Calibration of parameters for estimating sampling variance

This paper aims to show alternatives to the estimation methods used for finding the parameters in Gy's well known model for sampling variance in the case of particulate materials. Many experiments designed for gathering data on the sampling variance for specific mineral deposits allow the experimenter to use approximations in the calculation of the parameters of the mathematical model involved, which sometimes can be very useful. However, there are some instances where approximations lead to biased estimates of the parameters, and consequently, lead to errors in the establishment of the sampling protocol and treatment of quality control data. In the present work, an alternative is presented for computing the parameter values based in any experimental set up, without the need for any simplification. The method was derived using the method of least squares and evaluations are made using the usual tools in this kind of methodology: residual analysis and evaluation of the fit by means of a plot of calculated versus experimental variances. With the aid of these tools, one can better evaluate the structure of the experimental errors in such applications, and the adherence to the proposed model. In addition, it is possible to perform hypothesis testing for the equality of different sampling procedures in terms of sampling variance. The full mathematical details are given, together with an algorithm for applying the method, which can be implemented easily using any computer language. An illustration of the method is shown, considering the international work done in ISO/TC 102. This example is a determination of the minimum sample mass to be collected in iron ore shipments, in order to achieve a specified sampling precision.