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APPENDIX D STATISTICAL METHODS TO DETERMINE CONCENTRATION LIMITS TOLERANCE LIMIT METHODOLOGIES The purpose of a tolerance interval approach is to define a concentration range from background well data, within which a large proportion of the monitoring observations should fall with a high probability. The proportion of the population included is referred to as the coverage. The probability with which the tolerance interval includes the proportion of the population is referred to as the tolerance coefficient. ' Consistent with USEPA and state recommendations, Sanitas (computer program utilized) uses a 95 percent coverage and 95 percent tolerance coefficient. The upper 95 percent ' tolerance limit will contain at least 95 percent of the distribution of observations from background well data. The tolerance interval method is described in the following documents: -- Introduction to Statistical Quality Control, D.C. Montgomery. John Wiley Publishing, New York. 1985. -- Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Interim Final Guidance Document, USEPA. USEPA/530-SW-89-026. February 1989. -- Statistical Analysis of Groundwater Monitoring Data at RCRA Facilities, Addendum to Interim Final Guidance, USEPA. USEPA/530--93-003. July 1992. San Joaquin County uses Groundwater Statistical Analysis System (DSAS, now referred to as Sanitas) to calculate tolerance limits for County Landfills. Sanitas is a statistical software program developed by Intelligent Decision Technologies, Ltd. (IDT). It is specifically designed to evaluate water quality monitoring data for landfills. Sanitas performs all pre- and post -analysis tests required so that the data do not violate size and distribution assumptions of the relevant statistical analysis. ' Parametric Tolerance Limit When conducting the tolerance interval method, Sanitas automatically evaluates the ' distribution of the data. For data sets with 50 or fewer samples the Coefficient of Variation test for normality is used, and for data sets greater than 50 samples the Shapiro-Francia test is used. Sanitas applies the parametric tolerance limit test when the background data ' set is found to have less than 50 percent non -detects and the background data have a normal or transformed normal distribution. If greater than 15 percent but less than 50 percent of the background data set consist of non -detect values, the mean and standard ' deviation of the data set are adjusted using the Cohen's Method. The tolerance limit is then calculated using the adjusted values. Nonparametric Tolerance Limit When the background data set contains greater than 50 percent but less than 100 percent nondetect values and/or its distribution is not normal (or transformed normal), Sanitas applies the nonparametric tolerance limit method. However, this method requires a large number of samples to achieve a false positive rate of 1 percent or less, which is required