Description
The purpose of this study is to assess the efficiency of the bootstrap method versus conventional statistical methods for determining the confidence intervals for compositional data. Eight samples were taken from a large outcrop of the Oriflamme Canyon protomylonite within the Cuyamaca-Laguna Mountain shear zone. Each sample was made into a thin section. During point counting minerals that fell under the cross hair were assigned to quartz, feldspar, or biotite. Following study of thin sections, slabs of each sample were stained, and then scanned into a computer file using Adobe PhotoShop. A 0.25 cm by 0.25 cm grid was placed over the scanned images and points were again counted and assigned to quartz, feldspar, or biotite. Statistical data derived from point counting thin sections and stained rock slabs included the mean, standard deviation, standard error, t critical, and 95% confidence interval. The 95% confidence interval about the mean was estimated using the Student's t distribution and the bootstrap program Bootstraping Compositional Data (BOCD) written by Mr. Brett Heitman. Statistical data resulting from the two different methods for estimating the 95% confidence interval were reasonably close. For example, the Student's t distribution indicated that the 95% confidence band for the number of counts of quartz is ± 9 for data collected from thin sections, while the same statistic estimated from the bootstrap method is± 7. Similarly, the Student's t distribution gave± 6 while the bootstrap method yielded +4.5/-5 as estimates for the 95% confidence interval for the number of counts of quartz in stained slabs. Based on these data, and the commonly observed asymmetric form of frequency distributions derived from compositional data, the bootstrap method appears to provide a better estimate of the 95% confidence interval given its range preserving and nonparametric characteristics. It is therefore recommended that BOCD be considered when estimating the confidence intervals for compositional data.
