Application of the Bootstrap Method for chemical data from the Boda Claystone Formation

In this paper we will demonstrate the use and efficiency of the bootstrap on a geologic problem. The tools of classical statistics are often not applicable because they strongly depend on certain conditions that are not fulfilled. Explicit mathematical formulas for standard errors and confidence intervals with respect to a parameter either require some specific (generally normal) distribution, or they do not exist at all. Hypothesis tests may also only be carried out if some conditions are satisfied. Using the bootstrap method one can simulate the unknown distribution of an arbitrary statistic by its bootstrap replicates; hence any characteristics (standard error, confidence intervals, and test significance levels) can be obtained through direct empirical calculations. We applied the bootstrap to the chemical composition data of rock samples from the Boda Claystone Formation, Hungary. First we investigated the distribution of 8 chemical components in a rock sample group of few elements, computing standard errors and confidence intervals for the mean, the standard deviation and the skewness of these distributions. Then two groups of rock samples from different sampling regions were compared using hypothesis tests.