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Appendix A Mann-Kendall Analysis Description of the Test: The Mann-Kendall test is a non-parametric statistical test, n example of a sign test. The first step in the Mann-Kendall test is to list the data in the order in which they were collected over time (e.g., x1, x2, X3,..,Xn). Then the signs, positive or negative, of all possible differences between x;-xk where j > k are determined (e.g., x2-x1, x3-x1,..., xn-x1, x3-x2,..., xn-x2,...). The Mann-Kendall statistic (S) is then calculated as the number of positive differences minus the number of negative differences. If this statistic is a large positive number, measurements taken later in time tend to be larger than those taken earlier in time. If this statistic is a large negative number, the opposite is true. To identify an upward trend, the hypothesis of no trend is tested against the hypothesis of an upward trend. The hypothesis of no trend is rejected and the hypothesis of an upward trend accepted if the Mann-Kendall statistic (S) is positive and a probability value, which is dependent on the value of the statistic and the number of data points, is less than a specified significance level for the test. The probability value is determined by referring to Mann- Kendall test tables that are available in many statistical references (e.g., Gilbert, 1987). A downward trend is tested in the same manner, except the Mann-Kendall statistic is then a negative number. The Mann-Kendall test is described in detail in references such as Gilbert (1987) and EPA's Guidance for Data Quality Assessment(EPA OA/G-9, 1998). The number of results, n, and the calculated statistic, S, are used to look up a probability on statistical tables. The probability represents the likelihood of getting the result of S based purely on chance. The probability (P) is then compared to the selected confidence level for the testing procedure. A value of P=0.1 is equivalent to a 90% confidence level, for which there is less than a 10% chance that the calculated trend is based on chance rather than representing an actual trend in concentration. If the probability value is less than the selected confidence level, the null hypothesis (no trend) would be rejected and the alternate hypothesis (an upward or downward trend) would be accepted. At a confidence level of 90% (i.e., P=0.1), there is a 10% chance of a false positive result (Type I error), that is, identifying a trend when none actually exists. Choice of the Mann-Kendall Method of Trend Analysis: For the site, a non-parametric trend analysis(Mann-Kendall) has been selected as a statistical method to evaluate changes in concentrations over time at individual wells. The Mann-Kendall test for trend is recommended in EPA guidance (USEPA, 1989; USEPA, 2000) and other literature concerning environmental data (e.g., Gilbert, 1989; Gibbons, 1994). This analysis is an intra-well evaluation rather than a comparison of the group of 10 upgradient wells with the group of downgradient wells. A non-parametric method was