrees of freedom. Neither did his disciples.

Appendix A - Interleaved sampling protocol, Sample selection
Appendix B - Interleaved sampling protocol, Sample preparation
Appendix C - Measures for variability and precision, Mined ore
Appendix D - Measures for variability and precision, Mill feed
Appendix E - Student's t-test for paired data
These appendices are part of 'Sampling in Mineral Processing'

 
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