Hello Paul,

I question the effectiveness of Gy's sampling formula in practical applications for several reasons. In sampling theory, Gy's sampling constant, just like the variance and the central value of a population (a sampling unit or space), is one of those ubiquitous "unknown true values". In sampling practice, however, Gy's sampling constant, or any other "unknown true value" for that matter, can only be estimated with a finite degree of precision. Examine page 10 of "Sampling in Mineral Processing" (see Reviewed papers on geostatscam.com) to find out why I have misgivings about Gy's formula in sampling practice.

If a sampling unit (a mass of crushed lead ore?) is homogeneous, the variance of the primary sample selection stage is, in fact, the composition variance (Gy's fundamental error). If a sampling unit is heterogeneous, however, the variance of the primary sample selection stage is the sum of the composition variance and the distribution variance. It is the latter variance that defies a priori estimation.

The variance of Gy's sampling constant (see also page 10) explains why Gy's formula is frequently used in esoteric applications such as deriving the top size of gold particles in crushed ore. Applying Gy's sampling formula to the sulfur distribution in lead ore seems a similar exercise in fuitility.

All you need to know about the variabililty of sulfur, or any other random variable in lead ore, can be estimated at the lowest possible cost by applying an interleaved sampling protocol. Select a set of primary increments, divide the set into a pair of interleaving subsets such that one consists of all odd-numbered increments (A-primary sample) and the other of all even-numbered increments (B-primary sample), prepare a test sample of each primary sample (A- and B-test samples), and assay duplicate test portions of each test sample (A1-, A2-, B1- and B2-test results). Such data sets can be used to optimize sampling protocols in terms of the mass and number of primary increments.

Since a pair of A- and B-primary samples gives only a single degree of freedom, it makes sense to apply interleaved sampling protocols to the most important daily mass flows in a mineral processing plant (mill feed, concentrate, tailing), and obtain no less than 27 degrees of freedom for the monthy metallurgical balance.



Kind regards,

Jan W Merks ■

Paul,

Somewhat similar but not quite the same. The t-test does not give useful info in this case. Here's what you can do with your data. Calculate the mean of each pair, var(x), the variance of these means (Excel function), and var1(x), the first variance term of ordered means (see "Sampling in Mineral Processing").

Next, calculate F=var(x)/var1(x) and compare this calculated F-ratio with tabulated F-values at 5% and 1 % probability at df(r)=n-1 degrees of freedom for var(x), and df(o)=2(n-1) degrees of freedom for var1(x).

Finally, calculate 95% confidence interval for the mean of means as follows: 95% CI=square root (lowest variance/n) * t0.05;df, in which df is either df(r)=n-1 for the randomized set of means, or df(o)=2(n-1) for the ordered set.

Given that Gy's sampling formula derives from the variance of a binomial distribution, applying it to a multinomial distribution makes just as much sense as ignoring the existence of spatial dependence in the sampling unit of interest. Please keep me posted on your investigation into the applicability of Gy's theory to all your process streams.

Kind regards,

Jan W Merks ■

I have a sample of mineral..so i need to sampling and quartering thai sample...if i took 15Kilos from 300 Kilos,This weight is enought for a googd sampling?..or depend of the granulometric and volumetric factor? ■

Select a pair of interleaved primary samples and you'll get a reliable estimate for the precision of the measured value(s). Working with Gy's sampling constant does not give unbiased precision estimates for the stochastic variable of interest. ■