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B.1 Development of a decision rule

There are three activities associated with this step:

  • Specifying the statistical parameter that characterizes the parameter of interest.
  • Specifying the action level for the study.
  • Combining the outputs of the previous DQO steps into an ‘if…then…’ decision rule that defines the conditions that would cause the decision maker to choose among alternative actions.

Certain aspects of the site investigation process, such as the Historical Site Assessment (HAS), are not so quantitative that a statistical parameter can be specified. Nevertheless, a decision rule should still be developed that defines the conditions that would cause the decision maker to choose among alternatives.

Certain aspects of the site investigation process, such as the Historical Site Assessment (HAS), are not so quantitative that a statistical parameter can be specified. Nevertheless, a decision rule should still be developed that defines the conditions that would cause the decision maker to choose among alternatives.

The expected outputs of this step are:

  • The parameter of interest that characterizes the level of residual radioactivity.
  • The action level.
  • An ‘if…then…’ statement that defines the conditions that would cause the decision maker to choose among alternative actions.

The parameter of interest is a descriptive measure (such as a mean or median) that specifies the characteristic or attribute that the decision maker would like to know about the residual contamination in the survey unit.

The mean is the value that corresponds to the ‘centre’ of the distribution in the sense of the ‘centre of gravity’. Positive attributes of the mean include:

  • It is useful when the action level is based on long-term, average health effects.
  • It is useful when the population is uniform with relatively small spread.
  • It generally requires fewer samples than other parameters of interest.

Negative attributes include:

  • It is not a very representative measure of central tendency for highly skewed distributions.
  • It is not useful when a large proportion of the measurements are reported as less than the detection limit.

The median is also a value that corresponds to the ‘centre’ of a distribution, but where the mean represents the centre of gravity the median represents the ‘middle’ value of a distribution. The median is that value such that there is the same number of measurements greater than the median as less than the median. The positive attributes of the median include:

  • It is useful when the action level is based on long term, average health effects.
  • It provides a more representative measure of central tendency than the mean for skewed populations.
  • It is useful when a large proportion of the measurements are reported as less than the detection limit.
  • It relies on few statistical assumptions.

Negative attributes include:

  • It will not protect against the effects of extreme values.
  • It is not a very representative measure of central tendency for highly skewed distributions.

The non-parametric statistical tests discussed in Section 3.10 are designed to determine whether or not the level of residual activity uniformly distributed throughout the survey unit exceeds the DCGLW. Since these methods are based on ranks, the results are generally expressed in terms of the median. When the underlying measurement distribution is symmetric, the mean is equal to the median. The assumption of symmetry is less restrictive than that of normality because the normal distribution is itself symmetric. If, however, the measurement distribution is skewed to the right, the average will generally be greater than the median. In severe cases, the average may exceed the DCGLW while the median does not. For this reason, EURSSEM recommends comparing the arithmetic mean of the survey unit data to the DCGLW as a first step in the interpretation of the data.

The action level is a measurement threshold value of the parameter of interest that provides the criterion for choosing among alternative actions. EURSSEM uses the investigation level, a radionuclide-specific level of radioactivity based on the release criterion that results in additional investigation when it is exceeded, as an action level. Investigation levels are developed for both the elevated measurement comparison (EMC) using scanning techniques and the statistical tests using direct measurements and samples.
The mean concentration of residual radioactivity is the parameter of interest used for making decisions based on the final status survey. The definition of residual radioactivity depends on whether or not the contaminant appears as part of background radioactivity in the reference area. If the radionuclide is not present in background, residual radioactivity is defined as the mean concentration in the survey unit. If the radionuclide is present in background, residual radioactivity is defined as the difference between the mean concentration in the survey unit and the mean concentration in the reference area selected to represent background. The term 1-sample case is used when the radio-nuclide does not appear in background, because measurements are only made in the survey unit. The term 2-sample case is used when the radionuclide appears in background, because measurements are made in both the survey unit and the reference area.

The decision rule for the 1-sample case is: ‘If the mean concentration in the survey unit is less than the investigation level, then the survey unit is in compliance with the release criterion’. To implement the decision rule, an estimate of the mean concentration in the survey unit is required. An estimate of the mean of the survey unit distribution may be obtained by measuring radionuclide concentrations in soil at a set of n randomly selected locations in the survey unit. A point estimate for the survey unit mean is obtained by calculating the simple arithmetic average of the n measurements. Due to measurement variability, there is a distribution of possible values for the point estimate for the survey unit mean, δ. This distribution is referred to as f(δ), and is shown in the lower graph of Figure B.1. The investigation level for the Sign test used in the 1-sample case is the DCGLW, shown on the horizontal axis of the graph.

If f(δ) lies far to the left (or to the right) of the DCGLW, a decision of whether or not the survey unit demonstrates compliance can be easily made. However, if f(δ) overlaps the DCGLW, statistical decision rules are used to assist the decision maker. Note that the width of the distribution for the estimated mean may be reduced by increasing the number of measurements. Thus, a large number of samples will reduce the probability of making decision errors.
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Figure A.1 Example of the parameter of interest for the 1-Sample Case
Figure B.1 Example of the parameter of interest for the 1-Sample Case

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Figure B.2 shows a simple, hypothetical example of the 2-sample case. The upper portion of the figure shows one probability distribution representing background radionuclide concentrations in the surface soil of the reference area, and another probability distribution representing radionuclide concentrations in the surface soil of the survey unit. The graph in the middle portion of the figure shows the distributions of the estimated mean concentrations in the reference area and the survey unit. In this case, the parameter of interest is the difference between the means of these two distributions, D, represented by the distance between the two vertical dotted lines.

The decision rule for the 2-sample case is: ‘If the difference between the mean concentration in the survey unit and the mean concentration in the reference area is less than the investigation level, then the survey unit is in compliance with the release criterion’. To implement the decision rule, an estimate of the difference is required. This estimate may be obtained by measuring radionuclide concentrations at a set of ‘n’ randomly selected locations in the survey unit and ‘m’ randomly selected locations in the reference area. A point estimate of the survey unit mean is obtained by calculating the simple arithmetic average of the n measurements in the survey unit. A point estimate of the reference area mean is similarly calculated. A point estimate of the difference between the two means is obtained by subtracting the reference area average from the survey unit average.
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Figure A.2 Example of the parameter of interest for the 2-Sample Case
Figure B.2 Example of the parameter of interest for the 2-Sample Case

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The measurement distribution of this difference, f(δ), is centred at D, the true value of the difference. This distribution is shown in the lower graph of Figure B.2.
Once again, if f(δ) lies far to the left (or to the right) of the DCGLW, a decision of whether or not the survey unit demonstrates compliance can be easily made. However, if f(δ) overlaps the DCGLW, statistical decision rules are used to assist the decision maker.