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Statistical Evaluation of Median Estimators for Lognormally Distributed Variables

USDA-ARS National Soil Tilth Lab., 2150 Pammel Dr., Ames, IA 50011

J. A. Robinson

7922-190-MR, the Upjohn Co., Kalamazoo, MI 49001

*Corresponding author.

ABSTRACT

The increased interest in the variability of soil properties is responsible for recent observations that soil variables are not normally distributed but are more closely approximated by the two-parameter lognormal frequency distribution. Statistical methods commonly applied in the estimation of the median of lognormally distributed data, however, are biased or inefficient. The purpose of this study was to evaluate four statistical methods for estimating, from sample data, the median of a lognormal population. The four statistical methods were: (i) the geometric mean (GM), (ii) a bias-corrected form of the geometric mean (BCGM), (iii) a uniformly minimum variance unbiased (UMVU) estimator, and (iv) the sample median (SM). In addition, two techniques for computing confidence limits about the median were evaluated. Monte Carlo simulations from four different lognormal populations were used in these evaluations to determine the efficacy of these methods as a function of both population variance and sample size (n = 4–100). Results of this work indicate that the UMVU estimator and the BCGM estimators are unbiased and yield estimates with the lowest mean square error. An example is provided that illustrates the application of these techniques.

Received for publication January 31, 1991.

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