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OHIO ENVIRONMENTAL PROTECTION AGENCYDIVISION OF EMERGENCY AND REMEDIAL RESPONSE

FINALHOW CLEAN IS CLEAN POLICY

July 26, 1991

I. INTRODUCTION

The Ohio Environmental Protection Agency (Ohio EPA), Division ofEmergency and Remedial Response (DERR) is responsible for thediscovery, investigation, enforcement and remediation ofunregulated hazardous waste sites. The Division conducts theseactivities under the authority vested in the Director of the OhioEPA by the Ohio Revised Code (ORC) Sections 3734 and 6111.The DERR conducts activities at sites where the Division hasreason to believe a release or the potential for a release of ahazardous waste, as defined under ORC 3734.01 (J), has or mayoccur due to the treatment, storage or disposal of such waste.These sites may pose a threat or potential threat to human healthor safety or contribute or threaten to contribute to air, wateror soil contamination.

The DERR generally restricts its activities to sites where thetreatment, storage or disposal of hazardous waste occured priorto the enactment of the Resource Conservation and Recovery Act of1976 (RCRA). Many of these sites are abandoned or uncontrolledand are not currently operating facilities. Therefore, thesesites are referred to as "unregulated" hazardous waste sites andare not regulated under RCRA.The DERR works in conjunction with other Federal and Ohio EPAprograms in the investigation and remediation of unregulatedhazardous waste sites. Activities conducted by DERR areconsistent with all applicable state and federal laws (i.e. CleanWater Act, Resource Conservation and Recovery Act, ComprehensiveEnvironmental Response, Compensation and Liability Act).

The Division's responsibilities are administered through threemajor program areas:

Emergency Response - Response to chemical and petroleum releases,spills and waste dumping incidents that present or nay present animmediate threat to human health or the environment.

Special Investigations - Investigations into environmental crimeallegations that can result in criminal, civil and/oradministrative enforcement.

Remedial Response - Discovery, investigation and remediation ofunregulated hazardous waste sites through enforcement.

The Division has developed this guidance to provide a generaloverview to hazardous waste site investigations and remediationsconducted by the DERR, Remedial Response Program. The primarypurpose of this guidance is to generate a consistent approach forevaluating site investigations and clean up. General proceduresare outlined which can be consistently and uniformly applied toevery situation. This guidance does not present site specificclean-up criteria or guidance. Every site is different in regardto magnitude and nature of contamination, no single approach canbe applied. Therefore, site specific issues will be addressed bythe DERR through individual enforcement agreements.

II. SITE INVESTIGATIONS

The DERR, Remedial Response Program conducts investigations atunregulated hazardous waste sites in a manner not inconsistentwith the National Contingency Plan (NCP), Therefore, the DERRreferences many of the same guidance and criteria documents asthe U.S. EPA Superfund program. Appendix A lists the guidanceand criteria documents that the DERR, Remedial Response Programadheres to in conducting site investigations and clean up. Thispolicy is intended to be used in conjunction with these guidancedocuments.

This section sets forth the general approach that the RemedialResponse Program will take as a site progresses through theinvestigative stage. The purpose of the site investigation is toadequately characterize the nature and extent of contamination.For the purposes of this policy a site is defined as the arealextent of contamination.

A. Determination of Contamination

DERR evaluates sites to determine whether or not there isevidence of a release, or the potential for a release, ofhazardous waste due to past treatment, storage, or disposal. Suchevidence includes environmental field data and/or writtendocumentation obtained through historical records and/orinterviews.

In investigating a site, the DERR considers a site to becontaminated if it meets the following criteria:

* The contaminant(s) detected is a hazardous waste as definedunder the Ohio Revised Code (ORC) 3734.02 (J) an<jf

* Contaminants are present on-site at concentrationssignificantly above background or.

* Contaminants arc present on-site and are not detected inrepresentative background samples.

a. Background

For the purposes of this policy, background is defined ascurrent conditions present at a site and areas surrounding a sitewhich are unaffected by past treatment, storage, or disposal ofhazardous waste. In order to determine the nature and extent ofcontamination, background conditions must be established. Anevaluation of background should be conducted concurrently withthe on-site investigation.

The DERJ* has developed specific guidance which outlines theprocedures to be followed in determining background conditions ata site. The guidance sets forth the DERK's criteria fordetermining the number of samples that should be collected inorder to adequately represent background. This guidance isattached in Appendix B of this document.

b. On-site vs. Background

Once background and on-site conditions have been adequatelycharacterized, results should be evaluated to determine whetheror not contamination exists.

i) Naturally occurring compounds - Many compounds that may bepresent as a result of the treatment, storage or disposal ofhazardous waste may also be present in the environment due to thenatural conditions of the surrounding environment. In order todetermine whether or not these compounds are present due to pastwaste disposal practices, on-site samples must be evaluatedagainst representative background samples.

In such a comparison, if on-site samples exhibit compounds atconcentrations greater than the mean background concentrationplus the product of the tolerance factor and the relativestandard deviation, then contamination is said to exist (SeeBackground Guidance, pg. 18).

If a compound is not detected in background samples then anyfinding in on-site samples greater than the method detectionlimit (MDL) is considered contamination. The MDL is the minimumconcentration of a substance that can be measured and reportedwith 99% confidence that the analyte's concentration is greaterthan zero. MDL's vary from method to method and application ofthe MDL will depend on the appropriate methodology applied.MDL's will be identified for individual contaminants in the sitespecific investigation workplan.

ii) Non-naturally occurring compounds - Compounds that arepresent in the environment due to human activity that aregenerally not naturally occurring must.also be evaluated.For the purposes of a site investigation, one must determine ifnon-naturally .occurring contamination is a result of past

disposal, treatment or storage of waste at the site. Since thesite is defined as the areal extent of contamination theinvestigation must also include areas where waste has beentransported through air, leachate, surface or groundwater. Theinvestigation must also include waste constituents that nay bepresent due to the transformation or biodegredation of hazardouswaste.Background must also be determined for comparison to on-sitesamples, especially if the site is in a highly industrializedarea or where the site is downgradient from another unrelatedhazardous waste source.

If a contaminant is detected at the MDL or greater in on-sitesamples and is not detected in representative background samples,then contamination is said to exist.

If a compound is detected in on-site samples and inrepresentative background samples, then any concentration greaterthan the mean background concentration plus the product of thetolerance factor and the relative standard deviation (seeBackground Guidance, pg. IS) is considered site relatedcontamination and must be addressed. In order to determinecontamination at a site where non-naturally occurring compoundsare found both on-site and in background samples, the DERR mustfirst approve background sampling data and agree that suchcontamination is not related to the site under investigation.

B. Determination of Risk

Once it has been established that contamination exists at a site,it must then be determined whether or not the contaminationpresents a threat to public health or the environment. The DERRconsiders a threat to be present under either of the followingconditions:

* Contamination exists at levels that present or have thepotential to present a current or potential future unacceptablerisk to human health.

