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APPENDIX D SECTION 1 DESCRIPTION OF STATISTICAL ANALYSES I 6 1 1 . ii - I I It If the data set is normal, a parameteric method will be selected based on the percentage of detected values in the data set as shown on Figure D-1. The unquantified values in the data set are nondetects, trace, and in the historic data "absent". If the percentage of detects is 85 percent or higher of the total number of results and there are at least three detected values, a tolerance interval will be used with replacement of the nondetect values at one- half the reported method detection limit. If the percentage of detected values is less than 85 percent but greater than or equal to 50 percent and the number of detected values is at least three, a tolerance interval will be used with Cohen's method to adjust the mean and standard deviation. If the percentage of detected values is greater than or equal to 10 percent but less than 50 percent and there are at least five detected values, a test of proportions will. be used. If one of the above methods is not applicable to the dataset _J because of a limited number or percentage of detected values, a statistical procedure will not be used to determine if there is statistical evidence of contamination in the detection monitoring wells. However, the data from the background well will be compared with the detection monitoring well to determine if any conclusions regarding contamination can be made. Tolerance Intervals A tolerance interval is established to encompass a concentration range that contains a specified proportion (P=0.95) of the population with a specified confidence coefficient (Y= 0.95). An upper tolerance limit with 95 percent coverage gives an upper bound below which 95 percent of the observations of the distribution should fall. If observations exceed the tolerance limit, there is statistically significant evidence of contamination. The one-sided upper tolerance limit, TL, is calculated as shown below, where K is the one-sided normal tolerance factor (EPA, 1989). TL = X + K*S For pH a two sided tolerance limit was calculated. The upper and lower tolerance limit encompass 90 percent of the population. If the percentage of detected values is less than 85 percent but not less than 50 percent, _J Cohen's method is used to adjust the sample mean and standard deviation to account for data below the detection limit. The parameters h and y are calculated as shown below, where n is the total number of observations, DL is the detection limit, m is the number of values above the detection limit, and Xd is the mean and S d is the standard deviation of the m values. h=(n-m)/n -0 Y=S,12 / (Xd - DL)' These parameters are used to determine the value of the parameter X (EPA, 1989). The corrected sample mean and sample standard deviation can then be calculated as follows: X = Xd - X(Xd _DL) S = (Sd 2 + x(x,, -DL)2)1/2 RDDIAPPD4097=