Relative Efficiency of Single‐Outlier Discordancy Tests for Processing Geochemical Data on Reference Materials and Application to Instrumental Calibrations by a Weighted Least‐Squares Linear Regression Model

Abstract

Numerous studies report geochemical data on reference materials (RMs) processed by outlier‐based methods that use univariate discordancy tests. However, the relative efficiency of the discordancy tests is not precisely known. We used an extensive geochemical database for thirty‐five RMs from four countries (Canada, Japan, South Africa and USA) to empirically evaluate the performance of nine single‐outlier tests with thirteen test variants. It appears that the kurtosis test (N15) is the most powerful test for detecting discordant outliers in such geochemical RM databases and is closely followed by the Grubbs type tests (N1 and N4) and the skewness test (N14). The Dixon‐type tests (N7, N8, N9 and N10) as well as the Grubbs type test (N2) depicted smaller global relative efficiency criterion values for the detection of outlying observations in this extensive database. Upper discordant outliers were more common than the lower discordant outliers, implying that positively skewed inter‐laboratory geochemical datasets are more frequent than negatively skewed ones and that the median, a robust central tendency indicator, is likely to be biased especially for small‐sized samples. Our outlier‐based procedure should be useful for objectively identifying discordant outliers in many fields of science and engineering and for interpreting them accordingly. After processing these databases by single‐outlier discordancy tests and obtaining reliable estimates of central tendency and dispersion parameters of the geochemical data for the RMs in our database, we used these statistical data to apply a weighted least‐squares linear regression (WLR) model for the major element determinations by X‐ray fluorescence spectrometry and compared the WLR results with an ordinary least‐squares linear regression model. An advantage in using our outlier procedure and the new concentration values and uncertainty estimates for these RMs was clearly established.

New computer program TecD for tectonomagmatic discrimination from discriminant function diagrams for basic and ultrabasic magmas and its application to ancient rocks.

“…We achieved this through the use of DODESSYS (Verma and Díaz-González, 2012) by applying all singleoutlier type tests (Barnett and Lewis, 1994;Verma, 1997Verma, , 2005Verma et al, 2009) to log-transformed ratios used in LDA by Verma and Agrawal (2011). We emphasize that discordancy tests should be applied to log-ratios and not to crude compositional data; see Verma (2012) for geochemometric reasons.…”

IAEA inter-laboratory comparisons of geothermal water chemistry: critiques on analytical uncertainty, accuracy, and geothermal reservoir modelling of Los Azufres, Mexico

“…Verma et al (2008a) simulated new critical values for these and other discordancy tests and implemented the modified version of Dixon and Grubbs test method in a computer program, DODESSYS (Discordant Outlier DEtection and Separation SYStem; Verma and Díaz-González, 2012) and named as the single-outlier type multiple-test method involving Dixon, Grubbs, skewness and kurtosis tests at 99% confidence level, initially proposed and used by Verma (1997) for processing inter-laboratory data on geochemical rock ref-erence materials. The evaluation of the relative efficiency of these single-outlier tests by Verma et al (2009) showed that the Dixon tests are less efficient than the other three types. In this method, the process of removal of outliers is iterated on the remaining dataset till there is no discordant outlier.…”

New critical values for F and their use in the ANOVA and Fisher’s F tests for evaluating geochemical reference material granite G-2 (U.S.A.) and igneous rocks from the Eastern Alkaline Province (Mexico)

“…Similarly, the standard deviation values from ANOVA were lower than the literature data (2s method) for 28 elements, equal for 2 elements, and higher for 30 elements. Such differences in the mean and standard deviation values, irrespective of whether statistically significant or not, may affect the calibration of instruments or the evaluation of analytical methods (e.g., Santoyo and Verma, 2003;Guevara et al, 2005;Verma et al, 2009;Verma, 2012a).…”

“…These significance tests also require that the individual data arrays (statistical samples under evaluation) be drawn from a normal distribution (Morrison, 1990). To ascertain this assumption, we used only the multiple-outlier type tests (Barnett and Lewis, 1994;González-Ramírez et al, 2009;Verma et al, 2009) programmed in DODESSYS (Verma and Díaz-González, 2012) for identifying and separating discordant outliers at the strict 99% confidence level. We applied the ANO-VA and F tests both before and after the application of Table 13 (Appendix A -Supplementary material) presents ANOVA results for 10 major-elements (Si to P, all in %), 13 rare-earth elements (La to Lu), and 33 other trace elements (B to W).…”