ASTM D6250-98(2009)
(Practice)Standard Practice for Derivation of Decision Point and Confidence Limit for Statistical Testing of Mean Concentration in Waste Management Decisions (Withdrawn 2018)
Standard Practice for Derivation of Decision Point and Confidence Limit for Statistical Testing of Mean Concentration in Waste Management Decisions (Withdrawn 2018)
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 D5792), 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 points 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.
WITHDRAWN RATIONALE
This practice covered a logical basis for the derivation of a decision point and confidence limit when mean concentration is used for making environmental waste management decisions.
Formerly under the jurisdiction of Committee D34 on Waste Management, this practice was withdrawn in January 2018. This standard is being withdrawn without replacement due to its limited use by industry.
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Standards Content (Sample)
NOTICE: This standard has either been superseded and replaced by a new version or withdrawn.
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Designation:D6250 −98 (Reapproved 2009)
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 data points below the detection limit, the methods in this
practice may not apply.
1.1 This practice covers a logical basis for the derivation of
a decision point and confidence limit when mean concentration
2. Referenced Documents
is used for making environmental waste management deci-
2.1 ASTM Standards:
sions.Thedeterminationofadecisionpointorconfidencelimit
D5792 Practice for Generation of Environmental Data Re-
should be made in the context of the defined problem. The
lated to Waste Management Activities: Development of
mainfocusofthispracticeisonthedeterminationofadecision
Data Quality Objectives
point.
D4790 Terminology ofAromatic Hydrocarbons and Related
1.2 In environmental management decisions, the derivation
Chemicals
of a decision point allows a direct comparison of a sample
E456 Terminology Relating to Quality and Statistics
mean against this decision point, where similar decisions can
E1138 Terminology for Technical Aspects of Products Li-
be made by comparing a confidence limit against a concentra-
ability Litigation (Withdrawn 1995)
tion limit (for example, a regulatory limit, which will be used
2.2 Other Documents:
as a surrogate term for any concentration limit throughout this
USEPA(1989a) StatisticalAnalysis of Ground-Water Moni-
practice). This practice focuses on making environmental
toring Data at RCRA Facilities. Interim Final Guidance.
decisions using this kind of statistical comparison. Other
Office of Solid Waste Management Division, Washington,
factors, such as any qualitative information that may be
D.C. (PB89-15-1047)
important to decision-making, are not considered here.
USEPA (1989b) Methods for Evaluating the Attainment of
1.3 A decision point is a concentration level statistically
Cleanup Standards. Vol. 1: Soils and Solid Media. Statis-
derived based on a specified decision error and is used in a
tical Policy Branch (PM-223)
decision rule for the purpose of choosing between alternative
USEPA(1992) Statistical Methods for Evaluating the attain-
actions.
ment of Superfund Cleanup Standards. Vol. 2: Groundwa-
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.
1.5 Determination of decision points and confidence limits
3. Terminology
for statistics other than mean concentration is not covered in
3.1 Definitions:
this practice. This practice also assumes that the data are
3.1.1 decision point, n—the numerical value which causes
normally distributed. When this assumption does not apply, a
the decision maker to choose one of the alternative actions (for
transformation to normalize the data may be needed. If other
example, conclusion of compliance or noncompliance).
statistical tests such as nonparametric methods are used in the
decisionrule,thispracticemaynotapply.Whentherearemany
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. The last approved version of this historical standard is referenced on
Current edition approved Sept. 1, 2009. Published November 2009. Originally www.astm.org.
approved in 1998. Last previous edition approved in 2003 as D6250–1998(2003). Available from the Superintendent of Documents, U.S. Government Printing
DOI: 10.1520/D6250-98R09. Office, Washington, DC 20402.
Copyright © ASTM International, 100 Barr Harbor Drive, PO Box C700, West Conshohocken, PA 19428-2959. United States
D6250−98 (2009)
3.1.1.1 Discussion—In the context of this practice, the 3.1.6 hypothesis, n—asuppositionorconjectureputforward
numerical value is calculated in the planning stage and prior to to account for certain facts and used as a basis for further
the collection of the sample data, using a specified hypothesis, investigation by which it may be proved or disproved. E1138
decision error, an estimated standard deviation, and number of 3.1.6.1 Discussion—For this practice, a hypothesis is a
samples.Inenvironmentaldecisions,aconcentrationlimitsuch postulation of what the true value is, typically framed for the
as a regulatory limit usually serves as a standard for judging purpose of making a statistical test of the hypothesis. In a
statistical test, there are two competing hypotheses: the null
attainment of cleanup, remediation, or compliance objectives.
Because of uncertainty in the sample data and other factors, hypothesis and the alternative hypothesis. The null hypothesis
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
3.1.2 confidence limits, n—the limits on either side of the
observations, most often to form an estimate of some popula-
mean value of a group of observations which will, in a stated
tion parameter. E456
fraction or percent of the cases, include the expected value.
Thus the 95 % confidence limits are the values between which
4. Significance and Use
the population mean will be situated in 95 out of 100 cases.
D4790
4.1 Environmental decisions often require the comparison
of a statistic to a decision point or the comparison of a
3.1.2.1 Discussion—Aone-sided upper or lower confidence
limit can also be used when appropriate. An upper confidence confidencelimittoaregulatorylimittodeterminewhichoftwo
alternate actions is the proper one to take.
limit is a value below which the population mean is expected
to be with the specified confidence. Similarly, a lower confi-
4.2 This practice provides a logical basis for statistically
dence limit is a value above which the population mean is
deriving a decision point, or a confidence limit as an
expected to be with the specified confidence. It is to be noted
alternative, for different underlying presumptions.
that confidence limits are calculated after the collection of
4.3 This practice is useful to users of a planning process
sample data.
generally known as the data quality objectives (DQO) process
3.1.3 decision rule, n—a set of directions in the form of a
(see Practice D5792), in which calculation of a decision point
conditional statement that specify the following: (1) how the
is needed for the decision rule.
sample data will be compared to the decision point, (2) which
decision will be made as a result of that comparison, and (3)
5. Overview of Decision Point Determination
what subsequent action will be taken based on the decisions.
