Performing the Statistical Tests - Nucleus Documents... · 2016-01-29 · Performing the...

Performing the Statistical Tests

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Wilcoxon Rank Sum Test

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WRS Test

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• WRS Test (2-sample test) used when:

Contaminant is in background soil at a level that cannot be ignored

• Null hypothesis (H0): residual radioactivity exceeds the release criteria

Applying the WRS Test

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(1) Obtain adjusted reference area measurements by adding DCGLW to each background reference area measurement

(2) Rank the pooled adjusted reference area measurements (m) and survey unit measurements (n) from 1 to N (N = m + n)

(3) If several measurements are tied, they are all assigned the average rank of that group of tied measurements

Applying the WRS Test

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(4) If there are t “< MDC” measurements, they are assigned

the average of the ranks from 1 to t, or (t+1)/2 (WRS test cannot be used with more than 40% “< MDC”)

(5) Sum the ranks of the adjusted measurements from the

background reference area, Wr.

(6) Compare Wr with tabulated critical value for appropriate

values of n, m, and α; reject H0 if Wr > critical value

Class Exercise: Perform WRS Test

6

• Outdoor soil survey unit contaminated with Cs-137

• Survey design parameters:

– DCGLW = 1.5 pCi/g (55.5 Bq/kg)

– LBGR = 0.5 pCi/g (18.5 Bq/kg)

– σs = 0.33 pCi/g (12.2 Bq/kg)

– σr = 0.25 pCi/g (9.25 Bq/kg)

– Type I error = 0.05

– Type II error = 0.10


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• Δ/σ = (1.5 - 0.5)/0.33 = 3 or (55.5 – 18.5)/12.2 = 3

• N/2 = 8 samples (MARSSIM Table 5.3)

• 8 soil samples were collected from both the survey unit and

the background reference area and analyzed for Cs-137

(pCi/g) (Bq/kg)


8

• Exercise: Perform the

WRS test on the Cs-137 results to determine if the survey unit meets the release criterion

• WRS test critical value is in MARSSIM App. I, Table I.4

Soil Sample Results (Cs-137 in pCi/g)

Soil Sample Results (Cs-137 in Bq/kg)

Survey unit Reference Survey unit Reference

2.0 0.6 74.0 22.2

1.4 0.5 51.8 18.5

1.5 0.4 55.5 14.8

1.8 0.2 66.6 7.4

1.3 0.7 48.1 25.9

0.9 0.1 33.3 3.7

1.5 0.1 55.5 3.7

1.6 0.7 59.2 25.9

AVG = 1.5 AVG = 0.43 AVG = 55.5 AVG = 15.9

Is the Test Necessary?

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Survey Result Conclusion Difference between largest survey unit

measurement and smallest reference area measurement is less than DCGLW

Survey unit meets release criterion

Difference of survey unit average and reference area average is greater than

DCGLW

Survey unit does not meet release criterion

Difference between any survey unit measurement and any reference area

measurement greater than DCGLW and the difference of survey unit average and

reference area average is less than DCGLW

Conduct WRS test and elevated measurement comparison

MARSSIM Table 8.2

Is the Test Necessary? Survey Result Conclusion Our Example

Difference between largest survey unit measurement and

smallest reference area measurement is less than

DCGLW


pCi/g 2.0 – 0.1 = 1.9 1.9 > DCGLW

Bq/kg 74 – 3.7 = 70.3 70.3 > DCGLW

(No—continue)

Difference of survey unit average and reference area

average is greater than DCGLW

Survey unit does not meet release criterion

pCi/g 1.5 – 0.43 = 1.07

1.07 < DCGLW

Bq/kg 55.5 – 15.9 = 39.6

39.6 < DCGLW

(No—continue)

Difference between any survey unit measurement and any

reference area measurement greater than DCGLW and the

difference of survey unit average and reference area average is less than DCGLW

Conduct WRS test and elevated measurement

comparison

pCi/g 1.9 > DCGLW

1.07 < DCGLW

Bq/kg 70.3 > DCGLW 39.6 < DCGLW

(Yes—perform test)

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Prep Work

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Reference DCGLw Adjusted Reference

Measurement Location Rank

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WRS Test Results

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• Wr = 91.5

• Critical value (CV) = 84 for N/2 = 8, α = 0.05 (MARSSIM Table I.4)

• Wr > CV (91.5>84), so we reject H0 and the survey unit PASSES

Sign Test

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Sign Test

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• Sign Test (1-sample test) used when:

– Radionuclide not in background soil (e.g., Co-60)

– Background can be ignored (i.e., background small fraction of DCGL) (e.g. Cs-137)

– Surface activity assessment performed with average background subtracted from each gross surface activity measurement

• Null hypothesis (H0): residual radioactivity exceeds the release criteria

Applying the Sign Test

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(1) List the survey measurements, xi , i = 1, 2,...N.

(2) Subtract each measurement, xi , from the DCGLW to obtain the differences: Di = DCGLW - xi , i = 1, 2,...N.

(3) Discard each difference that is exactly zero and reduce sample size, N, accordingly.

