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Resistant and Exploratory Techniques for Use in Semivariogram Analyses¹

ABSTRACT

"Traditional" statistical analyses based on the assumption of independent observations are being replaced by spatial analyses that take account of correlations between neighboring observations. Geostatistics is one approach; it characterizes the spatial relationships of data via the variogram, which is in turn used for kriging (optimal, unbiased linear interpolation). Exploratory data analysis techniques, relying on resistant measures, graphical tools, and robustness ideas, can be used to help "model" the spatial structure of data. Data should fulfill certain stationarity conditions before computing and interpreting the semivariogram. Data of soil-water pressure potential are analyzed by straight-forward techniques that assure the data meet the implicit assumptions of stationarity (of the mean and the variance) and at least symmetry. Stem-and-leaf plots and plots of mean vs. variance (or for a more resistant analysis, median vs. interquartile range squared) are used to assess the variance stationarity and data distributions. Median-based techniques (rather than polynomial modeling and generalized least-squares fitting of drift) are used to remove drift along both grid directions. Then the spatial structure is exposed through computing and interpreting semivariograms of the modified data.

¹ Journal Paper no. J.-11759 of the Iowa Agriculture and Home Economics Experiment Station, Ames, IA. Project no. 2556 and 2715.

² Research Associate, Dep. of Agricultural Engineering, Associate Professor, Dep. of Agronomy, and Professor, Dep. of Statistics, Iowa State Univ., Ames, IA. 50011. This research benefited from equal contribution from each author.

Received for publication January 31, 1985.

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