Application of the discordant outlier detection and separation system in the geosciences

Abstract

Basically, two main types of statistical methods – robust and outlier-based – are available for handling experimental data; we document here the application of the outlier-based method. Due to the unavailability of a suitable software system for statistically correct application of the outlier-based method, a new computer program, DODESSYS (Discordant Outlier DEtection and Separation SYStem), was written for the application of 33 discordancy test variants to experimental data, constituting contaminated or uncontaminated normal statistical samples. We illustrate the application of the discordant outlier-based scheme by five specific examples; three include univariate data for which this procedure was specifically designed and two are for bivariate data for which this methodology can be easily adopted. We thus report new statistical information on two reference materials (granite G-2 and sediment IAEA-417), bryozoan species from eastern Oman, a new improved Na/K geothermometric equation, and a more significant correlation with water depth of the abundance of meiofauna from the Gulf of Mexico. Recently, two sets of multi-dimensional discrimination diagrams for basic as well as acid rocks have been proposed from statistically correct methodology of natural logarithm-transformation of element ratios; the diagrams also require that these ratios should be normally distributed. We present numerous examples of application of these new diagrams for inferring tectonic setting of Archaean to Recent rocks, both before and after testing the datasets for discordant outliers. We recommend that outlying observations should always be evaluated for their discordancy.

Keywords:

• outlier methods
• discordancy tests
• reference materials
• univariate data
• studentized residuals
• geothermometric equation
• discrimination diagrams

Acknowledgements

The second author (LDG) is grateful to Conacyt for a doctoral fellowship during 2005–2008, during which most of the computer programming work was carried out. We are also much grateful to Alfredo Quiroz-Ruiz who provided frequent help during the programming and testing of DODESSYS and to Rosalinda González-Ramírez, Sanjeet K. Verma, and K. Pandarinath for help during the data compilation stage of our work. Andrej Ernst is thanked for sending us the raw data related to the paper by Ernst et al. (2008) on Stenolaemate bryozoa.