Applying the Sign Test

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(4) Count the number of positive differences, result is test

statistic S+. (Note: a positive difference corresponds to a measurement below the DCGLW and contributes evidence that the survey unit meets the release criterion.)

(5) Compare S+ with tabulated critical value for N and α; reject H0 if S+ > critical value.

Class Exercise: Perform Sign Test

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• Outdoor soil survey unit contaminated with Co-60

• Survey design parameters:

– DCGLW = 10 pCi/g (0.37 Bq/g)

– LBGR = 3 pCi/g (0.11 Bq/g)

– σs = 3.5 pCi/g (0.13 Bq/g)




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• ∆/σ = (10 - 3)/3.5 = 2 or (0.37 – 0.11)/0.13 = 2

• N = 15 samples (MARSSIM Table 5.5)

• 15 soil samples were collected from the survey unit and analyzed for Co-60


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• Exercise: Perform the Sign test on the Co-60 results to determine if the survey unit meets the release criterion—Does the survey unit pass?

• Sign test critical value is in MARSSIM App. I, Table I.3

Soil Sample Results (Co-60 in pCi/g)

5.6 3.1 12.3

10.8 7.2 8.7

22.5 3.8 12.5

15.0 6.5 11.3

9.9 7.4 3.5

Soil Sample Results (Co-60 in Bq/g)

0.21 0.11 0.46

0.40 0.27 0.32

0.83 0.14 0.46

0.56 0.24 0.42

0.37 0.27 0.13

Mean = 9.3 pCi/g (0.34 Bq/g) σ = 5.1 pCi/g (0.19 Bq/g)


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Survey Result Conclusion All measurements less than DCGLW Survey unit meets release

criterion

Average greater than DCGLW Survey unit does not meet

release criterion Any measurement greater than DCGLW

and the average less than DCGLW

Conduct Sign test and elevated measurement comparison

MARSSIM Table 8.2


Survey Result Conclusion Our Example

All measurements less than DCGLW


pCi/g 22.5 > 10 Bq/g 0.83 > 0.37

No—continue

Average greater than DCGLW

Survey unit does not meet release

criterion

pCi/g 9.5 < 10 Bq/g 0.35 < 0.37

No—continue

Any measurement greater than DCGLW and the average

less than DCGLW

Conduct Sign test and elevated measurement comparison

pCi/g 22.5 > 10 and

9.5 < 10

Bq/g 0.83 > 0.37 and

0.35 < 0.37 Yes—perform test

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Prep Work

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DCGLw Co-60 DCGLw – Co-60 Sign

Sign Test Results

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• S+ = 9

• Critical value (CV) for N=15 and α = 0.05 is 11 (MARSSIM Table I.3)

• Since S+ is not greater than the critical value we cannot reject H0 and the survey unit FAILS

Class Exercise: Perform Sign Test Structural Survey Unit

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• Building survey unit contaminated with Am‐241, Co‐60, Sr/Y‐90, Cs‐137

• DCGLs from prior example:

Class Exercise: Perform Sign Test Structural Survey Unit

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• Survey design parameters (from prior example):

– DCGLW : – Alpha (same as Am‐241) = 130 dpm/100 cm2 (0.02 Bq/cm2)

– Beta (gross beta due to multiple contaminants) = 23,000 dpm/100 cm2 (3.8 Bq/cm2)

– Alpha and beta measurements were performed; unity rule necessary;

therefore, DCGL = 1

– LBGR = 0.53

– σs = 0.29




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/ = (1‐0.53)/0.29 = 1.60

• N = 17 samples (MARSSIM Table 5.5)

• 17 direct alpha and beta measurements were performed


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• Exercise: Perform the Sign test on the alpha and beta surface activity results to determine if the survey unit meets the release criterion—Does the survey unit pass?

• Sign test critical value is in MARSSIM App. I, Table I.3

Alpha Surface Activity Results

99 74 31 19

91 107 78 125

48 157 66

8 61 32

45 118 58

Beta Surface Activity Results

8,796 4,259 4,085 11,256

7,002 5,763 11,218 12,592

8,006 11,950 2,216

8,029 11,460 8,195

13,246 8,338 2,647

Mean: Alpha = 72; Beta = 8,512; SOR = 0.92 σ: Alpha = 41 pCi/g; Beta = 2,990; SOR = 0.13


Survey Result Conclusion Our Example

All measurements less than DCGLW


pCi/g 22.5 > 10Bq/g 0.83 > 0.37

No—continue

Average greater than DCGLWSurvey unit does not meet release

criterion

pCi/g 9.5 < 10Bq/g 0.35 < 0.37

No—continue

Any measurement greater than DCGLW and the average

less than DCGLW

Conduct Sign test and elevatedmeasurement comparison

pCi/g22.5 > 10 and

9.5 < 10

Bq/g0.83 > 0.37 and0.35 < 0.37

Yes—perform test

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Prep Work

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DCGLw Alpha Beta SOR DCGLw – SOR Sign

Sign Test Results

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• S+ = ____

• Critical value (CV) for N=17 and = 0.025 is 12 (MARSSIM Table I.3)

• Do we accept or reject the null hypothesis?

Performing the Statistical Tests - Nucleus Documents... · 2016-01-29 · Performing the...

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