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Description
In the geological sciences it is normally impossible to obtain all the information needed to precisely calculate the mean, µ, and standard deviation, o-, of a given population. Hence, conventional statistical methods for determining these parameters involve collecting a random sample from the population. From this sample an estimate of the mean, X, and the standard deviation, s, are determined. The investigator then assumes that the actual distribution of the population follows a Student's t distribution. With this assumption in hand the 95% confidence interval is calculated from the relationship !critical* (s/ ✓n ). However, if the population does not follow a Student's tdistribution, then X ands may be in error. In contrast, in a typical bootstrap experiment the original data are used as an empirical distribution. This distribution is then randomly sampled a large number of times (e.g., 5000 times). During each resampling the mean is calculated, and the sampled data are returned to the original distribution. From such data the sampling distribution of the means is formed, and the 2.5 and 97.5 percentiles are precisely located. Hence, the bootstrap method for determining confidence level intervals is nonparametric and range preserving. Because of these properties it may prove more useful than classical parametric statistical methods, such as those based on the Student's t distribution. In an attempt to make such a process quick and efficient, a software program termed Bootstrapping the Uncertainties in Compositional Data was written in Visual Basic 6.0. The program allows users to (1) enter data in one of several formats, (2) calculate the 95% confidence level within seconds, and (3) view a frequency histogram of the resulting data.
