ASTM D6250-98(2003)
(Practice)Standard Practice for Derivation of Decision Point and Confidence Limit for Statistical Testing of Mean Concentration in Waste Management Decisions
Standard Practice for Derivation of Decision Point and Confidence Limit for Statistical Testing of Mean Concentration in Waste Management Decisions
SIGNIFICANCE AND USE
Environmental decisions often require the comparison of a statistic to a decision point or the comparison of a confidence limit to a regulatory limit to determine which of two alternate actions is the proper one to take.
This practice provides a logical basis for statistically deriving a decision point, or a confidence limit as an alternative, for different underlying presumptions.
This practice is useful to users of a planning process generally known as the data quality objectives (DQO) process (see Practice D 5792), in which calculation of a decision point is needed for the decision rule.
SCOPE
1.1 This practice covers a logical basis for the derivation of a decision point and confidence limit when mean concentration is used for making environmental waste management decisions. The determination of a decision point or confidence limit should be made in the context of the defined problem. The main focus of this practice is on the determination of a decision point.
1.2 In environmental management decisions, the derivation of a decision point allows a direct comparison of a sample mean against this decision point, where similar decisions can be made by comparing a confidence limit against a concentration limit (for example, a regulatory limit, which will be used as a surrogate term for any concentration limit throughout this practice). This practice focuses on making environmental decisions using this kind of statistical comparison. Other factors, such as any qualitative information that may be important to decision-making, are not considered here.
1.3 A decision point is a concentration level statistically derived based on a specified decision error and is used in a decision rule for the purpose of choosing between alternative actions.
1.4 This practice derives the decision point and confidence limit in the framework of a statistical test of hypothesis under three different presumptions. The relationship between decision point and confidence limit is also described.
1.5 Determination of decision point and confidence limits for statistics other than mean concentration is not covered in this practice. This practice also assumes that the data are normally distributed. When this assumption does not apply, a transformation to normalize the data may be needed. If other statistical tests such as nonparametric methods are used in the decision rule, this practice may not apply. When there are many data points below the detection limit, the methods in this practice may not apply.
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Designation: D6250 – 98 (Reapproved 2003)
Standard Practice for
Derivation of Decision Point and Confidence Limit for
Statistical Testing of Mean Concentration in Waste
Management Decisions
This standard is issued under the fixed designation D6250; the number immediately following the designation indicates the year of
original adoption or, in the case of revision, the year of last revision. A number in parentheses indicates the year of last reapproval. A
superscript epsilon (´) indicates an editorial change since the last revision or reapproval.
1. Scope 2. Referenced Documents
1.1 This practice covers a logical basis for the derivation of 2.1 ASTM Standards:
a decision point and confidence limit when mean concentration D4687 Guide for General Planning of Waste Sampling
is used for making environmental waste management deci- D5792 Practice for Generation of Environmental Data Re-
sions.Thedeterminationofadecisionpointorconfidencelimit lated to Waste Management Activities: Development of
should be made in the context of the defined problem. The Data Quality Objectives
mainfocusofthispracticeisonthedeterminationofadecision D4790 TerminologyofAromaticHydrocarbonsandRelated
point. Chemicals
1.2 In environmental management decisions, the derivation E456 Terminology Relating to Quality and Statistics
of a decision point allows a direct comparison of a sample E1138 Terminology for Technical Aspects of Products Li-
mean against this decision point, where similar decisions can ability Litigation
be made by comparing a confidence limit against a concentra- 2.2 Other Documents:
tion limit (for example, a regulatory limit, which will be used USEPA(1989a) StatisticalAnalysisofGround-WaterMoni-
as a surrogate term for any concentration limit throughout this toring Data at RCRA Facilities. Interim Final Guidance.
practice). This practice focuses on making environmental Office of Solid Waste Management Division, Washington,
decisions using this kind of statistical comparison. Other D.C. (PB89-15-1047)
factors, such as any qualitative information that may be USEPA (1989b) Methods for Evaluating the Attainment of
important to decision-making, are not considered here. Cleanup Standards. Vol. 1: Soils and Solid Media. Statis-
1.3 A decision point is a concentration level statistically tical Policy Branch (PM-223)
derived based on a specified decision error and is used in a USEPA(1992) StatisticalMethodsforEvaluatingtheattain-
decision rule for the purpose of choosing between alternative ment of Superfund Cleanup Standards. Vol. 2: Groundwa-
actions. ter. DRAFT, Statistical Policy Branch, Washington, D.C
1.4 This practice derives the decision point and confidence USEPA (1994) Guidance for the Data Quality Objectives
limit in the framework of a statistical test of hypothesis under Process. EPA QA/G4, Quality Assurance Management
three different presumptions. The relationship between deci- Staff, USEPA, September, 1994
sion point and confidence limit is also described.
