ASTM D6250-98
(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
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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Standards Content (Sample)
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
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Designation: D 6250 – 98
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 D 6250; 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 (e) indicates an editorial change since the last revision or reapproval.
1. Scope D 4687 Guide for General Planning of Waste Sampling
D 5792 Practice for Generation of Environmental Data
1.1 This practice covers a logical basis for the derivation of
Related to Waste Management Activities: Development of
a decision point and confidence limit when mean concentration
Data Quality Objectives
is used for making environmental waste management deci-
D 4790 Terminology of Aromatic Hydrocarbons and Re-
sions. The determination of a decision point or confidence limit
lated Chemicals
should be made in the context of the defined problem. The
E 456 Terminology Relating to Quality and Statistics
main focus of this practice is on the determination of a decision
E 1138 Terminology of Technical Aspects of Products Li-
point.
ability Litigation
1.2 In environmental management decisions, the derivation
2.2 Other Documents:
of a decision point allows a direct comparison of a sample
USEPA (1989a) Statistical Analysis of Ground-Water Moni-
mean against this decision point, where similar decisions can
toring Data at RCRA Facilities. Interim Final Guidance.
be made by comparing a confidence limit against a concentra-
Office of Solid Waste Management Division, Washington,
tion limit (for example, a regulatory limit, which will be used
D.C. (PB89-15-1047)
as a surrogate term for any concentration limit throughout this
USEPA (1989b) Methods for Evaluating the Attainment of
practice). This practice focuses on making environmental
Cleanup Standards. Vol. 1: Soils and Solid Media. Statis-
decisions using this kind of statistical comparison. Other
tical Policy Branch (PM-223)
factors, such as any qualitative information that may be
USEPA (1992) Statistical Methods for Evaluating the attain-
important to decision-making, are not considered here.
ment of Superfund Cleanup Standards. Vol. 2: Groundwa-
1.3 A decision point is a concentration level statistically
ter. DRAFT, Statistical Policy Branch, Washington, D.C
derived based on a specified decision error and is used in a
USEPA (1994) Guidance for the Data Quality Objectives
decision rule for the purpose of choosing between alternative
Process. EPA QA/G4, Quality Assurance Management
actions.
Staff, USEPA, September, 1994
1.4 This practice derives the decision point and confidence
limit in the framework of a statistical test of hypothesis under
3. Terminology
three different presumptions. The relationship between deci-
3.1 Definitions:
sion point and confidence limit is also described.
3.1.1 decision point, n—the numerical value which causes
1.5 Determination of decision points and confidence limits
the decision maker to choose one of the alternative actions (for
for statistics other than mean concentration is not covered in
example, conclusion of compliance or noncompliance).
this practice. This practice also assumes that the data are
3.1.1.1 Discussion—In the context of this practice, the
normally distributed. When this assumption does not apply, a
numerical value is calculated in the planning stage and prior to
transformation to normalize the data may be needed. If other
the collection of the sample data, using a specified hypothesis,
statistical tests such as nonparametric methods are used in the
decision error, an estimated standard deviation, and number of
decision rule, this practice may not apply. When there are many
samples. In environmental decisions, a concentration limit such
data points below the detection limit, the methods in this
as a regulatory limit usually serves as a standard for judging
practice may not apply.
attainment of cleanup, remediation, or compliance objectives.
2. Referenced Documents Because of uncertainty in the sample data and other factors,
2.1 ASTM Standards:
Annual Book of ASTM Standards, Vol 11.04.
1 3
This practice is under the jurisdiction of ASTM Committee D34 on Waste Annual Book of ASTM Standards, Vol 06.04.
Management and is the direct responsibility of Subcommittee D34.01.01 on Annual Book of ASTM Standards, Vol 14.02.
Planning for Sampling. Available from the Superintendent of Documents, U.S. Government Printing
Current edition approved April 10, 1998. Published December 1998. Office, Washington, DC 20402.
Copyright © ASTM, 100 Barr Harbor Drive, West Conshohocken, PA 19428-2959, United States.
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
D 6250
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. E 456
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
D 4790 of a statistic to a decision point or the comparison of a
3.1.2.1 Discussion—A one-sided upper or lower confidence confidence limit to a regulatory limit to determine which of two
alternate actions is the proper one to take.
limit can also be used when appropriate. An upper confidence
limit is a value below which the population mean is expected 4.2 This practice provides a logical basis for statistically
deriving a decision point, or a confidence limit as an alterna-
to be with the specified confidence. Similarly, a lower confi-
dence limit is a value above which the population mean is tive, for different underlying presumptions.
4.3 This practice is useful to users of a planning process
expected to be with the specified confidence. It is to be noted
that confidence limits are calculated after the collection of generally known as the data quality objectives (DQO) process
(see Practice D 5792), in which calculation of a decision point
sample data.
is needed for the decision rule.
