Improved composition of Hawaiian basalt BHVO-1 from the application of two new and three conventional recursive discordancy tests

Abstract

In order to establish the best statistical procedure for estimating improved compositional data in geochemical referencematerials for quality control purposes, we evaluated the test performance criterion ( π D|C ) and swamping ( π swamp ) and masking ( π mask )effects of 30 conventional and 32 new discordancy tests for normal distributions from central tendency slippage δ = 2 10, number ofcontaminants E = 1 4, and sample sizesn= 10, 20, 30, 40, 60, and 80. Critical values or percentage points required for 44 test variantswere generated through precise and accurate Monte Carlo simulations for sample sizesn min (1)100. The recursive tests showed overall thehighest performance with the lowest swamping and masking effects. This performance was followed by Grubbs and robust discordancytests; however, both types of tests have significant swamping and masking effects. The Dixon tests showed by far the lowest performancewith the highest masking effects. These results have implications for the statistical analysis of experimental data in most science andengineering fields. As a novel approach, we show the application of three conventional and two new recursive tests to an internationalgeochemical reference material (Hawaiian basalt BHVO-1) and report new improved concentration data whose quality is superior to allliterature compositions proposed for this standard. The elements with improved compositional data include all 10 major elements fromSiO 2to P 2 O 5 , 14 rare earth elements from La to Lu, and 42 (out of 45) other trace elements. Furthermore, the importance of larger samplesizes inferred from the simulations is clearly documented in the higher quality of compositional data for BHVO-1.