Statistics for Environmental Engineers

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TABLE 14.3

 Pb Added У 2 ( iUg/L) S, 0 2.73 0.38 1.25 3.07 0.55 2.5 4.16 0.41 5.0 5.08 0.70 10.0 11.46 2.42

parameter values are &l =0.267 and К = 0.016. These give &b =0.52 and к = 0.13. The MDL = 3.0&b = 3(0.52) = 1.56. This should be rounded to 1.6 jig /L.

The EPA method gave MDL = 1.7 lg/L. Pallesen’s method gave MDL = 1.6 lg/L. The difference has no practical importance, despite the following differences in the two methods.

1. The z or t statistic multipliers are different: z„=001 = 2.33 for the EPA method and za= 00013 = 3.00 for the Pallesen method. On purely statistical grounds, the EPA’s specification of a = 0.01 is no more justified than Pallesen’s recommended multiplier of 3.00.

2.    Users of the EPA method will often estimate the MDL using seven, or perhaps fourteen, replicate measurements because the procedure requires a minimum of seven replicates. In Example 14.2, the MDL (EPA method) for Laboratory B was based on 34 measurements. Pallesen’s method requires replicated measurements at several concentration levels (how many levels or replicates are not specified). The case study used 50 measured values, divided among five concentration levels. Each of these values contributes to the estimation of the MDL.

3.    The EPA method estimates the MDL from measurements in a given matrix containing the analyte and then assumes that the background noise observed is applicable to specimens that are blank (zero concentration). The alternate method extrapolates to zero analyte concentration to estimate the background noise (ob) that serves as the basis for computing the MDL. As shown in Table 14.3, the total error variance increases as the concentration increases and Pallesen’s method accounts for this property of the data. If the data have this property, the EPA approach of pooling replicates from two different concentrations will tend to inflate the MDL over the estimate of the alternate method.

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