* Contamination exists in air, water, soils or other media atlevels that present an unacceptable risk to the environment.

a. Human Health Risks

The DERR has not developed media specific action levels forchemical constituents. Therefore, a human health risk assessmentmust be performed in order to evaluate current and potentialfuture health effects posed by site specific contamination. Abaseline risk assessment must be performed to estimate thecurrent or the potential future risks presented under a no actionscenario. A no action scenario assumes that there are nocontrols, current or future, at the site (i.e., fences, deedrestrictions). The DERR has adopted U.S. EPA's Interim Final"Risk Assessment Guidance for Superfund. Volume I. Human HealthEvaluation Manual (Part A)" for conducting risk assessments atDERR unregulated sites. Appendix A lists additional guidance

necessary for conducting risk assessments.

The DERK relies on the following information sources for thetoxicological data necessary for conducting risk assessments:

* IRIS - U.S. EPA!s Integrated Risk Information System, IRIS isan electronic database containing the latest descriptive,quantitative and U.S.EPA regulatory information on chemicalconstituents. Chemical files maintained in IRIS containinformation relating to noncarcinogenic and carcinogenic healtheffects.

IRIS is accessible by means of Dialcom Inc.'s Electronic KailTelecommunication System and the Computer Information System(CIS). For information on IRIS contact U.S.EPA's Office ofHealth and Environmental Assessment, (202) 382-4317, or theOffice of Solid Waste, Characterization and Assessment Branch,Washington, D.C. (202) 382-4761.

Information in IRIS supersedes all other sources. If informationis not available in IRIS the sources given below should beconsulted.

* HEAST - Health Effects Assessment Summary Tables are citedreferences which are updated quarterly by U.S. EPA. HEAST is atabular presentation of toxicity information and values forchemicals for which Health Effects Assessments (HEA's), Healthand Environmental Effects Documents (HEED's), Health andEnvironmental Effects Profiles (HEEP's), Health AssessmentDocuments (HAD's), or Ambient Air Quality Criteria Documents(AAQCD's) have been prepared. For information pertaining toHEAST, contact the National Technical Information Service (NTIS),(703) 487-4780.

* EPA Criteria Documents - These documents include drinking watercriteria documents, drinking water Health Advisory summaries,ambient water quality criteria documents, and air qualitycriteria documents, and contain general toxicity information thatcan be used if information for a chemical is not availablethrough IRIS or the HEAST references. Criteria documents areavailable through NTIS at the number given above.

i. Carcinogens

In assessing the carcinogenic potential of compounds, U.S. EPA'sHuman Health Assessment Group classifies these compoundsaccording to the weight-of-evidence from availableepidemiological and animal studies. Compounds are classified aspossible, probable or known human carcinogens based on a systemdeveloped by U.S.EPA from the approach taken by the InternationslAgency for Research on Cancer (IAKC).

Group A Human Carcinogen

Group Bl or B2 Probable Human Carcinogen

Bl - limited human dataare available

B2 - sufficient evidence in animals andinadequate or no evidence in humans

Group C Possible Human Carcinogen

Group D Not classified as tohuman carcinogenicity

Group £ Evidence ofnoncarcinogenicity forhumans

Calculated risks are assumed to be additive between compounds andcumulative across routes of exposure. This approach assumes thatthere is no synergistic or antagonistic chemical interactions andall chemicals have the same endpoint, cancer.

In assessing the additive and cumulative effects of carcinogens,the DERH requires that Group A and Group B carcinogens beevaluated. Group C carcinogens shall be evaluated on a case-by-case basis. The DERH shall consider the appropriate site-specific environmental data and toxicological informationavailable in determining whether or not Group C carcinogens willbe included in evaluating risks.

ii. Noncarcinogens

In assessing the noncarcinogenic risk of systemic contaminants, areference dose, or RfD, is used. Additionally, one-day or ten-day Health Advisories (HA's) may be used to evaluate short termoral exposures. These values are based on subchronic and/orchronic animal studies and human epidemiological data, whereavailable. To assess the overall potential for noncarcinogeniceffects posed by multiple chemicals, a Hazard Index (HI)approach must be used. This approach assumes that simultaneoussubthreshold exposures to several chemicals could result in anadverse health effect. It also assumes that the magnitude of theadverse effect will be proportional to the sum of the ratios ofthe subthreshold exposures to acceptable exposures.

It is important to calculate the Hazard Index separately forchronic, subchronic and shorter term exposure periods. Onceagain, the Hazard Index approach assumes additivity betweencompounds and cumulative effects across exposures routes. Theassumption of dose additivity is most appropriately applied tocompounds that induce the same effect by the same mechanism ofaction. Therefore, in applying the Hazard Index approach thetotal Hazard Index should be calculated. If the total HazardIndex exceeds unity it is appropriate to segregate the compoundsby effect and by mechanism of action and to derive separatehazard indices for each group.

Example;

Hazard Index - fcl + £2 + . .. . EiRfDi RfD2 RfDi

Where Ei - Exposure level (or intake) for the ith toxicantRfDi - Reference dose for the ith toxicant

b. Environmental Risks

Where contamination is contributing to soil, sediment, air and/orwater pollution, the DERR requires an evaluation of theenvironmental impact of such contamination. Environmentalimpacts are evaluated by assessing adverse effects on the floraand fauna existing within or threatened by contaminated media(air, water, soils or sediments). Specific data must beavailable in order to establish the nature and magnitude of thecontamination and its effect(s) on the environment. The siteinvestigation must include the following in order to evaluatethese effects:

* Appropriate chemical and physical data describing thenature of contaminants and the contaminated media;

* Ecological assessment (e.g., habitat, variability inpopulation and diversity of species, food chaineffects) through toxicity tests, biomarker analysis andfield surveys;

* Toxicological data in regard to flora and fauna;

* Evaluation of especially sensitive habitats andcritical habitats of species protected under theEndangered Species Act and habitats of Ohio EndangeredSpecies as determined by the Ohio Department of NaturalResources, Division of Wildlife.

The DERH requires that an ecological assessment be evaluated foreach site. The Division recognizes that there will be instanceswhere ecological impact may be small or insignificant due to thenature of site contamination or the location of the site. Insuch instances it must be demonstrated, either qualitatively orquantitatively, that significant environmental impacts have notor will not occur and a full ecological assessment is notnecessary.

The DERR adheres to the procedures presented in U.S.EPA's"Ecological Assessment of Hazardous Waste Sites: A Field andLaboratory Reference" EPA/600/3-89/013, and "Risk AssessmentGuidance for Superfund, Volume II. Environmental EvaluationManual" EPA/540/1-69/001 when conducting ecological assessments.Additional references for conducting ecological assessments arelisted in Appendix A.

III. EVALUATION OF ALTERNATIVES

Once site contamination has been characterized and the threatposed by the contamination has been determined, remedialalternatives must be developed and evaluated if the contaminationis found to present an unacceptable risk to human health or theenvironment or if any promulgated standard or criteria has beenviolated. The development and evaluation of alternatives can beintegrated with site characterization activities. The DERRrequires that remedial alternatives be developed that areprotective of human health and the environment. Remedial actionalternatives shall be evaluated using the the following criteria:

1) Overall protection of human health and the environment2) Compliance with applicable or relevant and appropriatestandards and/or criteria3) Long term effectiveness and permanence4) Reduction of toxicity, mobility, or volume through treatment5} Short term effectiveness6) Implementability7) Cost8) Community Acceptance

Alternatives should establish remediation goals that meet thecriteria outlined in the following sections.

