# ASTM D7048-16

Designation: D7048 − 16Standard Guide forApplying Statistical Methods for Assessment and CorrectiveAction Environmental Monitoring Programs1This standard is issued under the fixed designation D7048; the number immediately following the designation indicates the year oforiginal adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. Asuperscript epsilon (´) indicates an editorial change since the last revision or reapproval.1. Scope1.1 The scope and purpose of this guidance is to present avariety of statistical approaches for assessment, complianceand corrective action environmental monitoring programs.Although the methods provided here are appropriate and oftenoptimal for many environmental monitoring problems, they donot preclude use of other statistical approaches that may beequally or even more useful for certain site-specific applica-tions.1.2 In the following sections, the details of select statisticalprocedures used in assessment and corrective action programsfor environmental monitoring (soil, groundwater, air, surfacewater, and waste streams) are presented.1.3 The statistical methodology described in the followingsections should be used as guidance. Other methods may alsobe appropriate based on site-specific conditions or for moni-toring situations or media that are not presented in thisdocument.1.4 This practice offers an organized collection of informa-tion or a series of options and does not recommend a specificcourse of action. This document cannot replace education,experience and professional judgements. Not all aspects of thispractice may be applicable in all circumstances. This ASTMstandard is not intended to represent or replace the standard ofcare by which the adequacy of a given professional servicemust be judged without consideration of a project’s manyunique aspects. The word Standard in the title of this documentonly means that the document has been approved through theASTM consensus process.1.5 This standard does not purport to address all of thesafety concerns, if any, associated with its use. It is theresponsibility of the user of this standard to establish appro-priate safety and health practices and determine the applica-bility of regulatory requirements prior to use.2. Referenced Documents2.1 ASTM Standards:2D653 Terminology Relating to Soil, Rock, and ContainedFluidsD5092 Practice for Design and Installation of GroundwaterMonitoring WellsD5792 Practice for Generation of Environmental Data Re-lated to Waste Management Activities: Development ofData Quality ObjectivesD6250 Practice for Derivation of Decision Point and Confi-dence Limit for Statistical Testing of Mean Concentrationin Waste Management DecisionsD6312 Guide for Developing Appropriate Statistical Ap-proaches for Groundwater Detection Monitoring Pro-grams3. Terminology3.1 Definitions—For definitions of common terms in thisguid, see Terminology D653.3.2 Definitions of Terms Specific to This Standard:3.2.1 corrective action monitoring—under RCRA (in theUnited States), corrective action monitoring is instituted whenhazardous constituents from a RCRA regulated unit have beendetected at statistically significant concentrations between thecompliance point and the downgradient facility propertyboundary as specified under 40 CFR 264.100. Correctiveaction monitoring is conducted throughout a corrective actionprogram that is implemented to address groundwater contami-nation. At non-RCRA sites, corrective action monitoring isconducted throughout the active period of corrective action todetermine the progress of remediation and to identify statisti-cally significant trends in groundwater contaminant concentra-tions.3.2.2 false positive rate—the rate at which the statisticalprocedure indicates contamination when contamination is notpresent.1This guide is under the jurisdiction ofASTM Committee D18 on Soil and Rockand is the direct responsibility of Subcommittee D18.21 on Groundwater andVadose Zone Investigations.Current edition approved Oct. 1, 2016. Published October 2016. Originallyapproved in 2004. Last previous edition approved in 2010 as D7048–04(2010).DOI: 10.1520/D7048-16.2For referenced ASTM standards, visit the ASTM website, www.astm.org, orcontact ASTM Customer Service at service@astm.org. For Annual Book of ASTMStandards volume information, refer to the standard’s Document Summary page onthe ASTM website.Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States13.2.3 lognormal distribution—a frequency distributionwhose logarithm follows a normal distribution.3.2.4 lower confidence limit, LCL—a lower limit that has aspecified probability (for example, 95 %) of including the trueconcentration (or other parameter). Taken together with theupper confidence limit, forms a confidence interval that willinclude the true concentration with confidence level thataccounts for both tail areas (for example, 90 %).3.2.5 lower prediction limit, LPL—a statistical estimate ofthe minimum concentration that will provide a lower bound forthe next series of k measurements from that distribution, or themean of m new measurements for each of k sampling locations,with specified level of confidence (for example, 95 %).3.2.6 nonparametric—a term referring to a statistical tech-nique in which the distribution of the constituent in thepopulation is unknown and is not restricted to be of a specifiedform.3.2.7 nonparametric prediction limit—the largest (or secondlargest) of n background samples. The confidence level asso-ciated with the nonparametric prediction limit is a function ofn, m and k.3.2.8 normal distribution—a frequency distribution whoseplot is a continuous, infinite, bell-shaped curve that is sym-metrical about its arithmetic mean, mode and median (whichare numerically equivalent). The normal distribution has twoparameters, the mean and variance.3.2.9 outlier—a measurement that is statistically inconsis-tent with the distribution of other measurements from which itwas drawn.3.2.10 parametric—a term referring to a statistical tech-nique in which the distribution of the constituent in thepopulation is assumed to be known.3.2.11 potential area of concern—areas with a documentedrelease or likely presence of a hazardous substance that couldpose an unacceptable risk to human health or the environment.3.2.12 upper confidence limit, UCL—an upper limit that hasa specified probability (for example, 95 %) of including thetrue concentration (or other parameter). Taken together withthe lower confidence limit, the UCL forms a confidenceinterval that will include the true concentration with confidencelevel that accounts for both tail areas.3.2.13 upper prediction limit, UPL—a statistical estimate ofthe maximum concentration that will not be exceeded by thenext series of k measurements from that distribution, or themean of m new measurements for each of k sampling locations,with specified level of confidence (for example, 95 %) basedon a sample of n background measurements.3.3 Symbols: µ = the true population mean of a constituentx¯ = the sample-based mean or average concentration of aconstituent computed from n background measurements whichdiffers from µ because of sampling variability, and other errorσ2= the true population variance of a constituents2= the sample-based variance of a constituent computedfrom n background measurementss = the sample-based standard deviation of a constituentcomputed from n background measurementsy¯ = the mean of the natural log transformed data (also thenatural log of the geometric mean)sy= the standard deviation of the natural log transformeddatan = the number of background (offsite or upgradient) mea-surementsk = the number of future comparisons for a single monitor-ing event (for example, the number of downgradient monitor-ing wells multiplied by the number of constituents to bemonitored) for which statistics are to be computedα = the false positive rate for an individual comparison (thatis, one sampling location and constituent)m = the number of onsite or downgradient measurementsused in computing the onsite mean concentrationα* = the site-wide false positive rate covering the samplinglocations and constituentst = the 100(1 − α) percentage point of Student’st-distribution on n − 1 degrees of freedomHL= the factor developed by Land (1971) (1)3to obtain thelower 100(α) % confidence limit for the mean of a lognormaldistributionHU= the factor developed by Land (1971) (1) to obtain theupper 100(α) % confidence limit for the mean of a lognormaldistribution4. Summary of Guide4.1 The guide is summarized as Figs. 1-7. These figuresprovides a flow-chart illustrating the steps used in computingthe comparisons to regulatory or health based groundwaterprotection standard (GWPS) in assessment and correctiveaction environmental monitoring programs.5. Significance and Use5.1 The principal use of this standard is in assessment,compliance and corrective action environmental monitoringprograms (for example, for a facility that could potentiallycontaminate groundwater). The significance of the guidance isthat it presents a statistical method that allows comparison ofgroundwater data to regulatory and/or health based limits.5.2 Of course, there is considerable support for statisticalmethods applied to detection, assessment and corrective actionmonitoring programs that can be applied to environmentalsites.NOTE 1—For example, in the United States, the 90 % upper confidencelimit (UCL) of the mean is used in USEPA’s SW846 (Chapter 9) fordetermining if a waste is hazardous. If the UCL is less than the criterionfor a particular hazardous waste code, then the waste is not a hazardouswaste even if certain individual measurements exceed the criterion.Similarly, in the USEPA Statistical Analysis of Groundwater MonitoringData at RCRA Facilities Addendum to the Interim Final Guidance (1992)(2), confidence intervals for the mean and various upper percentiles of