Alternative approach for precise and accurate Student´s t critical values and application in geosciences

Verma, Surendra P.; Cruz-Huicochea, René

doi:10.5209/rev_jige.2013.v39.n1.41747

Cited by 11 publications

(6 citation statements)

References 32 publications

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“…Our approach to the statistical problem of test performance is novel because, instead of using commercial or freely available software, we programmed and generated extremely precise and accurate random numbers and normally distributed data, used very large replications of 20,000,000, performed 102 independent experiments, and reduced the simulation errors to such an extent that the differences in test performance are far greater than the total uncertainties expressed as 99% confidence intervals of the mean. This is an approach hitherto practiced by none (see, e.g., [ 8 – 18 ]) except by our group [ 19 – 23 ]. This work, therefore, supersedes the approximate simulation results of test performance reported by the statisticians Hayes and Kinsella [ 7 ].…”

Section: Introductionmentioning

confidence: 99%

Comparative Performance of Four Single Extreme Outlier Discordancy Tests from Monte Carlo Simulations

Verma

Díaz-González

Rosales-Rivera

et al. 2014

The Scientific World Journal

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Using highly precise and accurate Monte Carlo simulations of 20,000,000 replications and 102 independent simulation experiments with extremely low simulation errors and total uncertainties, we evaluated the performance of four single outlier discordancy tests (Grubbs test N2, Dixon test N8, skewness test N14, and kurtosis test N15) for normal samples of sizes 5 to 20. Statistical contaminations of a single observation resulting from parameters called δ from ±0.1 up to ±20 for modeling the slippage of central tendency or ε from ±1.1 up to ±200 for slippage of dispersion, as well as no contamination (δ = 0 and ε = ±1), were simulated. Because of the use of precise and accurate random and normally distributed simulated data, very large replications, and a large number of independent experiments, this paper presents a novel approach for precise and accurate estimations of power functions of four popular discordancy tests and, therefore, should not be considered as a simple simulation exercise unrelated to probability and statistics. From both criteria of the Power of Test proposed by Hayes and Kinsella and the Test Performance Criterion of Barnett and Lewis, Dixon test N8 performs less well than the other three tests. The overall performance of these four tests could be summarized as N2≅N15 > N14 > N8.

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Section: Introductionmentioning

confidence: 99%

Comparative Performance of Four Single Extreme Outlier Discordancy Tests from Monte Carlo Simulations

Verma

Díaz-González

Rosales-Rivera

et al. 2014

The Scientific World Journal

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“…The statistical inference in these programs is made through the new, highly precise, and accurate critical values obtained from Monte Carlo simulations Quiroz-Ruiz, 2008, 2011;Cruz-Huicochea and Verma, 2013;Verma and Cruz-Huicochea, 2013).…”

Section: Citations Of Lementioning

confidence: 99%

Origin, evolution, and tectonic setting of the eastern part of the Mexican Volcanic Belt and comparison with the Central American Volcanic Arc from conventional multielement normalized and new multidimensional discrimination diagrams and discordancy and significance tests

Verma¹

2015

Turkish J Earth Sci

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If both the Mexican Volcanic Belt (MVB) and the Central American Volcanic Arc (CAVA) have been related to the subduction of the Cocos plate beneath the North American and Caribbean plates, respectively, their magmas, and especially the less evolved basic varieties, should show considerable similarities. The conventional multielement normalized diagrams indicate more complex petrogenetic processes for the MVB than the CAVA. Forty-five statistically coherent tectonomagmatic discrimination diagrams were used to infer the tectonic setting of the controversial geological subprovince of the eastern part of the MVB (E-MVB). Basic rocks from the E-MVB indicated a continental rift setting, whereas the intermediate rocks were more consistent with a transitional setting of rift to collision. The acid rocks, presumably having a larger crustal component than the intermediate and basic rocks, showed inconclusive results. The volcanic rock data from the CAVA were used to successfully test these diagrams. The expected arc setting was consistently indicated for the CAVA from basic, intermediate, and acid rocks, confirming the satisfactory functioning of the diagrams. The data for all three types of rocks from the E-MVB and CAVA were then objectively compared for their similarities and differences. Specially designed computer programs were used to efficiently apply discordancy and significance tests at the strict 99% confidence level. Most (43 out of 50) chemical elements and (25 out of 28) log-ratio parameters in basic rocks from the E-MVB and CAVA showed statistically significant differences. For intermediate rocks and, to a lesser extent, for acid rocks, a large number of parameters also showed differences between the E-MVB and CAVA. The differences in the inferred tectonic settings for basic and evolved rocks from the E-MVB are likely related to the different magmatic sources.

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“…Using UDASYS software (Verma et al, 2013a), we applied the analysis of variance (ANOVA) test at the 99% confidence level for the compositional data to statistically identify the similarities between the SN and SC sands. This software uses precise and accurate critical values of F (Cruz-Huicochea and Verma, 2013) and t (Verma and Cruz-Huicochea, 2013) for the application of significance tests (F, t, and ANOVA;Verma, 2005). The samples were differentiated as 4 independent groups for ANOVA, i.e.…”

Section: Methodsmentioning

confidence: 99%

Geochemistry of sands along the San Nicolás and San Carlos beaches, Gulf of California, Mexico: implications for provenance and tectonic setting

Armstrong‐Altrin¹,

Nagarajan²,

Lee³

et al. 2014

Turkish J Earth Sci

114

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Th, P, and Hf were immobile and Cu, Cr, and Zn were mobile during alteration processes. However, Torres-Alvarado et al. (2007) recently studied the effect of hydrothermal alteration on the chemistry of volcanic rocks from the Los Azufres geothermal field, Mexico, and found that most major elements and a few trace elements, including high field strength elements such as Zr, Ti, and P, were mobilized during hydrothermal alteration. They cautioned against the use of these elements for petrogenetic studies of igneous and metamorphic rocks. Although provenance studies are common (Hossain et al., 2010(Hossain et al., , 2014Armstrong-Altrin and Natalhy-Pineda, 2013), studies focused on the geochemical variation in sediments with respect to grain size are meagre (e.g., Ohta, 2008;Effoudou-Priso, 2014).The study areas of the San Nicolás (SN) and San Carlos (SC) beaches are located along the Gulf of California.

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Alternative approach for precise and accurate Student´s t critical values and application in geosciences

Cited by 11 publications

References 32 publications

Comparative Performance of Four Single Extreme Outlier Discordancy Tests from Monte Carlo Simulations

Comparative Performance of Four Single Extreme Outlier Discordancy Tests from Monte Carlo Simulations

Origin, evolution, and tectonic setting of the eastern part of the Mexican Volcanic Belt and comparison with the Central American Volcanic Arc from conventional multielement normalized and new multidimensional discrimination diagrams and discordancy and significance tests

Geochemistry of sands along the San Nicolás and San Carlos beaches, Gulf of California, Mexico: implications for provenance and tectonic setting

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