A. Promulgated Standards

Remediation goals must consider any cleanup standards, standardsof control, and other criteria or limitations promulgated underfederal or state environmental or facility siting laws thatspecifically address the circumstances at the site.There may be other requirements, criteria, or limitationspromulgated under federal or state environmental or facilitysiting laws that, although not directly applicable to the site,are sufficiently similar to be suitable to the situation.

There are several different types of requirements promulgatedunder State or Federal law which may apply:

* Ambient or chemical specific requirements - Thesevalues are usually health or risk based numericalstandards or criteria and establish the acceptableamount or concentration of a chemical that may be foundin, or discharged to, an environmental media.

* Performance, design, or other action-specificrequirements - Technology or activity basedrequirements or limitations.

* Location specific requirements - Restrictions placedon the concentration of a substance or the conduct ofactivities because of the location of the site orrelease.

The DERR has developed separate policy for the identification andapproval of promulgated standards to be applied at unregulatedhazardous waste sites. This policy was specifically developedfor the identification of state applicable or relevant andappropriate requirements (ARARs) at National Priority List (NPL)sites. However, the policy procedures are applicable to non-NPLsites as well. This policy, entitled "ARARs" is availablethrough the DERR.

Maximum contaminant level goals (MCLGs), established under theSafe Drinking Water Act, shall be attained by remedial actionsfor ground or surface waters that are current or potentialsources of drinking water, where the MCLGs are relevant andappropriate under the site specific circumstances. Where an MCLGfor a contaminant has been set at a level of zero, the maximumcontaminant level (MCL) promulgated for that contaminant underthe Safe Drinking Water Act shall be attained where the MCL isrelevant and appropriate under site specific curcumstances.

In cases involving multiple contaminants or pathways, chemicalspecific KCLs or MCLGs must meet a cumulative carcinogenic riskof 10-4 to 10-6 and Hazard Index less than one in order to beacceptable as remediation goals. This demonstration must beperformed through the baseline risk assessment conducted for thesite.

B. Acceptable Risk Criteria

If state or federal promulgated standards do not exist for acontaminant or contaminants in a specific environmental media, orif standards are not sufficiently protective due to multiplecontaminants or pathways, remediation goals shall be establishedto meet risk based criteria. The following criteria are deemedprotective of public health and the environment.

a. carcinogens - For Group A and Group B carcinogens acceptableexposure levels are generally concentration levels that representa cumulative excess upper-bound lifetime cancer risk to anindividual between 10-4 and 10-6. The 10-6 risk level shall beused as a point of departure for DERR remediation goals.

b. noncarcinogens - For noncarcinogens, acceptable exposurelevels are generally those levels which represent concentrationsto which the human population, including sensitive subgroups, maybe exposed without adverse effects during a lifetime or part of alifetime. Cumulative exposures which present a Hazard Index ofless than one are considered acceptable for site remediationgoals.

c. environment - Acceptable levels are generally those levelswhich represent concentrations to which the ecologicalenvironment, including sensitive species, habitats and criticalhabitats, may be exposed without adverse effects.

In order for a site to be considered unrestricted for future use,

cumulative carcinogenic risks oust meet the 10-6 goal andcumulative noncarcinogenic risks must have a Hazard Index belowone. Unrestricted use assumes that no future monitoring,controls or restrictions will be required at the site.Therefore, it must be demonstrated that any remainingcontamination left on site will not pose an unacceptable risk tohuman health or the environment.

The carcinogenic risk range allows for some flexibility inestablishing cleanup goals that are protective of human healthand the environment through applying a more restrictive usescenario. These scenarios may include long term monitoring andsite controls which will place restrictions on any wastes left onsite and limit future use of the site. Such alternatives »ay beconsidered based on site specific considerations and if anunrestricted future use scenario is technologically infeasible orcost prohibitive.

Remedies evaluated should use treatment to address contaminationwherever practicable. The use of innovative technologies isencouraged when such technology provides for comparable orsuperior treatment performance or implementability. The DERRwill require that environmental media be returned to usable andbeneficial uses wherever practicable.

IV. SUMMARY

The DERR, Remedial Response Program is responsible for thediscovery, listing, prioritization, investigation and potentialremediation of over 1300 unregulated sites in Ohio. These sitesmay be vastly different in regard to the nature and extent ofcontamination. Every site presents a unique set of circumstancesthat must be addressed individually. The DERR has developed thispolicy to provide a consistent approach to site investigation andremediation under the Remedial Response Program. This policy isintended to provide general guidance to DERR staff and theregulated community. This policy is not intended to be the solesource of guidance, it is intended to be used in conjunction withother DERR approved guidance and policy.

The essential steps in any site evaluation include:

1) Site Investigation - the determination of the nature andextent of contamination through on-site and backgroundcharacterization.

2) Risk Assessment - the determination of current or potentialrisk to human health and the environment by evaluating risksposed by on-site contamination.

3) Evaluation of Alternatives - the determination of a sitespecific remedial action by developing alternatives which areevaluated against applicable or relevant and appropriatepromulgated standards, human health and environmental criteria.

10

The DERR will adhere to the above steps when conductinginvestigations and clean-ups at unregulated sites or inconducting oversight at sites where action is being taken byanother party under an enforcement agreement.

Due to the large universe of unregulated cites listed by the DERRfor potential action, the Remedial Response Program will not beable to address every site as quickly as interested parties naywish. The Remedial Response Program prioritizes sites in orderthat the sites presenting the greatest risks be addressed first.Sites are addressed as resources and funding allow. The DERRwill only conduct oversight at sites where the Agency has aformal agreement in place. Parties may wish to proceed with asite assessment and remediation on their own, without any DERRoversight. The How clean is Clean policy, in conjunction withother DERR guidance and criteria (Appendix A) should be used asguidance in conducting these investigations.

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APPENDIX A

REFERENCES

1) ARAR's, Ohio EPA, Division of Emergency and RemedialResponse, July, 1991.

2) Background Guidance, Ohio EPA, Division of Emergency andRemedial Response, July, 1991.

3) CERCLA Compliance with Other Laws Manual, OSWER 9234.1-01,March 6, 1988.

4) CERCLA Compliance with Other Laws Manual, Part II, OSWER9234.1-02, August 1989.

5) Guidance for Conducting Remedial Investigation andFeasibility Studies under CERCLA, Interim Final, OSWER9355.3-01, October, 1988, EPA/540/G-89/004.

6) Data Quality Objectives for Remedial Response Activities,Volume I, EPA/540/G-87/004.

7) Ecological Assessments of Hazardous Waste Sites: A Field andLaboratory Reference, EPA/600/3-89/013, March, 1989.

8} Exposure Factors Handbook; EPA/600/8-89/043, July, 1989.

