Statistics for Environmental Engineers

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4.    The EPA’s MDL gives some information about the precision of measurements at low concentrations, but it says nothing about bias, which can be a major problem. Pallesen’s model distinguishes between error contributions from the analytical method and from background noise. It also retains the average values, which could be compared with the known concentrations to make an assessment of bias.

Calibration Designs

Another way to estimate MDLs is to use a calibration design (Gibbons, 1994). A series of samples are spiked at known concentrations in the expected range of the MDL. Prediction limits (or tolerance limits in some methods) are determined for the very low concentrations and these define a limit of detection. Frequently, calibration data have nonconstant variance over a range of concentrations. If this is the case, then weighted least squares must be used to fit the calibration curve or else the variability is overestimated at low concentrations and the detection limit will be overestimated. Zorn et al. (1997) explain how this is done. Calibration is discussed in Chapter 37 and weighted least squares is discussed in Chapter 38.


The limit of detection is a troublesome concept. It causes difficulties for the chemist who must determine its value, for the analyst who must work with data that are censored by being reported as < MDL, and for the regulator and discharger who must make important decisions with incomplete information. Some statisticians and scientists think we would do better without it (Rhodes, 1981; Gilbert,1987). Nevertheless, it is an idea that seems firmly fixed in environmental measurement methods, so we need to understand what it is and what it is not. It is an attempt to prevent deciding that a blank sample is contaminated with an analyte.

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