Index > 3 Characterisation of radioactively contaminated sites >

3.10.3 Example of statistical data processing: Contaminant not present in background

Contents
3.10.3.1 Site and data description
3.10.3.2 One-sample Sign test
3.10.3.3 Applying the Sign test
3.10.3.4 Sign test example: Class 2 exterior soil survey unit
3.10.3.5 Sign Test example: Class 3 exterior soil survey unit

The one-sample statistical test (Sign test) described in Section 3.5 should only be used if the contaminant is not present in background and radionuclide-specific measurements are made. The one-sample test may also be used if the contaminant is present at such a small fraction of the derived concentration guideline levels (DCGLW) value as to be considered insignificant. In this case, background concentrations of the radionuclide are included with the residual radioactivity (i.e., the entire amount is attributed to facility operations). Thus, the total concentration of the radionuclide is compared to the release criterion. This option should only be used if one expects that ignoring the background concentration will not affect the outcome of the statistical tests. The advantage of ignoring a small background contribution is that no reference area is needed. This can simplify the final status survey considerably.

The one-sample Sign test (see Section 3.10.3.2) evaluates whether the median of the data is above or below the DCGLW. If the data distribution is symmetric, the median is equal to the mean. In cases where the data are severely skewed, the mean may be above the DCGLW, while the median is below the DCGLW. In such cases, the survey unit does not meet the release criterion regardless of the result of the statistical tests. On the other hand, if the largest measurement is below the DCGLW, the Sign test will always show that the survey unit meets the release criterion.

3.10.3.1 Site and data description

To illustrate the data interpretation process, consider an example facility with 14 survey units consisting of interior concrete surfaces, one interior survey unit with drywall surfaces, and two exterior survey units. The contaminant of concern is 60Co. The interior surfaces were measured with a gas-flow proportional counter (see Appendix C) with an active surface area of 20 cm2 to determine total beta-gamma activity. Because these measurements are not radionuclide specific, appropriate reference areas were chosen for comparison. The exterior soil was measured with a germanium spectrometer to provide radionuclide-specific results. A reference area is not needed because 60Co does not have a significant background in soil.

The exterior Class 3 survey unit incorporates areas that are not expected to contain residual radioactivity. The exterior Class 2 survey unit is similar to the Class 3 survey unit, but is expected to contain residual radioactivity below the DCGLW. The Class 1 interior concrete survey units are expected to contain small areas of elevated activity that may or may not exceed the DCGLW. The Class 2 interior drywall survey unit is similar to the Class 1 interior concrete survey unit, but the drywall is expected to have a lower background, less measurement variability, and a more uniform distribution of contamination. The Class 2 survey unit is not expected to contain areas of activity above the DCGLW. Section 3.10.3 describes the Sign test used to evaluate the survey units where the contaminant is not present in background. Section 3.10.4 describes the WRS test used to evaluate the survey units where the contaminant is present in background. Section 3.10.8 discusses the evaluation of the results of the statistical tests and the decision regarding compliance with the release criterion. The survey design parameters and DQOs developed for these survey units are summarized in Table 3.53.

Survey unit Type DQO DCGLW Estimated standard
deviation, σ
Test/section
α β Survey Reference
Interior Concrete Class 1 0.05 0.05 5000 dpm per 100 cm2 625 dpm per 100 cm2 220 dpm per 100 cm2 WRS/App. A and App. D

Interior Drywall Class 2 0.025 0.05 5000 dpm per 100 cm2 200 dpm per 100 cm2 200 dpm per 100 cm2 WRS/3.10.4.3

Exterior Lawn Class 2 0.025 0.025 140 Bq/kg 3.8 Bq/kg N/A Sign/3.10.3.4

Exterior Lawn Class 3 0.025 0.01 140 Bq/kg 3.8 Bq/kg N/A Sign/3.10.3.5

Table 3.53 Final status survey parameters for example survey units

The statistical test discussed in this section is used to compare each survey unit directly with the applicable release criterion. A reference area is not included because the measurement technique is radionuclide-specific and the radionuclide of concern is not present in background. In this case the contaminant levels are compared directly with the DCGLW. The method in this section should only be used if the contaminant is not present in background or is present at such a small fraction of the DCGLW value as to be considered insignificant. In addition, one-sample tests are applicable only if radionuclide-specific measurements are made to determine the concentrations. Otherwise, the method in Section 3.10.4 is recommended.