9) Guidelines and Specifications for Preparing QualityAssurance Project Plans, Ohio EPA) Division of Emergency andRemedial Response, March, 1990.

10) Guidance for Data Useability in Risk Assessment, InterimFinal; EPA/540/G-90/008, October, 1990.

11) Guidelines for Carcinogen Risk Assessment. Federal Register,Volume 51, No. 165, Semptember, 24, 1986. pp.33992-34003.

12) Health Effects Assessment Summary Tables, OERR 9200.6-303,published quarterly.

13) Human Health Evaluation Manual, Supplemental Guidance:"Standard Default Exposure Factors", OSWER 9285.6-03, March,1991.

14) Integrated Risk Information System (IRIS) data base, 1989.U.S. EPA, Office of Health and Environmental Assessment.

15) National Oil and Hazardous Substances Pollution ContingencyPlan, Final Rule. 40 CFR Part 300, March 8, 1990.

16) RCRA Groundwater Monitoring Technical Enforcement GuidanceDocument (TEGD), OSWER 9283.1-2, August, 1988.

17) Remedial Actions for Contaminated Groundwater at SuperfundSites, OSWER 9283.1-2, August, 1988.

18) Risk Assessment Guidance for Superfund, Volume I. HumanHealth Evaluation Manual (Part A), Interim Final.EPA/540/1-89/002, December, 1989.

19) Risk Assessment Guidance for Superfund, Volume II.Environmental Evaluation Manual, Interim Final. EPA/540/1-89/001A, 1989.

20) Superfund Exposure Assessmennt Manual, EPA/540/1-88/001,April, 1988.

APPENDIX B

BACKGROUND SAMPLING GUIDANCE

I. INTRODUCTION

This technical guidance has been developed as an extension to the

Division of Emergency and Remedial Response (DERR) Final How

Clean is Clean policy. DERR policy requires background sampling

in order to determine natural conditions of an area and provide a

basis for comparison to on-site sample results. Background

conditions can only be determined through representative

environmental sampling.

This guidance was thoroughly researched, and was reviewed by

statisticians from The Ohio State University and from the US EPA

Environmental Monitoring Systems Laboratory (EM5L), Las Vegas for

statistical Tightness.

This guidance sets forth the basic sampling criteria and the

statistical theory and procedures that can be used to calculate

the number of samples necessary to represent background. This

procedure can be utilized best at sites where there is adequate

information to perform the calculation for the estimation of

background sample numbers. It also provides guidance in

determining the information needed to perform the calculations

when data are missing or are inadequate.

JULY 1991

This guidance also describes a method to be used for determining

if on site concentrations are indeed significantly higher than

background by using the calculated confidence interval (see

Section V).

The statistical methods described in this document conform to

known and proven statistical analysis. The references are

included for users who wish to increase their understanding of

the concepts used in this guidance document. Unfortunately, there

is little information on the statistics of environmental

background sampling so these concepts may seem new to most users.

This guidance document does not address the spatial and temporal

aspects of sampling for determining background variability. It

only addresses the number of samples needed to accurately assess

the variability of background constituents as applied to a

specific waste site.

It will be assumed that contaminant concentrations will follow a

normal distribution - one distribution for the background

contamination and one for the on site contamination. In caseswhere a large number of camples are collected (i.e. >30) this

assumption becomes unimportant. The analysis will be valid

whether or not this assumption is satisfied. When the number of

samples collected are small (Ol), this assumption is important.

The user is cautioned to the fact that non-normally distributed

JULY 1991 2

concentrations used with a t-confidence interval may be quite

misleading. Because of the uncertainty of the distribution, this

guidance includes a method for examining the data for normality

and a method for transforming the data if needed.

This guidance document does not apply to ground water background

sampling. Ground water sampling follows the Guidance Document on

the Statistical Analysis of Ground Water Monitoring Data at RCRA

Facilities. announced in the September 11, 1989 Federal Register.

II. BACKGROUND SAMPLING

A. LOCATION

Background samples should be representative of natural local

conditions. Representative samples are those that accurately and

precisely represent an environmental condition.

Representativeness criteria are best satisfied by making certain

that sampling locations are selected properly and a sufficient

number of samples are collected.

Background samples should be collected at locations unaffected by

the site (i.e., upgradient, upwind). The rational used to select

sampling locations should be clearly explained. In situations

where a site is affected by other contaminating sources (i.e.,

industrialized areas) true background conditions nay not be

represented by the immediate surrounding areas (approximately 1

sq. mile); therefore, best professional judgement must be used to

JULY 1991 3

select sampling locations and criteria. Examples of areas that

would not usually be considered appropriate for determining

background conditions include, but are not limited to:

1. past waste management areas where solid and/or hazardous

wastes or wastewater may have been placed on the ground, or

the areas affected by their runoff,

2. .roads, roadside, parking lots, areas surrounding parking

lots or other paved areas, railroad tracks or railway areas

or areas affected by their runoff,

3. storm drains or ditches presently or historically receiving

industrial, urban or agriculture runoff,

4. material handling areas (i.e., truck or rail car loading

areas, pipeline areas),

5. fill areas,

6. spill areas.

B. SAMPLING AND ANALYTICAL METHODS

It is critical that background samples be collected using

identical procedures as employed for on-site sample collection.

They should also be collected within the same matrix (same soil

horizon, for example) as on-site, if possible. To illustrate, for

samples taken on-site in a stream bed the background samples

should be collected in the same stream bed upstream and at the

same depth and location within the stream, within areas of

JULY 1991 4

deposition such as a sand bar. This sane concept applies to soil

and surface water as well.

Sampling methods and equipment should follow approved Ohio EPA

guidance or applicable US EPA guidance. Procedures for choosing

appropriate analytical methods for sample analysis will be based

on sample matrix and the analytes to be determined. Detection

limits will vary according to matrix effects, analyte, and method

used; however, detection limits should correspond to those

specified in the methodology (method detection limits) and be

able to meet Data Quality Objectives criteria. Where multiple

analytical methods exist for a particular matrix, the method that

meets the Data Quality Objectives (DQO) and/or with the lowest

detection limit should be used.

Some background samples, such as surface water and stream

sediments, should be collected over a period of time sufficient•to represent the variability of the matrix analyzed. This is

because waste characteristics may fluctuate based on seasonal and

temporal variations.

Sampling and analysis of groundwater should follow the guidelines

and procedures set forth in the RCRA Groundwater Monitoring

Technical Enforcement Guidance Document fTEGDl; USEPA, OSWER-

9950.1. September, 1986.

JULY 1991

III. USE OF PREVIOUS INFORMATION

There may be sources other than actual sampling data to establish

background conditions for an area. These sources nay be in the

form of published literature or data compiled by other agencies

and/or organizations such as the U.S. Geological Survey, the Soil

Conservation Service, The United States Department of Agriculture

and the Army Corps of Engineers* Such sources of background

information that are applicable to a specific site may be used in

conjunction with background sampling data. The key issue to

consider when using this data is the comparability of such data

to on-site generated data.

