If this type of mathematical analysis is to be used, the following suggestions are provided:

• Explicitly define the assumptions behind the analysis applied to obtain estimates of background distribution.

• Adopt objective techniques to obtain the parameters of interest with known uncertainty bounds (for example, the ten-step process relies on subjective approaches).

• Use appropriate statistical techniques, either explicitly proving any required statistical properties or citing literature for such support (for example, there is no evidence that the ten-step process is reasonably unbiased, and no estimator of its uncertainties is available).

• Implement adequate quality control to ensure that all the data used are included in the report—for example, the data for zinc concentrations in sediments of the lower basin are not provided in the report as they are for the other metals (URS Greiner, Inc. and CH2M Hill 2001, Table C-2).

Royston, P. 1993. A toolkit for testing for non-normality in complete and censored samples. Statistician 42(1):37-43.

Royston, P. 1995. AS R94 A remark on algorithm AS 181: The W-test for normality. Appl. Statist. 44(4):547-551.

URS Greiner, Inc., and CH2M Hill. 1998. Sediment Contamination in the Lower Coeur d’Alene River Basin (LCDARB): Geophysical and Sediment Coring Investigations in the River Channel, Lateral Lakes, and Floodplains. Bunker Hill Facility Basin-Wide RI/FS Data Report, Vol.1, Section 1-9. Contract No. 68-W-98-228. Prepared for U.S. Environmental Protection Agency, Region 10, Seattle, WA, by URS Greiner, Inc., Seattle, WA, and CH2M Hill, Bellevue, WA. October 1998.

URS Greiner, Inc., and CH2M Hill. 2001. Final Technical Memorandum (Rev. 3) Estimation of Background Concentrations in Soil, Sediment, and Surface Water in the Coeur d’Alene and Spokane River Basins. URSG DCN 4162500.6790.05a. EPA Site File No. 2.7. Prepared for U.S. Environmental Protection Agency, Region 10, Seattle, WA, by URS Greiner, Inc., Seattle, WA, and CH2M Hill, Bellevue, WA. October 2001.