Reference areas and reference samples are not needed when there is sufficient information to indicate there is essentially no background concentration for the radionuclide being considered. With only a single set of survey unit samples, the statistical test used here is called a one-sample test. See Section 3.10.3.2 for further information appropriate to following the example and discussion presented here.

3.10.3.2 One-sample Sign test

The Sign test is designed to detect uniform failure of remedial action throughout the survey unit. This test does not assume that the data follow any particular distribution, such as normal or log-normal. In addition to the Sign test, the DCGLEMC (see Section 3.5) is compared to each measurement to ensure none exceeds the DCGLEMC. If a measurement exceeds this DCGL, then additional investigation is recommended, at least locally, to determine the actual areal extent of the elevated concentration.
The hypothesis tested by the Sign test is:

  • Null Hypothesis
    H0: The median concentration of residual radioactivity in the survey unit is greater than the DCGLW

versus

  • Alternative Hypothesis
    Ha: The median concentration of residual radioactivity in the survey unit is less than the DCGLW.

The null hypothesis is assumed to be true unless the statistical test indicates that it should be rejected in favour of the alternative. The null hypothesis states that the probability of a measurement less than the DCGLW is less than one-half, i.e., the 50th percentile (or median) is greater than the DCGLW. Note that some individual survey unit measurements may exceed the DCGLW even when the survey unit as a whole meets the release criterion. In fact, a survey unit average that is close to the DCGLW might have almost half of its individual measurements greater than the DCGLW. Such a survey unit may still not exceed the release criterion.

The assumption is that the survey unit measurements are independent random samples from a symmetric distribution. If the distribution of measurements is symmetric, the median and the mean are the same.

The hypothesis specifies a release criterion in terms of a DCGLW. The test should have sufficient power (1-β, as specified in the DQOs) to detect residual radioactivity concentrations at the lower boundary of the gray region (LBGR). If σ is the standard deviation of the measurements in the survey unit, then Δ/σ expresses the size of the shift (i.e., Δ = DCGLW – LBGR) as the number of standard deviations that would be considered ‘large’ for the distribution of measurements in the survey unit. The procedure for determining Δ/σ is given in Section 3.5.

3.10.3.3 Applying the Sign test

The Sign test is applied as outlined in the following five steps, and further illustrated by the examples in Section 3.10.3.4 and Section 3.10.3.5.

  1. List the survey unit measurements, Xi , i = 1, 2, 3…, N.
  2. Subtract each measurement, Xi , from the DCGLW to obtain the differences:
    Di = DCGLW – Xi , i = 1, 2, 3…, N.
  3. Discard each difference that is exactly zero and reduce the sample size, N, by the number of such zero measurements.
  4. Count the number of positive differences. The result is the test statistic S+. Note that a positive difference corresponds to a measurement below the DCGLW and contributes evidence that the survey unit meets the release criterion.
  5. Large values of S+ indicate that the null hypothesis (that the survey unit exceeds the release criterion) is false. The value of S+ is compared to the critical values in Figure E.2 of Appendix E. If S+ is greater than the critical value, k, in that table, the null hypothesis is rejected.

3.10.3.4 Sign test example: Class 2 exterior soil survey unit

For the Class 2 exterior soil survey unit, the one-sample non-parametric statistical test is appropriate since the radio-nuclide of concern does not appear in background and radio-nuclide-specific measurements were made.

