Analytical methods basic error model

Figure 14-7 Outline of basic error model for measurements by a field method. Upper part The distribution of repeated measurements of the same sample, representing a normal distribution around the target value (vertical line) of the sample with a dispersion corresponding to the analytical standard deviation, Oa- Middle part Schematic outline of the dispersion of target value deviations from the respective true values for a population of patient samples, A distribution of an arbitrary form is displayed.The vertical line indicates the mean of the distribution. Lower part The distance from zero to the mean of the target value deviations from the true values represents the mean bias of the method.

As probabilistic exposure and risk assessment methods are developed and become more frequently used for environmental fate and effects assessment, OPP increasingly needs distributions of environmental fate values rather than single point estimates, and quantitation of error and uncertainty in measurements. Probabilistic models currently being developed by the OPP require distributions of environmental fate and effects parameters either by measurement, extrapolation or a combination of the two. The models predictions will allow regulators to base decisions on the likelihood and magnitude of exposure and effects for a range of conditions which vary both spatially and temporally, rather than in a specific environment under static conditions. This increased need for basic data on environmental fate may increase data collection and drive development of less costly and more precise analytical methods. 

NIR models are validated in order to ensure quality in the analytical results obtained in applying the method developed to samples independent of those used in the calibration process. Although constructing the model involves the use of validation techniques that allow some basic characteristics of the model to be established, a set of samples not employed in the calibration process is required for prediction in order to conhrm the goodness of the model. Such samples can be selected from the initial set, and should possess the same properties as those in the calibration set. The quality of the results is assessed in terms of parameters such as the relative standard error of prediction (RSEP) or the root mean square error of prediction (RMSEP). 

A straight-line model is the most used, but also the most misused, model in analytical chemistry. The analytical chemist should check five basic assumptions during method validation before deciding whether to use a straight-line regression model for calibration purposes. These five assumptions are described in detail by MacTaggart and Farwell [6] and basically are linearity, error-free independent variable, random and homogeneous error, uncorrelated errors, and normal distribution of the error. The evaluation of these assumptions and the remedial actions are discussed hereafter. 

Another method more intuitively understandable is the fitting in the time domain. Obviously in the cases when it is possible to obtain an analytical solution for the basic equations to describe a model, the comparison with the response curve is easily made. When a numerical solution is to be employed, the effect of each parameter on the calculated concentration curve cannot be easily visualized so the comparison needs repeated calculations for optimum parameter search. Anderssen and White (1970) introduced the error map method to show the deviation of the calculated curves and the response curves, which was later utilized by Wakao et al. (1979, 1981). 

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