The MARSSIM Sign test( MARSSIM §8.3.1) is a one-sample, nonparametric statistical test used to determine compliance with a release criterion (Weighted Derived Concentration Guidance Level, or DCGLw) when the radionuclide of concern is not present in background. The purpose of a MARSSIM sign test is to test a hypothesis involving the true mean or median of a population against an Action Level. This "Unity Rule for Soils" sub-design is for use when more that one contaminant nuclide is present on the site. The appropriate use of the sign test for final status surveys is discussed in §5.5.2.1 of Multi-Agency Radiation Survey and Site Investigation Manual (MARSSIM) (EPA 2000). This document is currently available at: https://www.epa.gov/radiation/multi-agency-radiation-survey-and-site-investigation-manual-marssim
This design assume that you have more than one contaminant nuclide in the surface soil study area. To enter the nuclides of concern, use the MARSSIM button on the Analyte page. The nuclides will have standard DCGLw values which may need to be modified for your particular application.
If you are an expert in MARSSIM designs, you can choose to enter all your own design parameters including:
Confidence%: Minimum desired probability of concluding the site is dirty if the true sum-of-fractions exceed the DCGLw.
Beta%: Maximum desired probability of concluding the site is dirty if the true sum-of-fractions is less than the lower bound of the gray region.
Lower bound of the gray region (LBGR): A true sum-of-fractions value (below the DCGLw) above which you are willing to accept an increased risk of concluding the site is dirty.
Estimated standard deviation for the sum-of-fractions.
Estimated mean of the sum-of-fractions (in order to compute the power of the test).
As an alternative, you can have VSP assist you with the computation of the Sum of Fractions values. This approach will be emphasized here. Begin by entering an estimated mean and standard deviation for each of the nuclides as illustrated below.
After entering all the values, VSP will calculate the Mean and Standard Deviation Sum-of-Fractions for you. VSP uses the following formulas:
\begin{equation} Mean_{\text{sof}} = \dfrac{Mean_1}{DCGL_1} + \dfrac{Mean_2}{DCGL_2} + etc.\end{equation}
\begin{equation} S_{\text{sof}} = \sqrt{\Bigg(\dfrac{S_1}{DCGL_1}\Bigg)^2 + \Bigg(\dfrac{S_2}{DCGL_2}\Bigg)^2 + etc.}\end{equation}
You will need to enter the remaining design parameters:
Confidence%: Minimum desired probability of concluding the site is dirty if the true sum-of-fractions exceed the DCGLw.
Beta%: Maximum desired probability of concluding the site is dirty if the true sum-of-fractions is less than the lower bound of the gray region.
Lower bound of the gray region (LBGR): A true sum-of-fractions value (below the DCGLw) above which you are willing to accept an increased risk of concluding the site is dirty.
A DCGLw of 1 is assumed for the unity rule calculations.
The number of samples is calculated using Eq. (3) (EPA 2000, p. 5-33).
\begin{equation} n = \frac{(z_{1-\alpha}+z_{1-\beta})^2}{4(\text{Sign} P-0.5)^2} \quad \mbox{where} \quad \text{Sign} P = \Phi\Big(\frac{\Delta}{S_{\text{sof}}}\Big) \end{equation}
where:
\(n\) |
is the recommended minimum sample size. |
\(S_{\text{sof}}\) |
is the estimated standard deviation for the sum-of-fractions defined in equation (2) above. |
\(z_{1-\alpha}\) |
is the value of the standard normal distribution for which the proportion of the distribution to the left of \(z_{1-\alpha}\) is \(1-\alpha\). |
\(z_{1-\beta}\) |
is the value of the standard normal distribution for which the proportion of the distribution to the left of \(z_{1-\beta}\) is \(1-\beta\). |
\(\Delta\) |
is the width of the gray region. |
\(\alpha\) |
is the probability of rejecting the null hypothesis when the null hypothesis is true. Also: \(\frac{(100\% - Confidence)}{100\%}\) |
\(\beta\) |
is the probability of not rejecting the null hypothesis when the null hypothesis is false. |
\({\Phi}_{\text{(x)}}\) |
is the probability that a standard normal variate takes on a value \(\le\) x (CDF). |
The assumptions associated with the formulas for computing the number of samples are:
1. The computed sign test statistic is normally distributed.
2. The mean and standard deviation (\(S\)) estimates are reasonable and representative of the population being sampled.
3. The population values are not spatially or temporally correlated.
4. The sampling locations will be selected randomly.
The first three assumptions will be assessed in a post data collection analysis. The last assumptions is valid because the sample locations were selected using a random process.
EPA. 2000. Multi-Agency Radiation Survey and Site Investigation Manual (MARSSIM). NUREG-1575, Rev. 1, EPA 402-R-97-016, Rev.1, DOE/EH-0624, Rev. 1. Environmental Protection Agency, Office of Research and Development, Quality Assurance Division, Washington DC.
Gilbert, RO, JR Davidson, JE Wilson, BA Pulsipher. 2001. Visual Sample Plan (VSP) models and code verification. PNNL-13450, Pacific Northwest National Laboratory, Richland, Washington.
Lower Bound of the Gray Region (LBGR)
Estimated Standard Deviation (Sum of Fractions)
Estimated Mean (Sum of Fractions)