3. Terminology
1.5 Determination of decision points and confidence limits
3.1 Definitions:
for statistics other than mean concentration is not covered in
this practice. This practice also assumes that the data are 3.1.1 decision point, n—the numerical value which causes
the decision maker to choose one of the alternative actions (for
normally distributed. When this assumption does not apply, a
transformation to normalize the data may be needed. If other example, conclusion of compliance or noncompliance).
3.1.1.1 Discussion—In the context of this practice, the
statistical tests such as nonparametric methods are used in the
decisionrule,thispracticemaynotapply.Whentherearemany numerical value is calculated in the planning stage and prior to
data points below the detection limit, the methods in this
practice may not apply.
For referenced ASTM standards, visit the ASTM website, www.astm.org, or
contact ASTM Customer Service at service@astm.org. For Annual Book of ASTM
This practice is under the jurisdiction of ASTM Committee D34 on Waste Standards volume information, refer to the standard’s Document Summary page on
Management and is the direct responsibility of Subcommittee D34.01.01 on the ASTM website.
Planning for Sampling. Withdrawn.
Current edition approved April 10, 1998. Published December 1998. DOI: Available from the Superintendent of Documents, U.S. Government Printing
10.1520/D6250-98R03. Office, Washington, DC 20402.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959, United States.
D6250 – 98 (2003)
the collection of the sample data, using a specified hypothesis, 3.1.6.1 Discussion—For this practice, a hypothesis is a
decision error, an estimated standard deviation, and number of postulation of what the true value is, typically framed for the
samples.Inenvironmentaldecisions,aconcentrationlimitsuch purpose of making a statistical test of the hypothesis. In a
as a regulatory limit usually serves as a standard for judging statistical test, there are two competing hypotheses: the null
attainment of cleanup, remediation, or compliance objectives. hypothesis and the alternative hypothesis. The null hypothesis
Because of uncertainty in the sample data and other factors, is a hypothesis “put up” for consideration and is the presumed
actual cleanup or remediation, for example, may have to go to hypothesis of choice before the data are collected. The alter-
a level lower or higher than this standard. This new level of native hypothesis is favored only when the data reject the null
concentration serves as a point for decision-making and is, hypothesis.
therefore, termed the decision point. 3.1.7 statistic, n—a quantity calculated from a sample of
observations, most often to form an estimate of some popula-
3.1.2 confidence limits, n—the limits on either side of the
tion parameter. E456
mean value of a group of observations which will, in a stated
fraction or percent of the cases, include the expected value.
4. Significance and Use
Thus the 95 % confidence limits are the values between which
the population mean will be situated in 95 out of 100 cases.
4.1 Environmental decisions often require the comparison
D4790
of a statistic to a decision point or the comparison of a
3.1.2.1 Discussion—Aone-sided upper or lower confidence
confidencelimittoaregulatorylimittodeterminewhichoftwo
limit can also be used when appropriate. An upper confidence
alternate actions is the proper one to take.
limit is a value below which the population mean is expected
4.2 This practice provides a logical basis for statistically
to be with the specified confidence. Similarly, a lower confi-
deriving a decision point, or a confidence limit as an alterna-
dence limit is a value above which the population mean is
tive, for different underlying presumptions.
expected to be with the specified confidence. It is to be noted
4.3 This practice is useful to users of a planning process
that confidence limits are calculated after the collection of
generally known as the data quality objectives (DQO) process
sample data.
(see Practice D5792), in which calculation of a decision point
3.1.3 decision rule, n—a set of directions in the form of a is needed for the decision rule.
conditional statement that specify the following: (1) how the
sample data will be compared to the decision point, (2) which 5. Overview of Decision Point Determination
decision will be made as a result of that comparison, and (3)
5.1 Thedeterminationofadecisionpointisusuallyapartof
what subsequent action will be taken based on the decisions.
an overall planning process. For example, the decision rule in
D5792
the DQO planning process often includes the specification of a
3.1.3.1 Discussion—For this practice, the comparison in (1)
decision point. A brief summary of the steps needed to
in 3.1.3 can be made in two equivalent ways: (1) a comparison
determine a decision point is given below.
between the sample mean (calculated from the sample data)
5.1.1 State the problem and the decision rule (see Section
and a decision point (calculated during the planning stage), or
6),
(2) a comparison between a confidence limit(s) (calculated
5.1.2 Consider the alternative presumptions in the hypoth-
from the sample data) and a regulatory limit.
eses based on the relative consequences of false positive and
3.1.4 false negative error, n—occurs when environmental
false negative errors (see 7.6),
data mislead decision maker(s) into not taking action specified
5.1.3 Choose the form of the hypotheses to be used in the
by a decision rule when action should be taken. D5792
decisionrulebasedonthechosenpresumption(see7.5through
3.1.4.1 Discussion—For this practice, this is an error de- 7.6 and Fig. 1),
fined in the context of a regulatory decision in waste manage- 5.1.4 Obtain an estimated standard deviation and the num-
ment. In this context, it is an error in concluding that the true ber of samples used in that estimation,
value is smaller than the regulatory limit when in fact it is not. 5.1.5 Specify acceptable decision errors (see Section8), and
The calculation of the false negative error will depend on how 5.1.6 Calculate the decision point (see Section 8).
the hypotheses are framed (see Appendix X1). 5.2 The following sections discuss in practical terms the
topics of decision rule, presumptions and test of hypothesis,
3.1.5 false positive error, n—occurs when environmental
calculation of a decision point for specified decision errors,
data mislead decision maker(s) into taking action specified by
ways to control decision errors, and the use of a confidence
a decision rule when action should not be taken. D5792
limit as an alternative approach in decision-making.
