On sensitivity analysis for Fisher-Behrens comparisons of soil contaminants in Arica, Chile

Abstract

We developed a tailored statistical methodology to compare the contamination by chemical elements in soil of Arica, Chile in 2013 and 2014. We study the differences in the consecutive years 2013 and 2014 between arsenic, mercury, chromium, lead, and cadmium occurrence. The complicated aspect of such comparisons is that the heavy-tailed part of the distribution is mixing with the light-tailed distribution of the measurements and annual distributions of each element differ in their variances. We developed a novel sampling methodology based on the generalized Hill approach, which separates extreme values and the central part of the data. We perform a sensitivity analysis of the Fisher-Behrens test and investigate the effect of violation of homoscedasticity depending on the distributions of random samples. Those methods are useful for experimenters when testing for equality of means in sets with homoscedasticity.