Data generated from these sources may or may not be comparable to

on-site sampling data due to matrix effect, season of sampling,

stratigraphic unit sampled, etc.. Data presented in literature

are seldom from a sufficiently limited geographical area and the

range of reported values are generally quite large. It is

difficult if not impossible to evaluate the quality of the

reported data in comparison to the strict quality assurance

requirements associated with a hazardous waste site

investigation. However, this data still can be useful as a

starting point in the background sampling investigation, as will

be discussed later in this document*

JULY 1991

IV. CENTRAL STATISTICAL THEORY

In order to calculate the appropriate number of samples needed to

accurately reflect background conditions, a statistical approach

oust be used.

The following equation will be used:1

(1)

Where:

N «= Number of samples to be collected;

t = The t-value taken from a Students1 t table using a 95%

confidence level (CL) and a given degrees of freedom (table

included in Appendix A of this document);

a «= estimate of "relative standard deviation" from an initial

exploratory sampling;

B * estimate of "relative desired confidence" for the population

from an exploratory campling.

There are some difficulties that occur when this formula is used

in environmental sampling. First, we normally do not know the

relative standard deviation, (s). Second, choosing a value for

^Statistics. Jav Devore and Roxy Peck. 1986. pq 279.

JULY 1991 7

the relative desired confidence depends on many site-specific

variables. Therefore, in order to calculate the number of samples

to be collected, the user has to make certain estimations

concerning the data when site information is deficient or

lacking. The user must be sure to consider such items as aerial

photos, past records, etc. when these estimations are being

formulated.

Estimation / 1- Relative Standard Deviation fs)

Since the relative standard deviation (a) is seldom known before

sampling, an estimation is needed. The relative standard

deviation can be approximated in two ways - by calculation from

information derived from previous work characterized for

background if available (e.g., previous sampling data) or by

estimation using the Practical Quantitation Limit (PQL- see

section IV).

Estimation 12 - t value

The t-value is the value that corresponds to the associated

critical area under a normal curve and a specific value for

degrees of freedom. A t-table is included in Appendix A for

JULY 1991 B

reference, and will be used in the determination of the number of

samples needed to be collected.

Estimation /3 - Confidence level

By definition, a confidence level of 951 states that, for a

specific compound, the mean concentration of a set of background

samples analyzed and its upper and lover limits (+/- (t)(s)) will

capture the true population mean (U) 95% of the time. A

confidence level of 95% is used by the US EPA Contract Laboratory

Program (CLP) and in the Guidance Document for Statistical

Analysis of Ground Water Monitoring Data, Federal Register, Sept.

11, 1989, and will be implemented here.

Estimation /4 * Relative Desired Confidence fBl

The "relative desired confidence" is a value judgement arrived at

by a consensus of the technical and administrative personnel

participating in the project. It is in the same units as the mean

and is the largest tolerable error (e.g., 10 ug/kg) in the mean

we want to accept a given percentage (e.g., 95%) of the tine. The

"relative desired confidence1* is an output or measure of the data

quality objectives. The "relative desired confidence*1 is a

compromise between the confidence the risk assessor wants, the

accuracy the analytical analysis can provide, the sampling

variance, the time variance, the space variance, and budget

JULY 1991 9

limitations. This value should be site specific, reflecting the

toxicity of the pollutant and the proximity of people. The table

on page ten shows that increased confidence cost more dollars by

increasing sampling and analysis. Therefore, best professional

judgement must be evaluated along with sampling goals and funding

in determining the degree of confidence used.

As general guidance, where little or no information is available

concerning background values, the value for the " relative

desired confidence", even though it is not causally related to

the relative standard deviation, can be estimated by using the

information described above, but can also be safely estimated to

equal the relative standard deviation.

The user should take note that in Equation /I, when the tolerable

error is decreased the number of samples to be collected

increases dramatically. To illustrate this a table has been

constructed below, using values from the previous example to

show the increase in the number of samples to be collected.

(x •» 30 mg/Kg)

DESIRED CONFIDENCE £ ft * SAMPLES

1.7 2.01 5 35

2.78 2.15 5 15

3.85 2.31 5 9

JULY 1991 10

DESIRED CONFIDENCE 1 4 / SAMPLES

5.24 2.57 5 6

7.95 3.18 5 4

12.42 4.3 5 3

Guidance for estimating the relative desired confidence when

certain information is available is explained later in the text,

V. CALCULATIONS USING PREVIOUS INFORMATION

To use information previously characterized froin the background

site in question, the user needs three pieces of information; (1)

the standard deviation (s) of the compound(s) in question derived

from previous analysis of environmental sampling, (2) the

compound(s) that were found and, (3) the number of samples

collected previously. Using this information the user can then

estimate the "relative desired confidence" (refer to page nine

for assistance). Furthermore, employing the corresponding t-

value for the number of samples collected minus one (N-l), the

user can then compute the number of samples that need to be

collected, using Equation /I . Care must be taken in using

information previously determined, however* The user nay not know

the methods employed in the development of the information (refer

to Section III).

JULY 1991 11

When the compound(s) are known but there is insufficient

information on the concentrations or standard deviations, the

user must then estimate this information. Standard deviation can

be estimated by using the Practical Quantitation Limit (PQL).

The POL is the estimated quantitation limit of a compound when

using a particular analytical procedure for a particular matrix

(ground vater, coil, sediment, etc.)* The PQL is calculated by

multiplying the Method Detection Limit (HDL), described in the

method, by a particular conversion factor associated with that

matrix also found in the method (sediment, surface water, etc).3

The equation proposed for the estimation of the standard

deviation (s) using the PQL as the highest concentration expected

and zero as the lowest concentration expected is the following4;

POL - LOW CONC. B s (2)4

It should be noted that this calculation only estimates

analytical error and not field error, which are sometimes ten

times the magnitude of the analytical error. In addition, this

formula normally gives the user an underestimation of the

standard deviation.

3SW-846 Test Methods for Evaluating Solid Wastes, US EPA

Statistics. Jay Devore and Roxy Peck, 1986, pg. 279.

JULY 1991 12

The method of choosing a standard deviation for use in Equation

#1 from multiple compounds present at a background site (as

opposed to only one compound) employs the use of certain

variables, such as sample concentration variability and the

availability of appropriate analytical methods. Generally, the

compound that exhibits the most variability (defined by previous

analysis), by expert opinions, or presents the greatest human

health and/or environmental risk will be chosen.

If, for a particular background site, sufficient information of

the associated organic/inorganic contaminant(s) does not exist

then standard deviation (s) and hence the number of background

samples needed cannot be calculated by the previous methods

described. However, background levels must be defined in order to

determine background variability. It is proposed that seven (7)

samples need to be collected, per matrix, when performing an

initial survey for background. This number was proposed based on

the following information assembled from expert estimation;

1. There could be volatile, semivolatile and inorganic

contaminants present at the background site;

2. The "desired confidence" and the "relative standard

deviation", although not causally related, are equal in

value, for initial surveys.