thedistribution are advocated for assessment and corrective action.Interestingly, both the 1989 and 1992 USEPA guidance documents (2, 3)suggest use of the lower 95 % confidence limit (LCL) as a tool for3The boldface numbers in parentheses refer to a list of references at the end ofthis standard.D7048 − 162FIG. 1 Decision Tree—Statistical Methods for Assessment Sampling and Corrective Action ProgramsD7048 − 163determining whether a criterion has been exceeded in assessment moni-toring.The latest guidance in this area calls for use of the LCL in assessmentmonitoring and the UCLin corrective action. In this way, corrective actionis only triggered if there is a high degree of confidence that the trueconcentration has exceeded the criterion or standard, whereas correctiveaction continues until there is a high degree of confidence that the trueconcentration is below the criterion or standard. This is the generalapproach adopted in this guide, as well.5.3 There are several reasons why statistical methods areneeded in assessment and corrective action monitoring pro-grams. First, a single measurement indicates very little aboutthe true concentration in the sampling location of interest, andwith only one sample it cannot be determined if the measuredconcentration is a typical or an extreme value. The objective isto compare the true concentration (or some interval thatcontains it) to the relevant criterion or standard. Second, inmany cases the constituents of interest are naturally occurring(for example, metals) and the naturally existing concentrationsmay exceed the relevant criteria. In this case, the relevantcomparison is to background (for example, off-site soil orupgradient groundwater) and not to a fixed criterion. As such,background data should be statistically characterized to obtaina statistical estimate of an upper bound for the naturallyoccurring concentrations so that it can be confidently deter-mined if onsite concentrations are above background levels.Third, there is often a need to compare numerous potentialconstituents of concern to criteria or background, at numeroussampling locations. By chance alone there will be exceedancesas the number of comparisons becomes large. The statisticalapproach to this problem can decrease the potential for falsepositive results.5.4 Statistical methods for detection monitoring have beenwell studied in recent years (see Gibbons, 1994a, 1996, USEPA1992 (2, 4, 5) and Practice D6312, formerly PS 64-96 authoredby Gibbons, Brown and Cameron, 1996). Although equallyimportant, statistical methods for assessment monitoring,Phase I and II Investigations, on-going monitoring and correc-tive action monitoring have received less attention, (Gibbonsand Coleman, 2001) (6).5.5 The guide is summarized in Fig. 1, which provides aflow-chart illustrating the steps in developing a statisticalevaluation method for assessment and corrective action pro-grams. Fig. 1 illustrates the various decision points at which theFIG. 2 Single PAOC Comparison to a Standard/CriteriaD7048 − 164general comparative strategy is selected, and how the statisticalmethods are to be selected based on site-specific consider-ations.6. Procedure6.1 In the following, the general conceptual and statisticalfoundations of the sampling program are described. Followingthis general discussion, media-specific details (that is, soil,groundwater, and waste streams) are provided.6.1.1 Identify relevant constituents for the specific type offacility, media (for example, soil and/or groundwater) and areaof interest. A facility is generally comprised of a series ofsubunits or “source areas” that may have a distinct set ofsampling locations and relevant constituents of concern (re-ferred to as a PAOC). The subunit may consist of a singlesampling point or collection of sampling points. In some cases,the entire site may comprise the area of interest and allsampling locations are considered jointly. The boundaries ofthe “source area” or “decision unit” should be defined. In mostcases, the owner/operator should select the smallest practicallist of constituents that adequately characterize the source areain terms of historical use.6.1.2 For each constituent obtain the appropriate regulatorycriterion or standard (for example, maximum contaminantlevel, MCL) if one is available. The appropriate criterion orstandard should be selected based on relevant pathways (forexample, direct contact, ingestion, inhalation) and appropriateland use criteria (for example, commercial, industrial, residen-tial).6.1.3 For each constituent which may have a backgroundconcentration higher than the relevant health based criterion,set “background” to the upper 95 % confidence prediction limit(UPL) as described in the Technical Details section. Theprediction limits are computed from available data collectedfrom background, or outside source areas that are unlikely tobe contaminated, upstream, upwind or upgradient locationsonly. Hence