Table 2Flow chart of statistical procedures for estimating soil contamination areas.|@|~(^,^)~|@|Correlation chart of multivariate soil data. The histogram of each variable is shown on the diagonal with primary variables (As and Pb determined using ICP-AES) in blue and auxiliary variables (Cu, Ni, and Zn using ICP-AES and all PXRF data) in green. The values on the upper right of the diagonal indicate the correlation coefficients. The stars indicate the significance levels (*** p < 0.001, ** p < 0.01, * p < 0.05). On the bottom left of the diagonal, the bivariate scatter plots are displayed with a fitted red line. Values on the boundaries indicate the concentrations on a log scale.|@|~(^,^)~|@|Pairwise probability density functions fitted to the Gaussian Mixture Model (GMM) and EVE (ellipsoidal, equal volume and orientation) model. Values on the boundaries indicate probability density.|@|~(^,^)~|@|Spatial distributions of As concentrations in the study area: (a) the results of ordinary kriging (OK) using 49 training data; (b) and (c) the results of ordinary co-kriging (OCK) and Gaussian Mixture Model (GMM), respectively, using 49 training data and 156 auxiliary data (As determined by PXRF for OCK and ICP-AES Pb, Cu, Ni, and Zn and PXRF As, Pb, and Cu for GMM); (d) the most realistic distribution of contamination that was estimated by OK using all the ICP-AES data (n=153). The black line indicates the regulatory level (25 mg/kg) by the Soil Environmental Conservation Act of the Republic of Korea.|@|~(^,^)~|@|Root mean-square errors (RMSE) between the measured and predicted values using the validation data (n=30) at different sampling densities for training (n=30 to 107 in Table 2). (a) As, (b) Pb.|@|~(^,^)~|@|Pearson correlation coefficients (r) between the measured and predicted values using the validation data (n=30) at different sampling densities for training (n=30 to 107 in Table 2): (a) As, (b) Pb.

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