Defining surfaces for skewed, highly variable data

Skewness of environmental data is often caused by more than simply a handful of outliers in an otherwise normal distribution. Statistical procedures for such datasets must be sufficiently robust to deal with distributions that are strongly non-normal, containing both a large proportion of outliers and a skewed main body of data. In the field of water quality, skewness is commonly associated with large variation over short distances. Spatial analysis of such data generally requires either considerable effort at modeling or the use of robust procedures not strongly affected by skewness and local variability. Using a skewed dataset of 675 nitrate measurements in ground water, commonly used methods for defining a surface (least-squares regression and kriging) are compared to a more robust method (loess). Three choices are critical in defining a surface: (i) is the surface to be a central mean or median surface? (ii) is either a well-fitting transformation or a robust and scale-independent measure of center used? (iii) does local spatial autocorrelation assist in or detract from addressing objectives? Published in 2002 by John Wiley & Sons, Ltd.