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Diamond Pet Food&Ripon Cogeneration January 31,2016 <br /> Attachment Pase I oft <br /> METHODS <br /> The Mann-Kendall test was used for the statistical analysis. The Mann-Kendall test is a <br /> test for whether concentrations tend to increase or decrease with time. The Mann- <br /> Kendall test is a variant of Kendall's tau test, a nonparametric, rank-based procedure. <br /> Because the Mann-Kendall/Kendall's tau tests use ranks of data, not actual data values, <br /> these tests are resistant to the effects of nonnormal data distribution and small numbers of <br /> unusual values (outliers), and can be used even when there are censored values (values <br /> less than the detection limit). These tests also measure both linear and nonlinear trends, <br /> as long as those trends are monotonic (e.g.,x increases as y increases). <br /> The Mann-Kendall test is conducted by first ordering the data pairs (date, concentration) <br /> sequentially by date. If a positive correlation exists (generally increasing trend), the <br /> concentrations will increase more often than decrease, as time progresses. If a negative <br /> correlation exists (generally decreasing trend), the concentrations will decrease more <br /> often than increase, as time progresses. If there is no trend, concentrations will increase <br /> and decrease about equally over time. <br /> The number of increases and decreases are counted by comparing each concentration to <br /> all successive concentrations. The test statistic is then computed by either the exact form <br /> (number of pairs < 10) or the large-sample approximation(number of pairs > 10): <br /> Exact form <br /> T = S=(nx(n-1) :2) <br /> where: <br /> S = Kendall's S statistic <br /> n = number of data pairs <br /> where: <br /> S = P-M <br /> where: <br /> P = #ofincreases <br /> M = #of decreases <br /> Large-sample approximation <br /> (S-1) =6s, ifS> 0 <br /> Zs = 01ifS= 0 <br /> (S+ 1) =6s, ifS> 0 <br /> where: <br /> S = P-M(as above) <br /> 6s = (n/18)x(n-1)x(2n+5) <br /> For the exact form of the test, i is compared to the probability, based on n and S, of no <br /> trend(e.g., i = 0).1 If i is further from 0 than expected, the conclusion is that there is a <br /> trend. The direction of that trend is indicated by S; a positive S indicates an increasing <br /> trend, a negative S indicates a decreasing trend. <br /> ' Helsel,D.R.and Hirsch,R.M., 1992,Statistical Methods in Water Resources,Appendix B,Table B, <br /> Elsevier. <br /> 010107.07 Task 4 Lawrence&Associates <br /> W.ICLIENTSIDiamond Pet Foods 1010107.01-Groundwater MonitoringlGroundwater Monitoring12016WQAnnual 201612016 Stats text.docx <br />