Errors and Uncertainties

Analytical chemists make a distinction between error and uncertainty Error is the difference between a single measurement or result and its true value. In other words, error is a measure of bias. As discussed earlier, error can be divided into determinate and indeterminate sources. Although we can correct for determinate error, the indeterminate portion of the error remains. Statistical significance testing, which is discussed later in this chapter, provides a way to determine whether a bias resulting from determinate error might be present. 

Pressure drop and heat transfer in a single-phase incompressible flow. According to conventional theory, continuum-based models for channels should apply as long as the Knudsen number is lower than 0.01. For air at atmospheric pressure, Kn is typically lower than 0.01 for channels with hydraulic diameters greater than 7 pm. From descriptions of much research, it is clear that there is a great amount of variation in the results that have been obtained. It was not clear whether the differences between measured and predicted values were due to determined phenomenon or due to errors and uncertainties in the reported data. The reasons why some experimental investigations of micro-channel flow and heat transfer have discrepancies between standard models and measurements will be discussed in the next chapters. 

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. 

General Approaches for Calculating Critical Loads of Heavy Metals Discussing the problems related to the critical load calculation, an attention should be paid to (i) selection of a receptor of concern, (ii) critical limits, (iii) possible calculation methods, (iv) the necessary input data and (v) the various sources of error and uncertainty (de Vries andBakker, 1998a, 1998b). 

Bais A. F. (1997) Spectrometers Operational errors and uncertainties, in C. S. Zerefos and A. F. Bais (eds,), Solar Ultraviolet Radiation Modelling, Measurements and Effects, NATO AS1 Series, Series 1 Global Environmental Change, Springer-Verlag, VoL 52, pp. 163-173. 

Accuracy (absence of systematic errors) and uncertainty (coefficient of variation or confidence interval) as caused by random errors and random variations in the procedure are the basic parameters to be considered when discussing analytical results. As stressed in the introduction, accuracy is of primary importance however, if the uncertainty in a result is too high, it cannot be used for any conclusion concerning, e.g. the quality of the environment or of food. An unacceptably high uncertainty renders the result useless. When evaluating the performance of an analytical technique, all basic principles of calibration, of elimination of sources of contamination and losses, and of correction for interferences should be followed (Prichard, 1995). 

The uncertainty associated with a traceable value must be related to a specified measurand (analyte) and be related to stated references. The following example illustrates the effect the choice of stated reference has on the stated uncertainty for the measurement of lead in milk. The uncertainty of a measurement of lead in milk, measured using a standard method, could be small, if stated relative to that standard method, where the measurand (analyte) is implicitly defined by the standard method. However, the method is likely to contain some additional errors and uncertainties if it were to be related to a primary method traceable to the SI, and these would need to be included in the estimate of uncertainty, if the SI was quoted as the stated reference. The interrelationship between uncertainty and... 

Where is the error on the ith reading and the expectation value of 1 is 0 and expectation value of e is a2. The values of x are taken to be Normally distributed with the mean p and the standard deviation cr. The values of p, and a are estimated from the actual readings. Thus although the analysis is carried out in terms of the random errors the data provides an estimate of <7 which is the uncertainty arising from random effects. This confusion between error and uncertainty is often added to by referring to cr as the standard error. In addition the statistical analysis is very rarely extended to include systematic errors. 

In principle, to carry out immersion microcalorimetry, one simply needs a powder, a liquid and a microcalorimeter. Nevertheless, it was early realized that the heat effects involved are small and the sources of errors and uncertainties numerous. Many attempts have been made to improve immersion microcalorimetric techniques. Before commenting on this type of experiment, we describe the equipment and procedure which has been found by Rouquerol and co-workers to be of particular value for energy of immersion measurements (Partyka et al., 1979). 

The most important parameter of each analytical result is its reUabUity. An analytical result is not a constant value each result has two properties, error and uncertainty. The sources of both these parameters have to be known and their values determined (estimated). 

There is a difference between measurement error and uncertainty. Measurement error is the difference between the determined and expected values, and uncertainty is a range into which the expected value may fall within a certain probability. Therefore, the uncertainty cannot be used to correct a measurement result. 

The values of errors and uncertainty strongly depend on the level of analyte content (concentration). High values of these parameters, unacceptable in the case of an analyte content at the percentage level, can be satisfying in the case of trace analysis. 

One of the most difficult tasks in day-to-day scientific activity is making reliable estimates of the errors and uncertainties in the data. How reliable are my data How accurate are the parameters calculated from them Can I, or should I, exclude particular models for explaining my data These are examples of the sort of questions that need to be asked. We have already discussed the question of judging how well... 

Measurements invariably involve errors and uncertainties. Only a few of these are due to mistakes on the part of the experimenter. More commonly, errors are caused by faulty calibrations or standardizations or random variations and uncertainties in results. Frequent calibrations, standardizations, and analyses of known samples can sometimes be used to lessen all but the random errors and uncertainties. In the limit, however, measurement errors are an inherent part of the quantized world in which we live. Because of this, it is impossible to peiform a chemical analysis that is totally free of errors or uncertainties. We can only hope to minimize errors and estimate their size with acceptable accuracy. In this and the next two chapters, we explore the nature of experimental errors and their effects on the results of chemical analyses. 

The errors and uncertainties of bioassay are becoming a more serious obstacle to progress as work extends (S2). Until biological assay can be dispensed with, it is therefore necessary to refine it as much as possible. A... 

Rabonovich, S.G., Measurement Errors and Uncertainties Theory and Practice, New York, Springer, 2000, 316. 

Here we discuss the concepts of error and uncertainty. In the world the word error implies a failure of some kind—synonyms include mistake, blunder, slip, and lapse. In metrology, error is defined as the result of a measurement minus a true value of the measurand and is free of such negative connotations. Error in an analysis is a particular value that may be known if the true value is given. 

Most of the commonly used models compute a cation/anion equivalent balance, but even this information is seldom translated into error for any subsequent calculation. No codes currently incorporate known analytical precision into evaluation of the error and uncertainty of speciation, saturation index, or mass transfer calculations. Future codes such as INTERP (Appendix) or the expert system of Pearson and others described in this volume, should include an optimization routine which would calculate the propagation of these reported errors, and compute bounding values that clearly define the magnitude of uncertainty. 

INTERP A menu-driven geochemical utility that provides an interpretive environment for geochemical codes. One selects from several models, views, edits and graphically displays results. Output is examined as elemental percentage distribution, saturation index, multi-window plots for Pitzer computations, and reaction path plots with overlays for error and uncertainty. 

A clear understanding of the limits of applicability of geochemical models and of the uncertainties and potential errors in the analytical and thermodynamic data is essential to the correct use of SOLMINEQ.88 and the interpretation of the results. These limits can be primarily divided into four different groups, which are errors and uncertainties in the physical parameters the chemical analysis and in the thermodynamic data and extrapolation of the equations and formulas beyond their range of applicability. 

GROUND-WATER SAMPLING RECOGNIZING AND CONTROLLING ERROR AND UNCERTAINTY... 

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