In order to establish the best statistical procedure for estimating improved compositional data in geochemical reference materials for quality control purposes, we evaluated the test performance criterion (πD|C) and swamping (πswamp) and masking (πmask) effects of 30 conventional and 32 new discordancy tests for normal distributions from central tendency slippage δ = 2-10, number of contaminants E = 1-4, and sample sizes n = 10, 20, 30, 40, 60, and 80. Critical values or percentage points required for 44 test variants were generated through precise and accurate Monte Carlo simulations for sample sizes nmin(1)100. The recursive tests showed overall the highest performance with the lowest swamping and masking effects. This performance was followed by Grubbs and robust discordancy tests; however, both types of tests have significant swamping and masking effects. The Dixon tests showed by far the lowest performance with the highest masking effects. These results have implications for the statistical analysis of experimental data in most science and engineering fields. As a novel approach, we show the application of three conventional and two new recursive tests to an international geochemical reference material (Hawaiian basalt BHVO-1) and report new improved concentration data whose quality is superior to all literature compositions proposed for this standard. The elements with improved compositional data include all 10 major elements from SiO2 to P2O5, 14 rare earth elements from La to Lu, and 42 (out of 45) other trace elements. Furthermore, the importance of larger sample sizes inferred from the simulations is clearly documented in the higher quality of compositional data for BHVO-1.