A Comparison of Statistical Techniques for Detecting Analytical Bias in Geoanalysis

Abstract

Detecting analytical bias is a valuable step during method validation and, in the case of the mining industry, fundamental when one validates the geological databases used for resource estimation. This will generally affect the costs of future investments in new or expanding projects. This paper details frequently used techniques for doing this, with their theoretical background, advantages and shortcomings, providing a deeper insight in how to choose a method for special applications. This is done by means of a review of the specialised literature, and by showing practical applications. The latter is done by choosing some of the most commonly used methods, comparing them using Monte Carlo simulations and testing in some real applications (analytical methods used in Brazilian prospects for copper, gold and iron). Consequently, laboratory specialists will have a better understanding of statistical tools for this purpose, being able to provide their customers with a very consistent assurance of chemical analytical results. It is shown that some commonly used statistical methods for this type of comparison are not applicable, and in some cases, one must resort to more complicated models. These are, however, easily implemented computationally, and the mathematical details are shown.

Linear regression analysis for comparing two measurers or methods of measurement: But which regression?

“…The conventional approach is a complex ANOVA in which covariant analysis for slope is performed. But this assumes 48 OLS, OLS bisector, MA, OLP n = 20-500; b = 1.0, 2.0; q = 0.25-1.0 OLS bisector Allometry 40 MA, SMA (OLP) n = 10, 20; q = 0.1-0.9 Log MA, OLP* Chemistry 33 OLS, MA, WMA n = 50; b = 1.0 WMA Chemistry 34 OLS, WLS, MA, WMA, P-B n = 50; b = 1.0 MA, WMA Chemistry 22 OLS, WMA, P-B n = 40; q ‡ 0.96 P-B, WMA Mathematics 49 OLS, LAD, LAPD, TLS (MA), SHVD n = 12-48; b = 1.0 SHVD, AHVD Chemistry 27 BLS, BLMS n = 6, 90; b = 1.0 BLMS Chemistry 50 OLS, WLS, BLS n = 5-100; b = 1.0 BLS Chemistry 51 EM, GLS, ODR, MM, CVR, OR (MA) n = 51; b = 0.67 EM, MM Biology 41 MA, SMA (OLP) n = 10-90; q = 0.5, 0.75 OLP Geology 52 OLS, WLS, MA, BLMS, EM, RR, RT ++ b = 1.0, 1.05 RR, RT, EM *If n < 20, r ‡ 0.6. n, sample sizes; b, slope of Y on X for population in model Y = a + bX; q, correlation coefficient for population; r, Pearson's correlation coefficient for sample; OLS, ordinary least squares regression; MA, major axis regression; WMA, weighted major axis regression; OLP, ordinary least products regression; WLP, weighted least products regression; Bartlett, Bartlett's 3 group method; Mandel, Mandel's method; SMA, standardized major axis regression; P-B, Passing-Bablok; LAD, least absolute deviations; LAPD, least absolute perpendicular deviations; TLS, total least squares; SHVD, squares of horizontal and vertical deviations; BLS, bivariate least squares; BLMS, bivariate least medians squared; WLS, weighted least squares; EM, expectation minimization; GLS, generalized least squares; ODR, orthogonal distance regression; MM, method of moments; CVR, constant variance ratio; OR, orthogonal regression; EM, expectation minimization; RR, Riu-Rius method; RT, Riply-Thompson method; WLP, weighted least products; +++, RT; ++, Ripley-Thompson; AHVD, absolute horizontal and vertical distances.…”

Comparison of inductively coupled plasma optical emission spectrometry, energy dispersive X-ray fluorescence spectrometry and laser ablation inductively coupled plasma mass spectrometry in the elemental analysis of agricultural soils

“…† All three methods of maximum likelihood estimation (BLS, YR, RTR) give identical values of estimates of slope and intercept as referred also in ref. 48. For all regression methods used the intercept (constant systematic error) was not found to be statistically signicant (on a condence level a ¼ 0.05).…”

Systematic errors in analytical measurement results

“…The implication is that most previous rainwater composition studies based on ionic analyses will have systematically underestimated nutrient deposition. The analysis of bias in geochemical analysis is of concern in a work by de Castilho, who reports Monte Carlo simulations to test statistical methods for detecting analytical bias [28]. Charlet and Marchal report the use of certified reference materials in making metrologically sound measurements of heavy metals in groundwater [29].…”