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Diamond Pet Food Processors of Ripon California,LLC January 31,2013 <br /> Attachment D Page I o 2 <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-(n x(n-I) :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 - #of increases <br /> M #of decreases <br /> Large-sample approximation <br /> (S-1) =6„ ifS> 0 <br /> Zs = 01 if S= 0 <br /> (S+ 1) Cr. ifS> 0 <br /> where: <br /> S - P-M(as above) <br /> 6s = (n118)x(n-1)x(2n+5) <br /> For the exact form of the test, ti is compared to the probability,based on n and S, of no <br /> trend (e.g., ti=0).1 If ti 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 /> 10107.03 Lawrence&Associates <br /> WA CLIENTSIDiamond Pet Foods W 1010 7.01-Groundwater MoniloringlGroundwater Monitaringt2012l4Q2012 L4ttach D Stats.docx <br />