ARCHIVED REPORTS_SECOND HALF AND ANNUAL 2010 GW MONITORING RPT

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Diamond Pet Food Processors of Ripon Colijonda, LLC Janitor),28,2011 Attachment B Page I of METHODS The Mann-Kendall test was used for the statistical analysis. The Mann-Kendall test is a test for whether concentrations tend to increase or decrease with time. The Mann- Kendall test is a variant of Kendall's tau test, a nonparametric, rank-based procedure. Because the Mann-Kendall/Kendall's tau tests use ranks of data, not actual data values, these tests are resistant to the effects of nonnormal data distribution and small numbers of unusual values (outliers), and can be used even when there are censored values (values less than the detection limit). These tests also measure both linear and nonlinear trends, as long as those trends are monotonic (e.g., x increases as y increases). The Mann-Kendall test is conducted by first ordering the data pairs (date, concentration) sequentially by date. If a positive correlation exists (generally increasing trend), the concentrations will increase more often than decrease, as time progresses. If a negative correlation exists (generally decreasing trend), the concentrations will decrease more often than increase, as time progresses. If there is no trend, concentrations will increase and decrease about equally over time. The number of increases and decreases are counted by comparing each concentration to all successive concentrations. The test statistic is then computed by either the exact form (number of pairs < 10) or the large-sample approximation (number of pairs > 10): Exact form T = S-(n x(n- 1) -2) where: S = Kendall'sSstatistic it = m niber of data pairs where: S = P-M where: P = 9 of increases X1 = #of decreases Large-sample approximation (S- 1) -q„ ifS>0 Z� = 0, ifS = 0 (S+ 1) -a„ fs> 0 where: S = P- M(as above) Us = (n118)x (n- 1 )x (2n+5) For the exact form of the test, T is compared to the probability, based on n and S, of no trend (e.g., T= 0).1 If T is further from 0 than expected, the conclusion is that there is a trend. The direction of that trend is indicated by S; a positive S indicates an increasing trend, a negative S indicates a decreasing trend. Helsel, D. R. and Hirsch, R. M., 1992,Statistical Methods in Water Resources, Appendix B,Table B, Elsevier, 10107.01 Lawrence&Associates V 1CLIENTSIDiammnd Pet Food.0010107hlonttarmgC01012nd Half 2010Waach B Stais docv