The use of non-parametric tests between subsamples and particle population for the assessment of minimum number of particles in microscopic analysis

Abstract

The use of small and reliable samples in a microscopic analysis can decrease the time to estimate the particle size and mineral grade distributions in a population of particles. This paper attempts to assess the minimum reliable sample size for the above-mentioned distributions, by implementing non-parametric tests on the subsamples taken from a specific population of 2800 particles. The Kolmogorov-Smirnov tests show that the subsamples which contain more than 800 particles (29% of the population) cannot give cumulative distributions of particle size and mineral grade different from their equivalents in the population. On the other hand, Chi-square tests show that 1500–1700 particles (54–61% of the population) may be sufficient to estimate the discrete distributions in the population. The minimum reliable sample size increases with an enlarging population because the sampling errors should increase while taking samples of equal size from larger populations. Nevertheless, the minimum reliable size should be 29–32% of the population if the distributions of mineral grade and particle size in the population are fitted to bimodal and normal distributions, respectively.

Keywords:

• Subsamples
• minimum number of particles
• Chi-square
• Kolmogorov–Smirnov
• microscopic analysis

Acknowledgments

The author acknowledges the Mining Engineering Department of Middle East Technical University for providing the optical microscope used in this study.