Table 3.53 shows that the DQOs for this survey unit include α = 0.025 and β = 0.025. The DCGLW is 140 Bq/kg (3.8 pCi/g) and the estimated standard deviation of the measurements is σ = 3.8 Bq/kg (0.10 pCi/g). Since the estimated standard deviation is much smaller than the DCGLW, the LBGR should be set so that Δ/σ is about 3.

If Δ/σ = (DCGLW – LBGR)/σ = 3

then LBGR = DCGLW – 3σ
. . . . . . . . .= 140 – (3 × 3.8)
. . . . . . . . .= 128 Bq/kg (3.5 pCi/g).

Table 3.37 indicates the number of measurements estimated for the Sign test, N, is 20 (α = 0.025, β = 0.025, and Δ/σ = 3). (Table E.1 in Appendix E also lists the number of measurements estimated for the Sign test.) This survey unit is Class 2, so the 20 measurements needed were made on a random-start triangular grid. When laying out the grid, 22 measurement locations were identified.

Data
[Bq/kg]
DCGLW–Data
[Bq/kg]
Sign
121 19 1
143 -3 -1
145 -5 -1
112 28 1
125 15 1
132 8 1
122 18 1
114 26 1
123 17 1
148 -8 -1
115 25 1
113 27 1
126 14 1
134 6 1
148 -8 -1
130 10 1
119 21 1
136 4 1
128 12 1
125 15 1
142 -2 -1
129 11 1
Number of positive differences S+ = 17

Table 3.54 Example Sign analysis: Class 2 exterior soil survey unit

The 22 measurements taken on the exterior lawn Class 2 survey unit are shown in the first column of Table 3.54. The mean of these data is 129 Bq/kg (3.5 pCi/g) and the standard deviation is 11 Bq/kg (0.30 pCi/g). Since the number of measurements is even, the median of the data is the average of the two middle values (126+128)/2 = 127 Bq/kg (3.4 pCi/g). A quantile plot of the data is shown in Appendix E Section E.3.3, Figure E.5.

There are five measurements that exceed the DCGLW value of 140 Bq/kg: 142, 143, 145, 148, and 148. However, none exceed the mean of the data plus three standard deviations: 127 + (3 × 11) = 160 Bq/kg (4.3 pCi/g). Thus, these values appear to reflect the overall variability of the concentration measurements rather than to indicate an area of elevated activity – provided that these measurements were scattered through the survey unit. However, if a posting plot demonstrates that the locations of these measurements are grouped together, then that portion of the survey unit containing these locations merits further investigation.

The middle column of Table 3.54 contains the differences, DCGLW – Data, and the last column contains the signs of the differences. The bottom row shows the number of measurements with positive differences, which is the test statistic S+. In this case, S+ = 17.

The value of S+ is compared to the appropriate critical value in Table E.2 of Appendix E. In this case, for N = 22 and α = 0.025, the critical value is 16. Since S+ = 17 exceeds this value, the null hypothesis that the survey unit exceeds the release criterion is rejected.

3.10.3.5 Sign Test example: Class 3 exterior soil survey unit

For the Class 3 exterior soil survey unit, the one-sample non-parametric statistical test is again appropriate since the radio-nuclide of concern does not appear in background and radio-nuclide-specific measurements were made.

Table 3.53 shows that the DQOs for this survey unit include α = 0.025 and β = 0.01. The DCGLW is 140 Bq/kg (3.8 pCi/g) and the estimated standard deviation of the measurements is σ = 3.8 Bq/kg (0.10 pCi/g). Since the estimated standard deviation is much smaller than the DCGLW, the lower bound for the gray region should be set so that Δ/σ is about 3.

If Δ/σ = (DCGLW – LBGR)/σ = 3

then LBGR = DCGLW – 3σ
. . . . . . . . .= 140 – (3 × 4)
. . . . . . . . .= 128 Bq/kg (3.5 pCi/g).

