Use of Goodness‐of‐fit Tests for Characterizing the Spatial Variability of Soil Properties

Abstract

Abstract Application of the empirical distribution function (EDF) statistics to describe the spatial variability of soil properties is discussed. The Kolmogorov statistic ( D ) and the Cramer‐von Mises statistics ( W 2 ) were utilized to statistically evaluate the goodness‐of‐fit of a hypothesized theoretical distribution function to a sample of measurements of spatially‐varying soil properties. Because normal and log‐normal distributions have been commonly used to describe the variability of several soil properties, a Monte Carlo study was performed to determine the sample size required for selecting, with a prescribed level of confidence, between these two distributions. It was found that the required sample size increased with decreasing coefficient of variation (CV = standard deviation/mean). However, both normal and log‐normal distributions may adequately describe a set of measurements with CV ⩽ 0.4. In such cases, it was shown that accepting normal distribution as the appropriate distribution when the true distribution is, in fact, log‐normal, would involve a maximum error of about 20% when the mean is used instead of the mode.