JULY 1991 13

Using Equation /I the following is the method that was developed

to demonstrate the number of samples proposed (seven) for

collection for initial background campling;

1. Estimate number of samples to be collected, N; (for

example, choose a number from three to ten);

2. Using the t-table in Appendix A of this policy and

employing a 95% confidence level, find the degrees of

freedom needed (the degrees of freedom is the estimated

number minus one, N-l). Locate value under the 95%

confidence level column (example; 7-l«6, the critical

value for 6 is 2.45);

3. Since we are expressing "relative standard deviation"

and "relative desired confidence" as the same value,

there is no reason to estimate these two variables when

using Equation I, since they will both cancel each

other out.

Equation I is then simplified to:

N* t2

Where;

N - number of samples to be collected;

t * t-value from the Students t table.

JULY 1991 14

The statistician then needs to choose an initial number of

samples, that when using the above technique, the t squared

value + 1 will equal the estimated number for N. This process may

involve calculating N more than once in order for the estimated N

to equal or come very near the value of the calculated N.

Below is a table that illustrates the above method to estimate

the initial sample number for background samples;

EST. N

3

4

5

6

7

8

9

10

t-VALUE ( N - l )

4 . 3

3.18

2.78

2.57

2.45

2.37

2.31

2 . 2 6

t2

18.5

10.2

7.7

6.6

6.0

5.6

5.3

5.1

t2 + l

19.5

11.2

8.7

7.6

7.0

6.6

6.3

6.1

from the above example, when N=7 and using Equation /3:

2.452 « 6.0 (4)

The method, as stated previously, is to natch the t-squared value

-t-1 to the estimated sample number. In this case the t-value,

JULY 1991 15

2.45, when squared equals 6.0. One (1) nust be added to the

number because 1 was subtracted when the degrees of freedom (N-l)

was used. As it turns out, 6+1-7, which equals the initial number

for sampling.

In order to verify this method, calculate using 6 as the number

of samples to collect in the above scenario* However, using 6

would not have given the user the correct number. For example;

1. estimate N « 6

2. t-critical value •= (6-l«5) critical value for 5 at 95%

confidence - 2.57

3. using equation 4;

2.572 * 6.60 (5)

As the user can see, 6.60+1-7.6 does not equal 6. In estimating

eight (8) samples, the value given, 5.6+l«6.6, does not equal

8. The estimate of N=7 is the only value that "fits".

Depending on the outcome of the analysis the sampling team may or

may not need to collect additional background samples. This will

depend on variability (large standard deviation), the number of

samples taken, analytical performance, the type of compounds

present and data quality objectives. If the data, shown by back

calculation for the number of samples needed to be collected•JULY 1991 16

the transformation of the data. If the background data is

normally distributed then no transformation of the data is

needed.6,7 The user can perform the classical statistics on the

data as is. However, if the background data is skewed, then the

user must first transform the data before performing the

statistics. The user can transform the data by obtaining the

log(ten) or square root of the data points to transform the data.

A log transformation is usually performed when the distribution

is positively skewed (a long upper tail)* This method yields a

more symmetric distribution of the data.

Once the data has been transformed, then classical statistics

(mean, standard deviation, etc.) can be performed.

The following equation will be used once the statistics have been

performed to determine if on-site contamination is statistically

greater than background;

1C + *<a)

Where:

X - mean of background compound;

a * relative standard deviation.

k - tolerance factor (table found in appendix)

^Statistical Methods for Environmental Pollution MonitoringrRichard 0. Gilbert, 1987, page 148.

7Statistics, Jay Devore and Roxy Peck, 1986, page 54.

JULY 1991 18

This calculation will give the user an upper control limit (a

confidence limit) that, by comparing the individual values found

on-site to the upper control limit, the values that are greater

than the Bean + (k(a)) will be considered statistically greater

than the mean background values* The user must be remember to

treat the on-site data the same as the background data when

applying the methods of transformation.

VI. APPLICATION

To demonstrate this method, three example scenarios will be

calculated for determining the number of background samples to be

taken. These examples involve sites where the contaminants are

known but not the concentrations, where no information is known,

and where the contaminants are well documented.

EXAMPLE SCENARIO 1

A sampling team is preparing to sample background for a

contaminated soil site where vinyl chloride is the contaminant of

concern. There is no estimate of concentration for vinyl

chloride. The sampling team determines, using method 8240 from

SW-846, that the PQL for vinyl chloride in soil is 10 ug/kg. With

this information they can estimate the "relative standard

deviation*9 needed for use in Equation /I from Equation /3 (from

page 12) as:

JULY 1991 19

(7,

The sampling team has estimated the "relative desired confidence**

(B) to be equal to (a). They are also using a 95% Confidence

Level, and they have estimated the number of samples to collect

at 7, with "t" being equal to 2.45, since little is known

concerning the vinyl chloride concentrations.

The sampling team receives the analysis, and as fate would have

it, there is vinyl chloride contamination at the background site!

The analysis for vinyl chloride are as follows;

N - 7

mean « 15 ug/kg

s « 12 ug/kg

min « <10 ug/kg (half the D.L. used)

max = 47 ug/kg

accuracy (from spike) •= 60%

The sampling team uses their information in order to verify that

they collected an adequate number of background samples. The team

estimates the relative desired confidence at 60% of the mean, or

a value of nine, due to the spike recovery characteristics of

vinyl chloride when using method 8240. Using Equation #1, the

team calculates the number of samples to collect, based on the

previously validated analytical data. The team estimates N to be

8, and thus the t-value to be 2.45. As it turns out the

JULY 1991 20

calculated H equals "17 (16+1), which does not equal 8, the

original estimate. The team then chooses N>=10, and using Equation

1 they compute N to equal "15 (14.2*1). After a couple more

calculations, the team finally chooses 14 samples to adequately

define background variability, based on Equation I.

The user will rarely compute a value for K to be equal to the

estimated value for N. The user will need to use their best

judgement in situations like this.

EXAMPLE SCENARIO 2

The Remedial Response Team has been involved in a site (a

landfill) in which samples need to be collected. Little is. known

concerning the contents of the landfill, however the team needs

to collect background samples from the soil in order to define

background concentrations. Since no prior information is

available concerning the contents of the landfill, the field team

must utilize the estimations contained in the Section V,

Calculations Using Previous Information, bottom of page 12 in

this guidance policy. The sampling team decides that volatile and»

semivolatile organic analysis and metal analysis from SW-846 will

be used for the characterization of the soil samples. Estimating

a sample number of 7, which is the prescribed number to be

collected and analyzed for volatiles, semi volatiles and

inorganics the sampling team conducts the background sampling.

JULY 1991 21

The campling team receives the lab report, with findings that all

volatile and semi volatile compounds analyzed for were all below

the detection limit. The metal analysis compare favorably to

previous information concerning background metals from

agricultural soil studies (be careful when using this type of

data for comparison). The sampling team concludes that the

background has been characterized sufficiently and will now

proceed to sample soils within the landfill.