3.1.3 decision rule, n—a set of directions in the form of a
conditional statement that specify the following: (1) how the
5. Overview of Decision Point Determination
sample data will be compared to the decision point, (2) which
5.1 The determination of a decision point is usually a part of
decision will be made as a result of that comparison, and (3)
an overall planning process. For example, the decision rule in
what subsequent action will be taken based on the decisions.
the DQO planning process often includes the specification of a
D 5792
decision point. A brief summary of the steps needed to
3.1.3.1 Discussion—For this practice, the comparison in (1)
determine a decision point is given below.
in 3.1.3 can be made in two equivalent ways: (1) a comparison
5.1.1 State the problem and the decision rule (see Section
between the sample mean (calculated from the sample data)
6),
and a decision point (calculated during the planning stage), or
5.1.2 Consider the alternative presumptions in the hypoth-
(2) a comparison between a confidence limit(s) (calculated
eses based on the relative consequences of false positive and
from the sample data) and a regulatory limit.
false negative errors (see 7.6),
3.1.4 false negative error, n—occurs when environmental
5.1.3 Choose the form of the hypotheses to be used in the
data mislead decision maker(s) into not taking action specified
decision rule based on the chosen presumption (see 7.5 through
by a decision rule when action should be taken. D 5792
7.6 and Fig. 1),
3.1.4.1 Discussion—For this practice, this is an error de-
5.1.4 Obtain an estimated standard deviation and the num-
fined in the context of a regulatory decision in waste manage-
ber of samples used in that estimation,
ment. In this context, it is an error in concluding that the true
5.1.5 Specify acceptable decision errors (see Section 8), and
value is smaller than the regulatory limit when in fact it is not.
5.1.6 Calculate the decision point (see Section 8).
The calculation of the false negative error will depend on how
5.2 The following sections discuss in practical terms the
the hypotheses are framed (see Appendix X1).
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. D 5792
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
6.1 A decision rule is constructed according to a problem
value is equal to or greater than the regulatory limit when in
statement defined and agreed to by all the parties concerned,
fact it is not. The calculation of the false positive error will
through a planning process. The decision rule can be carried
depend on how the hypotheses are framed (see Appendix X1).
out in two similar ways.
3.1.6 hypothesis, n—a supposition or conjecture put for-
6.1.1 When Using A Decision Point:
ward to account for certain facts and used as a basis for further
6.1.1.1 The general construct of the decision rule in this
investigation by which it may be proved or disproved.
case is:
E 1138
If ~sample mean! $ ~decision point!, then ~one action!. Otherwise, ~alternate action!.
3.1.6.1 Discussion—For this practice, a hypothesis is a
postulation of what the true value is, typically framed for the 6.1.1.2 Because a decision point is needed in the above
purpose of making a statistical test of the hypothesis. In a decision rule, this practice provides a logical basis for devel-
statistical test, there are two competing hypotheses: the null oping such a decision point. Because the above decision rule
hypothesis and the alternative hypothesis. The null hypothesis can also be carried out similarly using confidence limits, it is
is a hypothesis “put up” for consideration and is the presumed also presented that way in 6.2.
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
D 6250
FIG. 1 Decision Point Determination for Mean Concentration
Otherwise, ~dispose the waste fly ash in a sanitary landfill!.
6.1.1.3 Note that when data can be measured with certainty,
6.1.1.6 The inputs needed for the calculation of the decision
the regulatory limit defines the decision point. For example,
point in 6.1.1.5 are: form of the hypotheses to be tested,
sample data taken from a totally homogeneous population, in
acceptable maximum decision error, number of samples, and
the absence of measurement error, have no variability. This
estimated standard deviation. The standard deviation should
means that the standard deviation of the data is zero and the
include all the sources of variation in the sampling and
decision point is reduced to the regulatory limit (see 8.6.3).
measurement processes. Decision errors include the false
6.1.1.4 When data cannot be measured precisely or the
positive error and false negative error. Details are given in
population is not totally homogeneous, this variability needs to
Section 8.
be incorporated to obtain a decision point. The decision point
6.2 When Using Confidence Limit:
then includes both the original regulatory limit and a margin of
6.2.1 The general construct of the decision rule in this case
uncertainty that is reflected in the standard deviation, which is
is:
a component in the calculation of the decision point (see 8.6.3).
If ~confidence limit!. or < ~regulatory limit!, then ~one action!
The way to incorporate this uncertainty depends on how a
Otherwise, ~alternate action!.
hypothesis is formulated and which presumption is adopted.
This is discussed in Section 7.
where the confidence limit can be the upper confidence limit
6.1.1.5 An example of carrying out the decision rule using a
or the lower confidence limit, depending on the chosen
decision point is:
presumption in the null hypothesis (see Section 7). A special
case where the confidence limit is replaced by the sample mean
If ~average concentration of cadmium in a truck load! $ ~decision
point!, then ~dispose of the waste fly ash in an RCRA landfill!. in the above decision rule is also discussed in Section 7.
NOTICE: This standard has either been superceded and replaced by a new version or discontinued.
Contact ASTM International (www.astm.org) for the latest information.
D 6250
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
the true mean concentration is neither higher nor lower than the
waste fly ash in a sanitary landfill). Otherwise, (dispose of the
regulatory limit.
waste fly ash in a RCRA landfill).
7.5.3.1 This presumption would require “cleanup” down to
6.2.3 The relationship between the decision point approach
the regulatory limit
...
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