Table 3.37 indicates that the sample size estimated for the Sign test, N, is 23 (α = 0.025, β = 0.01, and Δ/σ = 3). This survey unit is Class 3, so the measurements were made at random locations within the survey unit.

The 23 measurements taken on the exterior lawn are shown in the first column of Table 3.55. Notice that some of these measurements are negative (-0.37 in cell A5). This might occur if an analysis background (e.g., the Compton continuum under a spectrum peak) is subtracted to obtain the net concentration value. The data analysis is both easier and more accurate when numerical values are reported as obtained rather than reporting the results as ‘less than’ or not detected. The mean of these data is 2.1 Bq/kg (0.057 pCi/g) and the standard deviation is 3.3 Bq/kg (0.089 pCi/g). None of the data exceed 2.1 + (3 × 3.3) = 12.0 Bq/kg (0.32 pCi/g). Since N is odd, the median is the middle (12th highest) value, namely 2.6 Bq/kg (0.070 pCi/g).

An initial review of the data reveals that every data point is below the DCGLW, so the survey unit meets the release criterion specified in Table 3.53. For purely illustrative purposes, the Sign test analysis is performed. The middle column of Table 3.55 contains the quantity DCGLW – Data. Since every data point is below the DCGLW, the sign of DCGLW – Data is always positive. The number of positive differences is equal to the number of measurements, N, and so the Sign test statistic S+ is 23. The null hypothesis will always be rejected at the maximum value of S+ (which in this case is 23) and the survey unit passes. Thus, the application of the Sign test in such cases requires no calculations and one need not consult a table for a critical value. If the survey is properly designed, the critical value must always be less than N.

Passing a survey unit without making a single calculation may seem an unconventional approach. However, the key is in the survey design which is intended to ensure that enough measurements are made to satisfy the DQOs. As in the previous example, after the data are collected the conclusions and power of the test can be checked by constructing a retrospective power curve as outlined in Appendix E, Section E.1.3.

One final consideration remains regarding the survey unit classification: ‘Was any definite amount of residual radioactivity found in the survey unit?’ This will depend on the MDC of the measurement method. Generally the MDC is at least 3 or 4 times the estimated measurement standard deviation. In the present case, the largest observation, 9.3 Bq/kg (0.25 pCi/g), is less than three times the estimated measurement standard deviation of 3.8 Bq/kg (0.10 pCi/g). Thus, it is unlikely that any of the measurements could be considered indicative of positive contamination. This means that the Class 3 survey unit classification was appropriate.

A
Data
B
DCGLW–Data
C
Sign
1 3.0 137.0 1
2 3.0 137.0 1
3 1.9 138.1 1
4 0.37 139.6 1
5 -0.37 140.4 1
6 6.3 133.7 1
7 -3.7 143.7 1
8 2.6 137.4 1
9 3.0 137 1
10 -4.1 144.1 1
11 3.0 137 1
12 3.7 136.3 1
13 2.6 137.4 1
14 4.4 135.6 1
15 -3.3 143.3 1
16 2.1 137.9 1
17 6.3 133.7 1
18 4.4 135.6 1
19 -0.37 140.4 1
20 4.1 135.9 1
21 -1.1 141.1 1
22 1.1 138.9 1
23 9.3 130.7 1
Number of positive differences S+ = 23

Table 3.55 Sign test example data for Class 3 exterior survey unit

If one determines that residual radioactivity is definitely present, this would indicate that the survey unit was initially mis-classified. Ordinarily, EURSSEM recommends a resurvey using a Class 1 or Class 2 design. If one determines that the survey unit is a Class 2, a resurvey might be avoided if the survey unit does not exceed the maximum size for such a classification. In this case, the only difference in survey design would be whether the measurements were obtained on a random or on a triangular grid. Provided that the initial survey’s scanning methodology is sufficiently sensitive to detect areas at DCGLW without the use of an area factor, this difference in the survey grids alone would not affect the outcome of the statistical analysis. Therefore, if the above conditions were met, a resurvey might not be necessary.