Calculating Confidence, Uncertainty, and Numbers of Samples When Using Statistical Sampling Approaches to Characterize and Clear Contaminated Areas

Abstract

This report discusses the methodology, formulas, and inputs needed to make characterization and clearance decisions for Bacillus anthracis-contaminated and uncontaminated (or decontaminated) areas using a statistical sampling approach. Specifically, the report includes the methods and formulas for calculating the • number of samples required to achieve a specified confidence in characterization and clearance decisions • confidence in making characterization and clearance decisions for a specified number of samples for two common statistically based environmental sampling approaches. In particular, the report addresses an issue raised by the Government Accountability Office by providing methods and formulas to calculate the confidence that a decision area is uncontaminated (or successfully decontaminated) if all samples collected according to a statistical sampling approach have negative results. Key to addressing this topic is the probability that an individual sample result is a false negative, which is commonly referred to as the false negative rate (FNR). The two statistical sampling approaches currently discussed in this report are 1) hotspot sampling to detect small isolated contaminated locations during the characterization phase, and 2) combined judgment and random (CJR) sampling during the clearance phase. Typically if contamination is widely distributed in a decision area, it will be detectable via judgmentmore » sampling during the characterization phrase. Hotspot sampling is appropriate for characterization situations where contamination is not widely distributed and may not be detected by judgment sampling. CJR sampling is appropriate during the clearance phase when it is desired to augment judgment samples with statistical (random) samples. The hotspot and CJR statistical sampling approaches are discussed in the report for four situations: 1. qualitative data (detect and non-detect) when the FNR = 0 or when using statistical sampling methods that account for FNR > 0 2. qualitative data when the FNR > 0 but statistical sampling methods are used that assume the FNR = 0 3. quantitative data (e.g., contaminant concentrations expressed as CFU/cm2) when the FNR = 0 or when using statistical sampling methods that account for FNR > 0 4. quantitative data when the FNR > 0 but statistical sampling methods are used that assume the FNR = 0. For Situation 2, the hotspot sampling approach provides for stating with Z% confidence that a hotspot of specified shape and size with detectable contamination will be found. Also for Situation 2, the CJR approach provides for stating with X% confidence that at least Y% of the decision area does not contain detectable contamination. Forms of these statements for the other three situations are discussed in Section 2.2. Statistical methods that account for FNR > 0 currently only exist for the hotspot sampling approach with qualitative data (or quantitative data converted to qualitative data). This report documents the current status of methods and formulas for the hotspot and CJR sampling approaches. Limitations of these methods are identified. Extensions of the methods that are applicable when FNR = 0 to account for FNR > 0, or to address other limitations, will be documented in future revisions of this report if future funding supports the development of such extensions. For quantitative data, this report also presents statistical methods and formulas for 1. quantifying the uncertainty in measured sample results 2. estimating the true surface concentration corresponding to a surface sample 3. quantifying the uncertainty of the estimate of the true surface concentration. All of the methods and formulas discussed in the report were applied to example situations to illustrate application of the methods and interpretation of the results.« less