# Statistics for Environmental Engineers

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One weakness of the usual definitions of the MDL is that it is defined for a single analyst. ASTM D2777 (1988) is very clear that instead of repeated single-operator MDLs, the correct approach is to use the interlaboratory standard deviation from round-robin studies. This can change the MDL by a factor of 0.5 to 3.0 (Maddelone et al., 1988, 1991, 1993).

The MDL is based directly on an estimate of the variance of the measurement error at low concentrations. This quantity is not easy to estimate, which means that the MDL is not a well-known, fixed value. Different chemists and different laboratories working from the same specimens will estimate different MDLs. A result that is declared <MDL can come from a sample that has a concentration actually greater than the MDL.

What are the implications of the MDL on judging violations? Suppose that a standard is considered to be met as long as all samples analyzed are “non-detect” By the EPA’s definition, if truly blank specimens were analyzed, the odds of a hit above the MDL on one particular specimen is 1%. As more specimens are analyzed, the collective odds of getting a hit increase. If, for example, a blank is analyzed every day for one month, the probability of having at least one blank declared above the MDL is about 25% and there is a 3% chance of having two above the MDL. Analyze blanks for 90 days and the odds of having at least one hit are 60% and the odds of having two hits is 16%. Koorse (1989, 1990) discusses some legal implications of the MDL.

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