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<br />7. Outliers--Outliers are data points which depart significantly from <br />the trend of the balance of the data. The retention, modification, or delet- <br />ion of these outliers will significantly affect the statistical parameters <br />computed from the data. All procedures for treating outliers ultimately <br />require judgment involving both mathematical and hydrologic considerations. <br />The recommended use of a generalized skew coefficient tends to reduce the <br />adverse effect of outliers. The treatment of high and low outliers is des- <br />cribed separately. If the station skew is positive, high outliers are con- <br />sidered first. If station skew is negative, low outliers are considered <br />first, and if station skew is near zero, both high and low outliers should <br />be considered simultaneously. <br />If a peak is considered a high outlier, a comparison with historical <br />flood data and flood information at nearby sites should be made. With this <br />information a plotting position is assigned to each outlier and it is then <br />treated as a historic flood peak using procedures described later in this <br />guide. The specific treatment used to handle outliers should become a matter <br />of record. If it is not possible to assign a revised plotting position to <br />the outlier, it is retained in the basic computations as is. <br />The existence of low outliers is to be judged using the following <br />relationship as a criterion: <br />(Xn-X)/S I > [2.5 + 1.2 log (N/10)] (1 - O.4G) (5) <br /> <br />in which <br /> <br />Xn = the logarithm of the lowest value (values) <br />in sample of N items <br />X = mean logarithm of all the data <br />G = generalized skew coefficient <br />... S = standard deviation of logarithm of all the data <br />When used to test for low outliers in a record adjusted for historic infor- <br />mation substitute H, M and S for N, X and S. When the criterion is true, ... <br />i.e.. I (Xn-X)/S I is greater than the expression on the right, then the <br />observation Xn is considered a low outlier. This test is applied to one <br />or more of the smallest values of the systematic flood record. Use of this <br />relationship is equivalent to rejection at the 1 percent level of signifi- <br />cance (one-sided), When one or more low outliers are identified, they <br />are deleted from the record and the remaining record should be treated <br />16 <br />