EXAMPLE SCENARIO 3

An old chemical plant that was used to manufacture the pesticide

2,4,5-T was discovered. The background soils surrounding the

processing buildings were previously analyzed for total Dioxins

back in 1980. The analysis is suspect, due to QA/QC problems

(there were no QA/QC protocol at the lab in 1980). There were

eighteen samples collected and analyzed in 1980, and results were

as follows;

f samples 18•

•ean 11.07 ug/kg

std. dev. 15.04 "

minimum .12 "

aaxioum 130 "

JULY 1991 22

The Ohio EPA decides that background must be resampled in order

to delineate the full extent of contamination (there is too much

variability in the previous sampling episode). The field team

will use existing data, analytical error values, and site

contaminants to estimate the relative desired confidence.

The value estimated for the relative desired confidence is 7,

which is roughly half of the standard deviation. The field team

felt that (l) since the standard deviation of the previous

analysis was greater than the mean (high variability), and (2)

the relative toxicity of dioxin being very high, they wanted to

be assured that the desired confidence would be less variable

than the site variability. The field employs Equation I to

calculate the number of samples to be collected;

2.11 x 15.04 ,2 _ * ,.,.)

Twenty one (21) additional background samples need to be

collected, based on prior information*

VI. pONCLUSION

These statistical methods have been provided to assist sampling

teams in calculating the correct number of background samples. It

also furnishes the sampling team with defensible evidence to base

their sample collection numbers on. When difficulties arise in•

JULY 1991 23

the field concerning the correct number of background samples to

be collected, the users should contact the Technical Support Unit

in Central Office for assistance.

JULY 1991 24

APPEKDI1 X

JULY 1991 25

I. REFERENCES

STATISTICS. Jay Devore and Roxy Peck, West Publishing Company,

1986.

Mr. George Flatman, US EPA, Environmental Monitoring Systems

Laboratory, Las Vegas, Nevada, 89193*3478.

Mr. Steve McEachern, Dept. of Mathematics, The Ohio State

University, Columbus, Ohio.

SW-846 Test Methods for Evaluating Solid Wastes. US EPA, 1986

Stastical Methods for Environmental Pollution Monitoring. Richard

0. Gilbert, 1987.

JULY 1991 26

II. TABLES AND STATISTICAL METHODS

JULY 1991 27

TABU IV t CRITICAL VALUES

fcurvtUppar-tailara*

r critical vahj<

Cantrat Arti CapturtdConfidenct Itvtl

.BOBOX

.BO80%

J6•5% Bt%

J999% 69.8% 8B.B%

Otgrt« off«OOm

1 '23456789

101112

— TT"141516171819202122232425262728293040BO

120

3.081.891.641.531.481.441.421.401.381.371.361.36

———— T35 ——1.351.341.341.331.331.331.331.321.321.321.321.32021.311.311311311.301.301.29

6312.922.352.132.02

.84

.80

.86

.83

.61

.80

.78— rn —

.76

.751751.741731731.731721.721.711.711.711.711.70t.701.701.701.881.671.86

12.714.303.182.782.572.452.372312_2«2.232-20MB

—— rra —•2.152.132.122.112.102.092.092.062.072.072.062.062.062.052.052-052.042.022.001JB

31.626.974.543.753.373.141002.802.822.762.722.68

—— rw —2.622.602.582.572.552.542.532.522.512.502.492.492.482.472.472.462.482.422-59236

63.669.935.844604.033.713.501363.2S1173.11106

—— 101- -•-2.982.952.922.902.882.862.852.832.822.812.802.792.782.772.762.762.752.702,662.62

318.3123.3310-217.175.B96-214,794.504304.144.033J3

—— 9.BS ——3.793.733.693.653.613.583.553.533.513.493.473.453.443.423.413.403.393313333.16

636.6231.6012J28.616-86ft-86141SJM4.784J84L44432

———— 443 ———— —————————C144,074.02197192IBSIBS3J2 ""17B3.771751731711B9187186IBS11514B137

j critical V*IWM

lavtl of aignrficaneafor • rwvnaitad laft

Lava* of lignrficaneator a orMHaitod tavt

13B 1J45 1J6

30 .10 .06

.10 M -O2&

233

.02

.01

2-SB

.01

.006

108

.002

.001

X2J

.001

*»

—. t**TTT*1 Tntllt -

TAALEI CXPCCTTD NORMAL SCORES (M - 0. tr - 1>

fl

Ortto'tdfwition

1234567a9

101112131415161710192021222324252627282930

10

-1.S39-1.001-.656-.376-.123

.123

.376

.6561.0011.539

20

-1J67-1.406-1.131-.921-.745-.690-.446-.315-.167-.062

.062

.187

.315

.446

.590

.745

.9211.1311.4061J67

25

-1.965-1.624-1.263-1.067-.105-.764-.637-.519-.409-.303-.200-.100

.000.100.200.303.409.519.637.764.105

1.0671.2631.5241.965

30

-1043-1.616-1J65-1.179-1.026-494-.777-.663-.568-.473-382-.294-.209-.125-.041

.041

.125

.709-2*4M2.473.568.669.777.•94

1.0261.1791.3651.6162.043

rASLE 5. TOLERANCE FACTORS (K) FOR ONE-SIDED NORMAL TOLERANCEuar c UTTU oonoaoTi T-^V i cwcr /rrucmcurr

Y • 0.9*5 "AND" CDVE"FAGE >"• 9sV "

n

3456789101112131415IS171813202122232425202540455055606570

X

7.6555.1454.2023.7073.3993.1883.0312.9112.8152.7362.6702.6142.5662.5232.4862.5432.4222.3962.3712.3502.3232.3092.2922. '2202.1662.1252.0922.0652.0362.0172.0001.986

11

n

75100125150175200225250275300325350375400425450475500

'"525550575500625650675700725750775800825850875900925950975

1000

K

1.9721.9241.8911.8681.8501.8361.8241.8141.8061.7991.7921.7871.7821.7771.7731.7691.7651.7631.7601.7571.7541.7521.7501.7481.7461.7441.7421.7401.7391.7370.7361.7341.7331.7321.7311.7291.7281.727

SOURC: (t) for itaole sizes i 50: Utbennan, Gerald F. 1958. 'Ttblw forSUtmical Tolerance L1«1ts.' Industrial Quality Controlle I1m * 50: ' vtlu"

B-9

The values -1.163, -.495. 0. .495. and 1.163 are called expeaed normalscores lor a sample ol size five trom a standard normal distribution. The val-ues .488, .495, .500, .505, and .512 are the expeaed normal scores for asample of sire five from a normal distribution with M • .500 and a * .010.In general, whatever the values of M and <r, the smallest expected normalscore in a sample of size Eve is M + (-I.l63)a, the second smallest expeaednormal score is p •*• (-.495)<7, etc. Once the expeaed normal scores forM " 0, a - 1 are available, those for any other values of M and a are easilycalculated.

For example, Table II shows that when n « 25, the third smallest expeaednormal score when M - 0, a « 1 is -1.263. If observations are taken ingroups of 25, the long-run average of the third smallest one will be roughly-1.263. If height is normally distnbuted with M • 69 in., tr « 3 in., andheight values are obtained in groups of 25, the long-run average value of thethird smallest height value would be 69 * 1-1.263M3) - 65.211.

