I am a little worried by the statements:
" As you point out, the sub-sample values should have a normal distribution. Increasing the number of samples (n) would help. "
" As you point out, the sub-sample values should have a normal distribution. Increasing the number of samples (n) would help. "
Averages of lognormal (or other highly skewed) data are not Normal. The lognormal, in particular, does not conform to the Central Limit Theorem. This is why Sichel in the South African GoldMines and Finney in the Royal Statistical Society worked out the lognormal estimation theories.
There are two issues here, I think:
(1) the sampling issue which uses a small aliquot to represent a large bulk of sample
(2) the estimation of an average value from highly skewed data -- or, if your prefer, data with the odd erratic high.
It was (2) that inspired Sichel to do his work. (1) is the province of such experts as Gy and Merks.
For those readers unfamiliar with South African Gold values, it is perfectly possible for neighbouring 'chip' samples to be two orders of magnitude different in value whether in situ or on a conveyor belt. It is less common but still perfectly feasible for bulk samples. Similar characteristics occur in hydrothermal veins and other 'erratic' geological environments. This is not a sampling issue but fact.
There are sampling and assaying issues, of course, and much has been published on this topic. I had the honour to be junior (very) author on a paper with Norman Lotter on this topic. This paper can also be downloaded from my personal site at http://uk.geocities.com/drisobelclark/resume Norm provides a lot of references which you might find useful.
Isobel
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