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i WISCONSIN ADMINISTRATIVE CODE 134 Unofficial Text(See Printed Volume}. Current through date and Register shown on Title Page. ' Continue for the remaining rows.Stam each row and enter result at the end of the row. Add the sum of each row down i to obtain the Mann-Kendall Statistic(S). See Table A as an example. ' Table A Mann-Kendall Statistic Sampling Sampling Sampling Sampling Sampling r I Event I Event 2 Event 3 Event 4 Event 5 Contaminant concentra- Sum Rows tion-; 1 100 50 85 75 50 Compare to Evart I -> -1 -1 -1 -1 -4 Compares to Event 2 —> +1 +1 0 +2 Compare to Event 3 -1 -I -2 Compare to Event 4 -I ' Mann Kendall Statistic(Total) -5 b. Manual Mann-Kendall Statistic Look up Table. Table B gives the maximum S statistic(S }to accept a declining , trend alternative at an a level of significance. If the eanputod S is greater than S,.(or S is a smaller negative number than Ste),then there is either a no-trend or an increasing trend in the data. Table B ' Mann-Kendall Statistic Look Up Table S. N Range of S a =0.2• 4 -6to+6 -4 5 - 10 to+ 10 -5 6 - 15 to+15 -6 7 -21 to+21 -7 8 -28 to+28 -8 9 -36 to+36 -10 10 -45 to+45 -11 ' The prvbsWity that the computed Mann-Kcadall sta istic S 5 S, is at most a. 5. Test for a declining trend. Evaluate data treads for each contanumant identified in the plume. Evaluate the null hypothe- sis of no trend against the altawtive of a decreasing trend. The null hypothesis can be rejected in favor of a decreasing , tread if both of the following conditions are met: a. S is a large negative number(see Table B for magnitude of S) ' b. The probability value,given n(number of data)and the absolute value of S.is LESS than the a priori significance level,oc of the test. An a:5 0.2 is acceptable. 6. Test for an increasing trend. An increasing trend alternative(i.e.,an advancing plume)is shown if both of the following conditions are mct: a. S is positive. b. S?I S.I at a given a level of significance(see Table 8). If the computed S is equal to or greater than the absolute ' value of S,..,then it can be concluded the plume is advancing at an a level of significance. An a S 0.2 is acceptable for this test. ' 7. Test for Plume Stability.If the Mann-Kendall Test indicates no-trend is present,perforin the coefficient of variation test. As a non-parametric test,the Mann-Kendall Test docs not take into account the magnitude of scatter in the data. A data set with a great deal of scatter may return a Mann-Kendall test indicating there is no trend,when,in fact,no conclusion can be drawn regarding trend because of data variability. In this case,additional data collection may be nc=sary to deter- mine that the plume is stable,declining or advancing. As a simple test,the coefficient of variation can assess the scatter in the data: Reeisier.January.2401.No.541 ' I i