Use of log normal transformation in environmental statistics
The log normal transformation is commonly used in the analysis of environmental data. The sample histogram of observed contaminant concentrations from a Superfund site typically appears to be log normal and the concentration data is log-transformed so that the classical statistical methods based on normal distribution can be used. USEPA guidance documents on statistical evaluation of attainment of cleanup standards for soils suggest using the log normal transformation in case the contaminant concentration data appears to be log normal. There are two basic problems with using a transformation in data analysis: (i) interpretation of results, and (ii) in transforming a formula based on the assumption of normality of the data so that it can be applied to transformed data; The present thesis will address the second problem associated with the log transformation. In addition, the performance of some of the common normal-theory based procedures applied on original concentration data when the data distribution is in fact log normal will be investigated. Real Superfund site characterization data and simulated data will be used to provide examples.