A Plot ior Chcclune The expeaed normal scores for a sample of size n - 5 when M * 50,Normals " a - 10 are 50 •*• (-1.163K10) - 38.37, 45.05, 50, 54.95, and 61.63. Sup-

pose we obtain a sample of five x values from a particular population undersrudy. If the population distribution is actually normal with M « 50, cr » 10,

_ __ _then the five observed scores should be reasonably close to the expeaed nor-mal scores. Consider the "pain (smallest expeaed normaTscore, smallest"observed value), (second smallest expeaed normal score, second smallest ob-served value), . . . , (largest expeaed normal score, largest observed value). Ifevery observed value coincides exactly with the corresponding expeaed nor-mal score, the resulting pair* are (38.37. 38.37), (45.05. 45.05), (50, 50),154.95. 54.951, and (61.63, 61.63). Figure 14(a) shows a plot of these pointswiih the horizontal axis identified with expeaed normal score and the verti-cal axis identified with observed value. The five points fa l l exaaly on a 45*line passing through the point (0, 0).

1 50H

I

ROUU14

Exptcttd

(b)

0 1Expect*) /

(c)

NORMAL PROBABILITY PLOTSHi Whtn Obttrvtd Vilut* • Exptcttd Scornibl Whtn Obitrvtfl Valuti Art Clou to Exptcttd Scorn,Ci Whtn ExptcitO Standard Normal Scortt Art Uttd

11 O4CXMG K* MOAMAUTY 211

In practice, even when the underlvmg distribution is identical 10 the normaldistribution for which the expeaed normal scores are computed (heren * iO . t r - 10), observed values usually do not coincide exactly with theexpeaed normal scores. The observed scores (ordered) might be 39.2, 43.5,49.1. 55.4, and 55.9, yielding the texpeaed, observed) pairs (38.37, 39.2),<45.Q5. 43.5), (50. 49.1). 154.95. 55.4). and (61.63, 59.9). Figure H(b) dis-plays a plot of these pairs. The points fall reasonably close to the 45* line.

Suppose that instead of plotting observed versus expeaed normal scoreswhen M » 50, Q • 10, we plot observed versus expected nonnal scoreswhen M " 0, y • 1 (the standard normal expeaed scores). For our example,this involves plotting (-1.163, 39.2), (-.495, 43.5), (0, 49.1), (.495. 55.4),and i1.163, 59.9). Figure 14(c) shows the resulting plot. It has exactly thesame general pattern as the plot of Figure 14(b); the points fall close to astraight line, but it is no longer the 45* line of the two earlier plots. This sug-gests that plotting observed values versus expeaed scores when M " 0,a = I will yield a straight line pan em if the underlying distribution is nor-mal irrespective of the aoual values of M and cr, and this is indeed the case.

To construa a plot for checking normality, order the n sample observa-DODS from smallest to largest, obtain the expeaed normal scorn whenM " 0, g * I from Table 11 (or some other more complete source), and

"TornTIhe n (expeaed score, observed valueT pain. If "the distribution"from which the sample was obtained is normal (at least approximately),a plot of these pain should show a reasonably strong linear pattern. Ifthe underlying distribution is disonaly nonnormal, the plot should showa rather pronounced departure from lineanry. The plot is usually called anormal probability plot.

Figure 15 contains four such plots for samples of n « 25 observationseach. The first plot shows the expeaed straight-line pattern consistent with anormal distribution. The second plot is the son of picture that rypicallv re-sults from sampling a distribution that is symmetric but has heavier tails thanthe nonnal curve. The middle pan of the plot is reasonably linear, but on theleft end the points fall below a straight line through the middle pan and onthe nght end the points fall above such a straight line. This difference occurssince, because of the heavy tails, observations at the upper end tend to belarger than what it expeaed from a nonnal distribution. Correspondingpoints at the upper end of the plot then tend to be higher than those resultingfrom a normal distribution. Figure 15(c) illustrates what would occur if theunderlying distribution had lighter tails than a nonnal distribution. The na-ture of the departure from lineanry at extreme ends of the plot is the mirrorimage of what happens in the heavy-tailed case. The plot in Figure 15(d) istypical of what results from sampling a distribution that is quite skewed—arather strong curved pattern in the plot.

In (he best of all possible worlds, the points in a nonnal probability plotfall exaaly on a straight tine, but in practice, sampling variability precludessuch an ideal picture. How far can the pattern in the plot deviate from linear-ity before the assumption of normality should be judged implausible? This is

212

-1 0Expcci«d

dl

60

SO

40

X

20- 2 - 1 0 1

Expccttd /

(b)

45

40

-60-> 50"

30-20-

30

25

AOUAC

-2 -2 -1

(c) (d)

NORMAL PROBABILITY PLOTS(•i Obiervitions from • Norm*I Diftnbutionib) Obtcrvaiioni from • HMvy-T»iltd Divtribulionic) Ob*trvfciiont from • Light-T»tl«o OittnbutionId) Obitrvtiiont from • Pontivtly Sk«w*d Diitnbution

not an easy question to answer. To get a reeling for what die plot might looklike when the distribution is normal, for each of a number of different valuesof the sample size rt, we could generate a number of samples of n normallydistributed observations and study the resulting plots. This obviously requiresa large investment of space (for us) and time (for you), both of which art inshort supply. The book Fining Equations to Data by Cuthbert Daniel andFred Wood (New York: John Wiley, 1980) presents a number of cucfa plotson pages 33-43. Tliese plots suggest that with small ample sizes (e.*.,n < 20), then can be so much sampling variability that substantial depar-tures from linearity can result even when the distribution is normal. So be

U O«CK»0 219

EXAMPLE 12

careful about deciding against the plausibil i ty ot a normal distnbution basedon a normal probability plot when n is small.

As previously mentioned, the computer is very good at constructing normalprobability plots. In particular, all the most frequently used packages ottuasncal computer programs have a command that will produce such a plot.The details of the plot vary somewhat from package to package—for exam-ple. MlNTTAB and BMDf use (different! internally calculated approximations tothe expected normal scores rather than tabulated values—but the key idea isalways TO look for linearity.Example 29 of the previous section referred to an article that containedn • 46 observations on the amount of oxides of nitrogen (NO.) emitted by aparticular type of automobile. Figure 16 shows a normal probability plot ofthe data produced by MINITAB. Where two points in the plot fell so close toone another that separate asterisks would not show, the charaaer 2 was usedinstead, and three close points were replaced by the charaaer 3. The plot has'a reasonably well defined straight-line charaaer, though there is a bit of wob-blinns in the two tails. With only a moderately large sample site, such wob-bling is quite common. We conclude that an assumption of normality for thedistribution of NO. emissions is quite plausible.

3 .30*

2.10*

Amnt0*

NO.

221 .40*

0.70*

• 2222

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MINITAB GENERATED NORMAL PROBABILITY PLOT FOR NO, EMISSION DATA

EXAMPU13 Example 18 of Chapter 2 presented data on cell interdivision times (IDT'S). Asample histogram of the original data was quite skewed, but transforming bylogarithms yielded a reasonably bell-shaped histogram. Figure 17 displays

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