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APPENN 0 SECnON 1 DESCPJPTM 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 condition-, 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 backgroundwell. If there is a significant differenc <br />there is statistically significant evidence of contamination. This test requires at least five <br />detected values and five nondetects. I <br />To perform the test, the proportion of detects in the background well P, and in the detection <br />well PKI are calculated. The standard error of the difference in proportions is calculated as <br />shown below, where B and n, are the number of detects and the total number of samples in <br />the background monitoring well, and D and n, are the number of detects and the total <br />number of samples in the detection monitoring well. <br />S. = j[(B + D) /(n, + n,)]*11-( B + D) <br />The test statistic is then calculated as follows: <br />S�- <br />The absolute value of Z is compared with 1.96, the 97.5hpercentile 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 monitori well. <br />mg <br />References <br />UnitedStates Environmental Protection Agency, Office of Solid Waste. April 1989. <br />Statistical Analysis of Ground -Water MonitoringData at RCRA Facilities:Interim Final <br />Guidance. P1389-151047. <br />u <br />