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APPENDIX D SECTION! 1 DESCRIPTION Of STATISTICAL ANALYSES The corrected mean and standard deviation are then used to determine the tolerance limit _. as described previously. This test statistic is not useful if the mean is slightly larger than the detection limit or if there are multiple reported detection limits. When these conditions interfered with the - ' application of Cohen's method, the nondetect values were replaced with one-half the detection limit and the tolerance interval was calculated. Test of Proportions If less than 50 percent but not fewer than 10 percent of the values are above the detection limit, a test of proportions was used to compare the background data with the detection well data. The test determines if the proportion of detects in the detection well differs significantly from the proportion in the background well. If there is a significant difference, there is statistically significant evidence of contamination. This test requires at least five detected values and five nondetects. To perform the test, the proportion of detects in the background well Pb and in the detection well Pd are calculated. The standard error of the difference in proportions is calculated as shown below, where B and nb are the number of detects and the total number of samples in the background monitoring well, and D and n, are the number of detects and the total number of samples in the detection monitoring well. 5P = {[(B + D)/(n,, + nd)]*[1-( B + D)/(n, + n,)]*[1/ nb + 1/ nd ]}72 The test statistic is then calculated as follows: z = (Pb - P,) / S, The absolute value of Z is compared with 1.96, the 97.5' percentile from the standard normal distribution. If the value exceeds 1.96, there is statistically significant evidence at the 5 percent significance level that the proportion of detects in the detection monitoring well exceeds the proportion in the background monitoring well. References United States Environmental Protection Agency, Office of Solid Waste. April 1989. Statistical Analysis of Ground -Water Monitoring Data at RCRA Facilities:Interim Final Guidance. PB89-151047. RDD/APPD4Q97.Dx