5.1 Thedeterminationofadecisionpointisusuallyapartof
D5792
an overall planning process. For example, the decision rule in
3.1.3.1 Discussion—For this practice, the comparison in (1)
the DQO planning process often includes the specification of a
in 3.1.3 can be made in two equivalent ways: (1) a comparison
decision point. A brief summary of the steps needed to
between the sample mean (calculated from the sample data)
determine a decision point is given below.
and a decision point (calculated during the planning stage), or
5.1.1 State the problem and the decision rule (see Section
(2) a comparison between a confidence limit(s) (calculated
6),
from the sample data) and a regulatory limit.
5.1.2 Consider the alternative presumptions in the hypoth-
3.1.4 false negative error, n—occurs when environmental eses based on the relative consequences of false positive and
false negative errors (see 7.6),
data mislead decision maker(s) into not taking action specified
by a decision rule when action should be taken. D5792 5.1.3 Choose the form of the hypotheses to be used in the
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 Specifyacceptabledecisionerrors(seeSection8),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
3.1.5 false positive error, n—occurs when environmental
topics of decision rule, presumptions and test of hypothesis,
data mislead decision maker(s) into taking action specified by
calculation of a decision point for specified decision errors,
a decision rule when action should not be taken. D5792
ways to control decision errors, and the use of a confidence
3.1.5.1 Discussion—For this practice, this is an error de-
limit as an alternative approach in decision-making.
fined in the context of a regulatory decision in waste manage-
ment. In this context, it is an error in concluding that the true
6. Decision Rule in Waste Management Decisions
value is equal to or greater than the regulatory limit when in
fact it is not. The calculation of the false positive error will 6.1 A decision rule is constructed according to a problem
depend on how the hypotheses are framed (see Appendix X1). statement defined and agreed to by all the parties concerned,
D6250−98 (2009)
FIG. 1Decision Point Determination for Mean Concentration
through a planning process. The decision rule can be carried 6.1.1.4 When data cannot be measured precisely or the
out in two similar ways. population is not totally homogeneous, this variability needs to
6.1.1 When Using A Decision Point: be incorporated to obtain a decision point. The decision point
6.1.1.1 The general construct of the decision rule in this then includes both the original regulatory limit and a margin of
case is: uncertainty that is reflected in the standard deviation, which is
acomponentinthecalculationofthedecisionpoint(see8.6.3).
If ~sample mean!$ ~decision point!, then ~one action!.
The way to incorporate this uncertainty depends on how a
Otherwise, alternate action .
~ !
hypothesis is formulated and which presumption is adopted.
6.1.1.2 Because a decision point is needed in the above
This is discussed in Section 7.
decision rule, this practice provides a logical basis for devel-
6.1.1.5 An example of carrying out the decision rule using a
oping such a decision point. Because the above decision rule
decision point is:
can also be carried out similarly using confidence limits, it is
If ~average concentration of cadmium in a truck load!$ ~decision
also presented that way in 6.2.
point), then dispose of the waste fly ash in an RCRA landfill .
~ !
6.1.1.3 Note that when data can be measured with certainty,
Otherwise, dispose the waste fly ash in a sanitary landfill .
~ !
the regulatory limit defines the decision point. For example,
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
D6250−98 (2009)
include all the sources of variation in the sampling and 7.4 Thus, it is the alternative hypothesis that bears the
measurement processes. Decision errors include the false “burden of proof.” That is, the alternative hypothesis is not
positive error and false negative error. Details are given in
favored until the data suggest that the null hypothesis is not
Section 8. tenable and cause the rejection of the null hypothesis.
6.2 When Using Confidence Limit:
7.5 Presumptions in Null Hypothesis—In environmental
6.2.1 The general construct of the decision rule in this case testing, two presumptions can be postulated for the null
is: hypothesis. A third presumption can be constructed as a
compromise between the first two presumptions based on
If ~confidence limit!.or,~regulatory limit!, then ~one action!
practical considerations.
Otherwise, alternate action .
~ !
7.5.1 Presumption Number 1—The true (population) mean
where the confidence limit can be the upper confidence limit
concentration is presumed to be below the regulatory limit,
or the lower confidence limit, depending on the chosen
with an opposite presumption in the alternative hypothesis.
presumption in the null hypothesis (see Section 7). A special
7.5.1.1 This presumption of no exceedance would require“
casewheretheconfidencelimitisreplacedbythesamplemean
cleanup” down to a concentration level not statistically signifi-
in the above decision rule is also discussed in Section 7.
cantlyhigherthantheregulatorylimit.Inthiscase,thedecision
6.2.2 Two examples corresponding to the > and < signs in
point will be higher than the regulatory limit.
the decision rule are:
7.5.2 Presumption Number 2—The true (population) mean
6.2.2.1 If upper confidence limit of mean concentration of
concentration is presumed to be equal to or greater than the
cadmium) > (regulatory limit), then (dispose of the waste fly
regulatory limit, with an opposite presumption in the alterna-
ash in a RCRA landfill). Otherwise, (dispose of the waste fly
tive hypothesis.
ash in a sanitary
...
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