Reference method error

Ghlorophenol Analysis. The chlorophenols can be analy2ed by acidimetric titration of the hydroxyl function (50). This overall method yields only an approximate evaluation for mixtures. To analy2e chlorophenol mixtures, gas chromatography has been the reference method used, as it made it possible to separate and quantify the various chlorophenols (51), but this technique can be a source of errors the gem-chlotinated cyclohexadienones that may be present along with the chlorophenols are broken back down iato lighter chlorophenols under the analysis conditions usually employed. 

Table III displays VEDEs obtained with the Brueckner-reference methods discussed in Section 5.2 and augmented, correlation-consistent, triple- basis sets [41]. AEDEs include zero-point energy differences and relaxation energies pertaining to geometrical relaxation on the neutral s potential energy surface. The average absolute error with respect to experiment is 0.05 eV [26].

The Brueckner-reference method discussed in Section 5.2 and the cc-pvqz basis set without g functions were applied to the vertical ionization energies of ozone [27]. Errors in the results of Table IV lie between 0.07 and 0.17 eV pole strengths (P) displayed beside the ionization energies are approximately equal to 0.9. Examination of cluster amplitudes amd elements of U vectors for each ionization energy reveals the reasons for the success of the present calculations. The cluster operator amplitude for the double excitation to 2bj from la is approximately 0.19. For each final state, the most important operator pertains to an occupied spin-orbital in the reference determinant, but there are significant coefficients for 2h-p operators. For the A2 case, a balanced description of ground state correlation requires inclusion of a 2p-h operator as well. The 2bi orbital s creation or annihilation operator is present in each of the 2h-p and 2p-h operators listed in Table IV. Pole strengths are approximately equal to the square of the principal h operator coefiScient and contributions by other h operators are relatively small. 

In the wine industry, FTIR has become a useful technique for rapid analysis of industrial-grade glycerol adulteration, polymeric mannose, organic acids, and varietal authenticity. Urbano Cuadrado et al. (2005) studied the applicability of spectroscopic techniques in the near- and mid-infrared frequencies to determine multiple wine parameters alcoholic degree, volumic mass, total acidity, total polyphenol index, glycerol, and total sulfur dioxide in a much more efficient approach than standard and reference methods in terms of time, reagent, and operation errors. 

A reference method is defined as a method of known and proven accuracy, thoroughly validated, and experimentally demonstrated to have negligible systematic errors and a high level of precision. Its development involves removing the principal systematic errors of the process, reducing them to tolerable levels, or when actual... 

There are many variations of this method. To illustrate the procedure, a variation developed by Rosenbrock will be discussed. It is one of the best optimization methods known8,7 when there is no experimental error. The method is also very useful for determining constants in kinetic and thermodynamic equations that are highly nonlinear. An example of this type of application is given in reference 9. 

The second possibility is called cross-validation. The test samples are measured by a reference method. Howevep the reference method cannot provide true values because measurement error occurs here as well. Nevertheless, well-characterized methods can provide generally accepted values, which are then compared to the ones obtained using the test calibration. Note that this comparison must be done using particularly suited regression methods, because the error for both methods will be in the same order of magnitude. Especially, cross-validation of CE and HPLC has been frequently reported. 

Figure 4 Errors in potential energies for CH4 in a 6-3IG basis using multi-reference methods. (Data from reference 14.)...

In order to construct a calibration model, the values of the parameters to be determined must be obtained by using a reference method. The optimum choice of reference method will be that providing the highest possible accuracy and precision. The quality of the results obtained with a multivariate calibration model can never exceed that of the method used to obtain the reference values, so the choice should be carefully made as the quality of the model will affect every subsequent prediction. The averaging of random errors inherent in regression methods can help construct models with a higher precision than the reference method. 

To invesigate whether run order influenced the results for this example, the compOBHit A concentration residuals are plotted versus the order in which the aeference values for component A were measured (Figure 5.17). The first sai Ie is the one with the unusually hi error, which may indicate problems wih the startup of the instrument used to determine the reference concentraticffi of component A. What appears to be a nonrandom pattern over time may innate instrumental fluctuations in the reference method determination. 

When the model is performing well, the RMSEP should be comparable to the known error in the concentration reference method. 

Root Mea Square Error of Prediction (RMSEP) (Model Diagnostic) The RMSEP values for all four components are numerically summarized in Table 5.6. They are large owing to the bias in the predictions. Several reasons for this bias can be proposed, including an inaccurate reference method, transcription errcKS, poor experimental procedures, changes in densiw and/or pathlength, l t scatter in the instrument or sample, chemical interactions,... 

A second possibility is described in reference [34]. It consists of summing all SSx values for which the %SSx value (see Table 3.19) is smaller than 5% to make an approximation of 5 5 error- The method assumes that these sums of squares come from effects that are negligible. The 5% value is an arbitrary value. The number of degrees of freedom is also equal to the sum of the dfx- The values for MSx od Fx are then calculated analogous to... 

As would be expected, in order to be able to have at least 95% confidence that the true CV p does not exceed its target level, we must suffer the penalty of sometimes falsely accepting a "bad" method (i.e. one whose true CV p is unsatisfactory). Such decision errors, referred to as "type-1 errors", occur randomly but have a controlled long-term frequency of less than 5% of the cases. (The 5% probability of type-1 error is by definition the complement of the confidence level.) The upper confidence limit on CV p is below the target level when the method is judged acceptable... 

Despite the fact that near infrared spectroscopy (NIR) has been used industrially for decades [36], there has been hesitance to accept and trust new process analytical measurement technologies as equivalent or superior to traditional methods. For example, when a discrepancy between online NIR and laboratory analyses is observed, it is rare that the destructive reference methods are ever targeted as the source of error, despite the fact that NIR is often the more precise method. The hesitance to trust more advanced, multivariate tools (which are perhaps less directly understood) has certainly been a detriment to progress in deploying PAT. 

The roles of method validation in the achievement of reliable results are (1) to include all possible effects or factors of influence on the final result, (2) to make them traceable to stated references [reference methods, reference materials, or International System of Units (SI)], and (3) to know the uncertainties associated with each of these effects and with the references. Validation is thus a tool to establish traceability to these references [2,4]. In this context, it is important to see the difference between traceability and accuracy. A method which is accurate, in terms of true (i.e., approximating the true value), is always traceable to what is considered to be the true value. The opposite however is not correct. A method that is traceable to a stated reference is not necessarely true (accurate). Errors can still occur in this method, depending on the reference [12]. 

We may note a number of features of these results. First, nondynamical correlation is known to be much more important in the singlet state than in the triplet. Hence it is not surprising that the multireference methods perform better here than the single reference methods. Nevertheless, the errors in the single reference meth-... 

These standard methods are outlined below but for a critical understanding of the problems of operation and likely errors reference should be made to, for example, the review by Lomax1 2. 

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