The MARSSIM Sign Test to compare the mean to a threshold as performed by VSP on the selected data values follows the procedure outlined in MARSSIM Section 8.3 (EPA 2000).
In the MARSSIM Sign Test, each measurement is subtracted from the action level (e.g. DCGLw) to obtain \( N \) differences \( d_i = AL - X_i \). Any differences of zero are discarded from consideration and the sample size is reduced accordingly. The test statistic \( S+ \) is calculated either by:
counting the positive differences, when testing the null hypothesis that the median concentration of residual radioactivity in the survey unit is greater than the DCGLw \( H_0 : \mu > AL \),
or by
counting the negative differences when testing the null hypothesis \( H_0 : \mu < AL \).
The test statistic \(S+ \) is then compared with the critical value \( k \), which is obtained from Table I.3 in Appendix I of MARSSIM (EPA 2000, I-5) for \( N \le 50 \), and calculated from the following formula for \( N > 50 \):
$$ \frac{N}{2} + \frac{Z_{1- \alpha}}{2} \sqrt{N} $$
where
\( z_{1- \alpha} \) is the \( (1- \alpha ) \) percentile of a standard normal distribution.
If \( S+ > k \) , then the null hypothesis is rejected in favor of the alternative hypothesis that the median concentration of residual radioactivity in the survey unit is less than the DCGLw.
Multi-Agency Radiation Surveys and Site Investigation Manual (MARSSIM), Revision 1 (August 2000), U.S. Environmental Protection Agency.
Available at http://www.epa.gov/radiation/marssim/obtain.html