Quality control in geochemistry from a comparison of four central tendency and five dispersion estimators and example of
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ORIGINAL PAPER
Quality control in geochemistry from a comparison of four central tendency and five dispersion estimators and example of a geochemical reference material Surendra P. Verma 1 & Lorena Díaz-González 2 & Javier A. Pérez-Garza 3 & Mauricio Rosales-Rivera 4
Received: 19 September 2016 / Accepted: 16 November 2016 # Saudi Society for Geosciences 2016
Abstract Data quality control in geochemistry constitutes a fundamental problem that is still to be solved from the application of statistics and computation. We used refined Monte Carlo simulations of 10,000 replications and 190 independent experiments for sample sizes of 5 to 100. Statistical contaminations of 1 to 4 observations were used to compare 9 statistical parameters (4 central tendency—mean, median, trimean, and Gastwirth mean, and 5 dispersion estimates— standard deviation, median absolute deviation, Sn, Qn, and σn ). The presence of discordant observations in the data arrays rendered the outlier-based and robust parameters to disagree with each other. However, when the mean and standard deviation (outlier-based parameters) were estimated from censored data arrays obtained after the identification and separation of outlying observations, they generally provided a better Electronic supplementary material The online version of this article (doi:10.1007/s12517-016-2764-4) contains supplementary material, which is available to authorized users. * Surendra P. Verma [email protected]
1
Instituto de Energías Renovables, Universidad Nacional Autónoma de México, Priv. Xochicalco s/no., Col. Centro, Apdo. 34, 62580 Temixco, Mexico
2
Centro de Investigación en Ciencias, Instituto de Investigación en Ciencias Básicas y Aplicadas, Universidad Autónoma de Estado de Morelos, Av. Universidad 1001, Chamilpa, 62209 Cuernavaca, Mor, Mexico
3
Licenciatura en Ciencias, Instituto de Investigación en Ciencias Básicas y Aplicadas, Universidad Autónoma de Estado de Morelos, Av. Universidad 1001, Chamilpa, 62209 Cuernavaca, Mor, Mexico
4
Doctorado en Ciencias, Instituto de Investigación en Ciencias Básicas y Aplicadas, Universidad Autónoma de Estado de Morelos, Av. Universidad 1001, Chamilpa, 62209 Cuernavaca, Mor, Mexico
estimate of the population than the robust estimates obtained from the original data arrays. This inference is contrary to the general belief, and therefore, reasons for the better performance of the outlier-based methods as compared to the robust methods are suggested. However, when all parameters were estimated from censored arrays and appropriate precise and accurate correction factors put forth in this work were applied, all of them became fully consistent, i.e., the mean agreed with the median, trimean and Gastwirth mean, and the standard deviation with the median absolute deviation, Sn, Qn, and σn . An example of inter-laboratory chemical data for a Hawaiian reference material BHVO-1 included sample sizes from 5 to 100, which showed that small samples of up to 20 provide inconsistent estimates, whereas larger samples of 20–100, especially >
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