Uncertainty pure error

Most textbooks refer to as the variance due to pure error , or the pure error variance . In this textbook, is called the variance due to purely experimental uncertainty , or the purely experimental uncertainty variance . What assumptions might underlie each of these systems of naming See Problem 6.14. [See, also, pages 123-127 in Mandel (1964).]... 

The book has been written around a framework of linear models and matrix least squares. Because we authors are so often involved in the measurement aspects of investigations, we have a special fondness for the estimation of purely experimental uncertainty. The text reflects this prejudice. We also prefer the term purely experimental uncertainty rather than the traditional pure error , for reasons we as analytical chemists believe should be obvious. 

Abundances of lUPAC (the International Union of Pure and Applied Chemistry). Their most recent recommendations are tabulated on the inside front fly sheet. From this it is clear that there is still a wide variation in the reliability of the data. The most accurately quoted value is that for fluorine which is known to better than I part in 38 million the least accurate is for boron (1 part in 1500, i.e. 7 parts in [O ). Apart from boron all values are reliable to better than 5 parts in [O and the majority arc reliable to better than I part in 10. For some elements (such as boron) the rather large uncertainty arises not because of experimental error, since the use of mass-spcctrometric measurements has yielded results of very high precision, but because the natural variation in the relative abundance of the 2 isotopes °B and "B results in a range of values of at least 0.003 about the quoted value of 10.811. By contrast, there is no known variation in isotopic abundances for elements such as selenium and osmium, but calibrated mass-spcctrometric data are not available, and the existence of 6 and 7 stable isotopes respectively for these elements makes high precision difficult to obtain they are thus prime candidates for improvement. 

The statistical prediction error is in concentration units and represents the uncertainty in the predicted concentrations due to deviations from the model assumptions, measurement noise, and degree of overlap of the pure spectra. As the system deviates from the underlying assumptions of CLS, the residual... 

Similarly, Thurmond (150) and Arthur (151) found that the interaction coefficients obtained from a fit of the experimental liquidus or vapor pressure in the arsenide and phosphide systems did not produce the same temperature dependence. Panish et al. (142, 154) pointed out that these discrepancies may be due to (1) errors resulting from the assumed values for AH/j and the approximation ACp[ij] = 0 in 0, (2) deviations from simple-solution behavior, or (3) uncertainties in the interpretation of the vapor pressure data, because some of the quantities necessary in the calculations are not accurately known (e.g., reference-state vapor pressures for pure liquid As and P). Knobloch et al. (184, 185) and Peuschel et al. (186, 187) have obtained excellent agreement between calculated and experimental activities and vapor pressures with the use of Krupkowski s asymmetrical formalism for activity coefficients, whereas Ilegems et al. (Ill) demonstrated that satisfactory agreement between liquidus and vapor pressure measurements exists when an accurate expression for the liquidus is used. 

There is general agreement that an artefact for the realisation of the unit mole as the top of the traceability chain is not needed/rational. However, there is a large variety of opinions on the nature of the link to the SI. They range from primary methods through pure elements to commercial substances. Often we hear objections that the uncertainty at this level is negligible compared to that in routine measurements, so that work at this level is unimportant. This is usually true for trace constituents, but for analysis of major or minor components standards may be a significant source of error. 

FIGURE 16.14 MFFS data for the PS flame retarded formulations measured in the RPA. The error bars represent a standard uncertainty of +lo. The data points labeled with a single number are the pure APP/PER (3 1) in PS, where the number refers to the mass fraction (%) of APP/PER. All two number labels (X-Y) refer to the mass fraction (%) of APP/PER (X) and organoclay (Y) in the APP/PER-15A-PS blends. 

It may be argued that if the actual extent of enantiomeric contamination of a CDA is known accurately, the reagent may be safely used, because the appropriate correction in diastereomeric peak ratios can be made. An objection (5) to this argument is that if the enantiomerically impure CDA is present in excess, differences, if any, between the CDA enantiomers in their reaction rates with the analyte enantiomers (i.e., diastereoselective kinetics) will stUl result in an error in the determination of the enantiomeric ratio. In practice, however, such kinetic differences are usually negligible. A more precise but cumbersome solution to this problem is to separate the four stereoisomeric derivatives using chiral chromatographic conditions, for example, a chiral stationary phase. Under such conditions, four distinct peaks are obtainable as a matter of principle (whether the four stereoisomers are actuaUy resolved depends, of course, on the chromatographic conditions chosen). A review of the literature indicates that small (1-2%) enantiomeric contamination of a CDA may not necessarily render the CDA useless in many applications. It is clear, nevertheless, that the CDA used should be enantiomerically pure whenever possible. This simplifies the analysis and eliminates any uncertainty associated with enantiomeric contamination. There is, in fact, an application in which enantiomerically impure CDAs cannot be used safely the determination of trace enantiomeric impurity in an analyte. If the CDA used is itself enantiomerically contaminated, the accurate determination of the extent of trace enantiomeric contamination of the analyte may be difficult if not impossible. 

The kinetic parameters for the n order kinetic model have been obtained using these definitions of reactivity for the pure steam gasification experiments of birch. All the activation energies lie between 228-238 kJ/mol and the reaction orders between 0.54 and 0.58, apart from definition 3. The frequency factors are somewhat more scattered, lying between 5-10 and 3-10 . Regarding the uncertainty of the calculation, definitions 2, 5 and 4 seem to give more precise results and it is interesting to notice that the error of the reaction order calculation does not depend on how a representative reactivity value is defined. 

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