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APPENDIX D SECTION f DESCFUP7 ON OF STATISTICAL ANALYSES <br /> The corrected mean and standard deviation are then used to determine the tolerance limit <br /> as described previously. <br /> This test statistic is not useful if the mean is slightly larger than the detection limit or if there <br /> are multiple reported detection limits. When these conditions interfered with the <br /> application of Cohen's method,the nondetect values were replaced with one-half the <br /> detection limit and the tolerance interval was calculated. <br /> Test of Proportions <br /> If less than 50 percent but not fewer than 10 percent of the values are above the detection <br /> _ limit,a test of proportions was used to compare the background data with the detection <br /> well data.The test determines if the proportion of detects in the detection well differs <br /> significantly from the proportion in the background well.If there is a significant difference, <br /> ,._ there is statistically significant evidence of contamination.This test requires at least five <br /> detected values and five nondetects. <br /> To perform the test, the proportion of detects in the background well P,and in the detection <br /> well Pd are calculated.The standard error of the difference in proportions is calculated as <br /> shown below,where B and nb are the number of detects and the total number of samples in <br /> the background monitoring well,and D and nd are the number of detects and the total <br /> number of samples in the detection monitoring well. <br /> S,= {((B+D)/(n,,+nd)j*[1-(B+D)/(nb+n,)j*[1/nb+1/ nd])"x <br /> The test statistic is then calculated as follows: <br /> Z= (Pb-Pd/ S, <br /> The absolute value of Z is compared with 1.96, the 97.5` percentile from the standard <br /> normal distribution.If the value exceeds 1.96,there is statistically significant evidence at the <br /> 5 percent significance level that the proportion of detects in the detection monitoring well <br /> exceeds the proportion in the background monitoring well. <br /> References <br /> United States Environmental Protection Agency,Office of Solid Waste.April 1989. <br /> Statistical Analysis of Ground-Water Monitoring Data at RCRA Facilities:Interim Final <br /> - Guidance. PB89-151047. <br /> - RDDIAPPD097.DOC 3 <br />