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Use of Goodness-of-fit Tests for Characterizing the Spatial Variability of Soil Properties¹

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 (W²) 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.

¹ Joint Contribution from Statistics Dept. and Soil Science Dept., Univ. of Florida. Florida Agric. Exp. Stn. J. Series no. 1316.

² Professor, Statistics Dept.; Assistant Research Scientist, and Professors, Soil Science Dept., Univ. of Florida, Gainesville, FL 32611, respectively.

Received for publication July 26, 1978. Accepted for publication November 8, 1978.

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