3.1.5.1 Discussion—For this practice, this is an error de-
fined in the context of a regulatory decision in waste manage-
6. Decision Rule in Waste Management Decisions
ment. In this context, it is an error in concluding that the true
value is equal to or greater than the regulatory limit when in
6.1 A decision rule is constructed according to a problem
fact it is not. The calculation of the false positive error will
statement defined and agreed to by all the parties concerned,
depend on how the hypotheses are framed (seeAppendix X1).
through a planning process. The decision rule can be carried
3.1.6 hypothesis, n—a supposition or conjecture put for- out in two similar ways.
ward to account for certain facts and used as a basis for further 6.1.1 When Using A Decision Point:
investigation by which it may be proved or disproved. 6.1.1.1 The general construct of the decision rule in this
E1138 case is:
D6250 – 98 (2003)
FIG. 1 Decision Point Determination for Mean Concentration
If ~sample mean!$ ~decision point!, then ~one action!.
acomponentinthecalculationofthedecisionpoint(see8.6.3).
Otherwise, ~alternate action!.
The way to incorporate this uncertainty depends on how a
6.1.1.2 Because a decision point is needed in the above hypothesis is formulated and which presumption is adopted.
decision rule, this practice provides a logical basis for devel- This is discussed in Section 7.
oping such a decision point. Because the above decision rule
6.1.1.5 An example of carrying out the decision rule using a
can also be carried out similarly using confidence limits, it is
decision point is:
also presented that way in 6.2.
If ~average concentration of cadmium in a truck load!$ ~decision
6.1.1.3 Note that when data can be measured with certainty,
point!, then ~dispose of the waste fly ash in an RCRA landfill!.
the regulatory limit defines the decision point. For example,
Otherwise, ~dispose the waste fly ash in a sanitary landfill!.
sample data taken from a totally homogeneous population, in
6.1.1.6 The inputs needed for the calculation of the decision
the absence of measurement error, have no variability. This
point in 6.1.1.5 are: form of the hypotheses to be tested,
means that the standard deviation of the data is zero and the
acceptable maximum decision error, number of samples, and
decision point is reduced to the regulatory limit (see 8.6.3).
estimated standard deviation. The standard deviation should
6.1.1.4 When data cannot be measured precisely or the
include all the sources of variation in the sampling and
population is not totally homogeneous, this variability needs to
measurement processes. Decision errors include the false
be incorporated to obtain a decision point. The decision point
positive error and false negative error. Details are given in
then includes both the original regulatory limit and a margin of
uncertainty that is reflected in the standard deviation, which is Section 8.
D6250 – 98 (2003)
6.2 When Using Confidence Limit: compromise between the first two presumptions based on
practical considerations.
6.2.1 The general construct of the decision rule in this case
is: 7.5.1 Presumption Number 1—The true (population) mean
concentration is presumed to be below the regulatory limit,
If ~confidence limit!. or < ~regulatory limit!, then ~one action!
with an opposite presumption in the alternative hypothesis.
Otherwise, ~alternate action!.
7.5.1.1 This presumption of no exceedance would require“
where the confidence limit can be the upper confidence limit
cleanup” down to a concentration level not statistically signifi-
or the lower confidence limit, depending on the chosen
cantlyhigherthantheregulatorylimit.Inthiscase,thedecision
presumption in the null hypothesis (see Section 7). A special
point will be higher than the regulatory limit.
casewheretheconfidencelimitisreplacedbythesamplemean
7.5.2 Presumption Number 2—The true (population) mean
in the above decision rule is also discussed in Section 7.
concentration is presumed to be equal to or greater than the
6.2.2 Two examples corresponding to the > and < signs in
regulatory limit, with an opposite presumption in the alterna-
the decision rule are:
tive hypothesis.
6.2.2.1 If upper confidence limit of mean concentration of
7.5.2.1 This presumption of exceedance would require“
cadmium) > (regulatory limit), then (dispose of the waste fly
cleanup” down to a concentration level statistically signifi-
ash in a RCRA landfill). Otherwise, (dispose of the waste fly
cantly lower than the regulatory limit. In this case, the decision
ash in a sanitary landfill).
point will be lower than the regulatory limit.
6.2.2.2 If lower confidence limit of mean concentration of
7.5.3 Presumption Number 3—a neutral presumption that
cadmium) < (background concentration), then (dispose of the
thetruemeanconcentrationisneitherhighernorlowerthanthe
waste fly ash in a sanitary landfill). Otherwise, (dispose of the
regul
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