A Comparative Analysis of Sampling Variance: Classical vs. Multi-Component Estimation of the Fundamental Sampling Error for a Gold Ore

Abstract The standard practical application of Pierre Gy’s fundamental sampling error (FSE) theory is often limited to an idealized binary mixture, a common shortcut that can lead to significant error. This study quantifies the cost of this simplification by applying Gy’s complete multi-component summation methodology to a comprehensive dataset of 448 samples from a characterized gold ore. We demonstrate that the common practical shortcut, using a liberation factor of $$\ell$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>ℓ</mml:mi> </mml:math> = 1 as a default when liberation data are unavailable, overestimates the sampling variance by a factor of 3.8, predicting an error of 2.59% compared to the true inherent error of 0.68%. This reveals the ore to be substantially more homogeneous than the simplified model suggests. The practical benefit of applying the proper, liberation-aware method is clear: the sample mass required for a given precision can be significantly reduced, yielding direct cost savings and providing higher confidence in resource estimation. This case study underscores the importance of moving beyond common shortcuts to implement Gy’s complete theoretical framework for accurate material characterization.