Statistics for Environmental Engineers

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1.25 p.gl’L


2.50 ^g/L


3.07


4.16


2


s


0.55


0.41


s


0.74


0.64


n


20


14

Pooling the sample variances yields:


2


spooled



19(0.55) -I- 13(0.41) 19 -I- 13



0.49


Spooled = 0.70 jlg/L


The appropriate t statistic is t32,0.01 = 2.457 and MDL = 2.457spooled = 2.457 (0.70) = 1.7^g/L .

An Alternate Model for the MDL


The purpose of giving an alternate model is to explain the sources of variation that affect the measurements used to calculate the MDL. Certified laboratories are obliged to follow EPA-approved methods, and this is not an officially accepted alternative.


Pallesen (1985) defined the limit of detection as “the smallest value of analyte that can be reliably detected above the random background noise present in the analysis of blanks.” The MDL is defined in terms of the background noise of the analytical procedure for the matrix being analyzed. The variance of the analytical error and background noise are considered separately. Also, the variance of the analytical error can increase as the analyte concentration increases.


The error structure in the range where limit of detection considerations are relevant is assumed to be:


У, =П + e, = П + a, + bi


The a, and b, are two kinds of random error that affect the measurements. a, is random analytical error and bi is background noise. The total random error is the sum of these two component errors: ei = a, + b,. Both errors are assumed to be randomly and normally distributed with mean zero.

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