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I 133 NIL Unofficial Te:t(See Printed Volume). Current through date and Register shown ou Title Page, Chapter NR 746 I ' APPENDIX A Nonparametric Statistical Tests for Determining the Effectiveness of Natural Attenuation i Two nonparametric statistical tests are described here:the Mann-Kendall(S)and Mann-Whitney(U)statistical tests. These tests can be i sed to show whether groundwater contaminant concentrations in a monitoring well are increasing, stable or decreasing. However,neither test is able to determine the rate in which the concentrations are changing over time. The Mann4Cendall Test can be used with a minimum of 4 rounds of sampling results;however,the Mann-Kendall Test is not valid for data that exhibit seasonal behavior The Mann-Whitney U Test is applicabld to data that may or may not ' exhibit seasonal behavior,but the test requires 8 consecutive rounds of quarterly or semi-annual sampling results. To dem- onstrate that natural attenuation is effective,the chosen statistical test must show decreasing contaminant concentrations at an appropriate confidence level,given in the test methodologies that follow. ' Mahn-Kendall Test 1. Assemble well data for at least 4 sampling events for each contaminant in the order in which the data was collected. j Include all contaminants that have exceeded the ES at one or more monitoring wells. Include data from: a. One or more contaminated monitoring wells hear the downgradient plume margin,which may include piezome- ters, j b. A monitoring well near the source zone,and c. At least one monitoring well along a flow line between the source zone well and plume margin well. 2. For purposes of the Macm-Kendall test,all non-detect data values should be assigned a single value that is less than the detection limit,even if the detection limit varies over time. 3. Tests for Seasonality in Data. For seasonally affected data,either remove the seasonality in the data(e.g.,by only testing data from the seasons with the highest contaminant concentrations)or use a statistical test that is unaffected by seasonality, such as the Mann-Whitney U Test. To test for data seasonality: ' a. Determine if groundwater flow direction changes with season by comparing a water table map frorn each season that the contaminant concentrations are measured. If the flow direction changes from one sampling period to another and shifts the plume away from the weds being used in the statistical test,then data from those seasons that are shifted ' away from the centerline monitoring wells can not be used in the Manz-Kendall Test. b. Determine if groundwater elevation and contaminant concentration change seasonally. plot contaminant con- centration versus groundwater level for each well to be assessed by the'Manz-Kendall Test. If groundwater con- centrations change as water level changes,then the data is seasonally affected. The seasons with the highest contami- nant concentrations should be included in the Mann-Kendal!Test. 4. Calculate the Mann-Kendall Statistic(S)using a manual method or a DNR supplied spreadsheet. Assess all conta ni- ' nants in the plume for the selected wells being assessed with the Mann--Kendall Test. Enter data for each contaminant in the order it was collected. a. Manual Method to Calculate Mann-Kendall Statistic. Compare data sequentially,comparing sampling event I to sampling events 2 through n,then sampling event 2 to sampling events 3 through n,etc. Each row is filled in with a 1,0 or-1,as follows: Along row 2,if: - Concentration of event xi>event 1: Enter+I - Concentration of event xi=event 1: Enter 0 - Concentration of event xi¢event 1: Enter- I Where: n=total number of sampling events xi=value of given sample event,with i=2 to n Register,January,2001,No.54t j