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Assessment of Agent Monitoring Strategies for the Blue Grass and Pueblo Chemical Agent Destruction Pilot Plants (2012) / Chapter Skim
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Appendix E: Sampling Variability and Uncertainty Analyses
Pages 163-172

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From page 163...
... NORMAL CONFIDENCE LIMITS FOR THE MEAN1 For a normally distributed constituent that is detected in all cases the (1 ) 100 percent normal lower confidence level (LCL)
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From page 164...
... can be used; however, the DL must be constant. LOGNORMAL CONFIDENCE LIMITS FOR THE MEDIAN For a lognormally distributed constituentthat is, y = log e ( x)
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From page 165...
... Approximate Lognormal Confidence Limit Methods There are also several approximations to lognormal confidence limits for the mean that have been proposed. These have been conveniently classified as either transformation methods or direct methods (Land, 1970)
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From page 166...
... = 2 . This 2 estimate is assumed to be normally distributed and approximate confidence limits are computed accordingly.
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From page 167...
... and UCL = exp ^z ^ (13) NONPARAMETRIC CONFIDENCE LIMITS FOR THE MEDIAN When data are neither normally or lognormally distributed or the detection frequency is too low (e.g., < 50 %)
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From page 168...
... Denote the arithmetic and geometric means based on this random sample by x and ~ x , respectively. The maximum likelihood estimators of and , denoted by ^ and ^ , are solutions to the following equations:
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From page 169...
... 1955. On the distribution of a positive random variable having a discrete probability mass at the origin.
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From page 170...
... 2010. ASTM D7048-04 Standard Guide for Applying Statistical Methods for Assessment and Corrective Action Environmental Monitoring Programs.
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From page 171...
... National Bureau of Standards Special Publication 422. Washington, D.C.: U.S.
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Key Terms

  • confidence limits
  • confidence limit
  • desired confidence
  • regulatory standard
  • nonparametric confidence

  • corrective action
  • percent normal
  • gamma distribution
  • confidence intervals
  • linear functions

  • measured concentrations
  • success probability
  • normal mean
  • binomial distribution
  • random sample

  • maximum likelihood
  • normal ucl
  • true concentration
  • groundwater monitoring
  • applying statistical

  • positive random
  • guidance document
  • approximate confidence
  • vadose meteoric
  • phreatic versus

  • concentration mean
  • sample measurement
  • fewer successes
  • positive results
  • normally distributed


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