A new computer program TecDIA written in Java, for the application of 35 previously-defined multidimensional diagrams for the tectonomagmatic discrimination of intermediate and acid magmas is briefly described. A detailed Readme document is presented in the Supplementary Electronic Material file. As an innovation, this program provides a ready to publish report containing a synthesis of all diagrams, including the total percent probabilities. The use of this program is illustrated by two examples of the Bohemian Massif (Czech Republic) for older Carboniferous (granitoids of the Central Bohemian Pluton) and younger Late Carboniferous-Early Permian igneous rocks (volcanics from late Variscan continental basins and granitoids of the Žulová Pluton). According to the results, the tectonic setting for the Early Carboniferous rocks was collisional, whereas for the Late Carboniferous-Early Permian igneous suite it was either a collision or a transition from collisional to a within-plate setting. The acid rocks probably dominated by a crustal component may provide a somewhat different result as compared to the intermediate rocks. TecDIA freely available from http://tlaloc.ier.unam.mx will certainly be useful for all interested in applying these 35 multidimensional diagrams.
We applied an alternative Monte Carlo simulation approach to obtain precise and accurate critical values (with 3 to 8 decimal places) for the Student´s t test for normal samples of degrees of freedom up to 6000 and for two-sided confidence levels of 50% to 99.9% and correspondingly for one-sided confidence levels of 75% to 99.95%. As an innovation, unlike the existing literature precision estimates of critical values are also individually reported. Prior to our work, critical values (with 2 or 3 decimal places) were available in tables in the published literature. Twenty-eight regression models were evaluated to obtain the best regression fitting of the tabulated data. All conventional polynomial (from quadratic up to 8th order) regressions failed for this purpose. New equations based on double or triple natural logarithm-transformations are proposed for all not-tabulated degrees of freedom, including fractional values if required as well as for probability computations. More importantly, we suggest that these kinds of log-transformations are likely to be useful for all cases where conventional polynomial regressions fail to perform satisfactorily. To demonstrate the utility of these new critical values and best-fit equations, we provide specific examples of applications in geochemistry, chemistry and medicine. The probability estimates, obtained from the present explicit approach, are consistent with commercial and freely available software. Additionally, a more extensive application of our t values is given for processing inter-laboratory data for geochemical reference materials granites G-1 and G-2 from U.S.A. as well as for evaluating geochemical data for basic rocks from the Canary and Azores Islands.Keywords: Monte Carlo simulation, Student t test, polynomial regressions, statistical method, geochemical reference material.
ResumenAplicamos un método de simulación alterno tipo Monte Carlo para obtener valores críticos precisos y exactos de t de Student (de 3 a 8 puntos decimales) para muestras normales con grados de libertad hasta 6000 y para niveles de confianza de dos colas de 50% a 99.9% y por consecuencia, para niveles de confianza de una cola de 75% a 99.95%. Como una innovación, se reporta en forma individual la precisión de los valores críticos, lo cual no sucede en la literatura publicada. Previo a nuestro trabajo, en las tablas de la li-32
Our aim is to show a statistical procedure along with two new computer programs (DODESSYS and UDASYS). For this task we compiled a database of 249 samples of dacite coming from four closely located Mexican Volcanic Belt (MVB) areas: monogenetic volcanoes from the Sierra de Chichinautzin and Valle de México, the Nevado de Toluca stratovolcano, the Iztaccíhuatl stratovolcano and the Popocatépetl stratovolcano. The discordancy and significance (ANOVA –ANalysis Of Variance–, Fishers´ F and Student´s t) statistical tests were applied at 99% confidence level. The final statistical was calculated for 98 geochemical parameters, these include major oxides, rare earth elements, trace elements and additional parameters, as well as log-ratio parameters used in new tectonic discrimination diagrams. These geochemical parameters were treated as univariate statistical samples and were classified according with the four MVB regions. Discordancy statistical tests detected discordant outliers in 124 (amount to about 35%) statistical samples. ANOVA tests showed significant differences among all groups in 32 parameters. The similarities and differences between the log-ratios parameters elements may eventually be useful in future to propose tectonic discrimination diagrams from a representative database.
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