Comparing Sampling Efficiency in Particulate materials using characteristic Functions: An Empirical Study of Scoop vs Riffle Methods
DOI: 10.62178/sst.005.002
Abstract
Representative sampling of particulate materials remains a critical challenge across scientifi c and industrial domains, yet traditional method comparisons based on means and variances fail to capture complete distributional diff erences. This study introduces Characteristic Function (CF) analysis as a comprehensive statistical framework for evaluating sampling methods, providing a complete spectral representation of sampling distributions that reveals features hidden from conventional statistics. We empirically compared two common methods, scoop sampling and ririffle e splitting, using four density tracers (blue corn at 1.3 g/cm³, steel at 7.8 g/cm³, lead at 11.3 g/cm³, and tungsten carbide at 14.9 g/cm³) mixed in a popcorn matrix, with 32 samples per method analysed for both particle counts and individual mass measurements. Results demonstrate that while both methods captured similar mean counts, riffle splitting maintained near-ideal Poisson behaviour across all density ranges (variance-to-mean ratio = 0.77–0.93), whereas scoop sampling exhibited severe density-dependent over-dispersion (variance-to-mean ratio up to 19.33) and failed to capture heavy particles in 28 – 47 % of samples. CF analysis revealed fundamental distributional diff erences (integrated CF distance D = 0.324), with scoop sampling producing multimodal, heavy-tailed distributions with oscillatory CF signatures indicative of particle clumping, while riffle splitting generated smooth, unimodal distributions approaching Gaussian form. The riffle method demonstrated superior performance across all metrics: perfect detection sensitivity, statistical independence between tracer captures (factorization error 4.9× lower), consistent mass measurements (CV 3.7–6.1× lower), and strong count-mass linearity (r > 0.98). A composite scoring system integrating six performance dimensions ranked riffle splitting signifi cantly higher (0.89/1.00) than scoop sampling (0.60/1.00). This study establishes Characteristic Function analysis as a powerful diagnostic tool that bridges theoretical sampling science and practical method validation, providing evidence-based recommendations for particulate sampling protocols and a generalizable template for evaluating any sampling method applied to heterogeneous materials.
Published in Issue 5 · June 2026
Citing this article
Minnitt, R. (2026). Comparing Sampling Efficiency in Particulate materials using characteristic Functions: An Empirical Study of Scoop vs Riffle Methods. Sampling Science & Technology, June 2026(5), 2-36. https://doi.org/10.62178/sst.005.002
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