Evaluation of Statistical Estimation Methods for Lognormally Distributed Variables

Abstract

Distributions of many chemical, physical, and microbiological properties of soils appear to be lognormal. Several conflicting recommendations exist in the soil science and statistical literature on how to best estimate the population mean, variance, and coefficient of variation of lognormally distributed data. We chose to determine with statistical certainty which of the following three methods is best: (i) the method of moments (method 1); (ii) maximum likelihood (method 2); and (iii) Finney's method (method 3). We assessed the efficacy of these three methods for estimating the mean, variance, and coefficient of variation of lognormal data in the range of sample sizes from = 4 to 100. Three test lognormal populations were used in our evaluation with coefficients of variation that span the range seen for many soil variables (CVs of 50%, 100%, and 200%). We found Finney's method was best for estimating the mean and variance of lognormal data when the coefficient of variation of the underlying lognormal frequency distribution exceeds 100%, below this value the extra computational effort required to implement Finney's technique buys little, relative to the method of moments. Finney's method has not been previously applied by soil scientists, but its superiority over maximum likelihood suggests that the latter should not be generally recommended for estimating the mean, variance and coefficient of variation of lognormal data.