Precision of results

The precision of our enthalpy of mixing results were evaluated starting from the formula of propagation of errors described previously [8, 19], Tables 3.5.1 and 3.5.2 indicate the relative errors on the enthalpy of mixing for all the ternary investigated sections. 

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The correlation, agreement, and precision of results of the different commer-... 

Flow injection analysis is based on the injection of a liquid sample into a continuously flowing liquid carrier stream, where it is usually made to react to give reaction products that may be detected. FIA offers the possibility in an on-line manifold of sample handling including separation, preconcentration, masking and color reaction, and even microwave dissolution, all of which can be readily automated. The most common advantages of FIA include reduced manpower cost of laboratory operations, increased sample throughput, improved precision of results, reduced sample volumes, and the elimination of many interferences. Fully automated flow injection analysers are based on spectrophotometric detection but are readily adapted as sample preparation units for atomic spectrometric techniques. Flow injection as a sample introduction technique has been discussed previously, whereas here its full potential is briefly surveyed. In addition to a few books on FIA [168,169], several critical reviews of FIA methods for FAAS, GF AAS, and ICP-AES methods have been published [170,171]. 

X-ray fiber diffraction can be used to visualize highly hydrated polymer specimens at atomic resolution. An essential part of such an analysis is the inclusion of reliable stereochemical information to supplement the diffraction data. Structure determination involves modelling and refinement of putative structures, and adjudication amongst the optimized models. This technique has been successfully applied to a number of polysaccharides. The precision of resulting structures is often sufficient to identify the critical interactions within and between molecules, that are responsible for the unique properties of these materials. 

The participants reported high precision of results (intralaboratory repeatability of measurements). The and M data obtained in particular laboratories scattered less than 3%, often even in the range of 1%. This is an excellent result, indeed. Unfortunately, the high repeatability of measurements may lead to a notion that the results are also exact. 

Integration by these devices is clearly more accurate and precise than by manual measurements and precision of results is in the order of 0.5%. Peak identification algorithms approach the reliability of a trained operator. Concentrations are normally calculated by one of four standard calculation procedures. 

Once the preliminary error checking of the raw data has been done, the control samples should be separated from the normal samples for more detailed examination. This process of separation is greatly aided by the inclusion of the STD SAMP field in the field database (see earlier) and a comprehensive sample list that identifies control samples and their relationships (Fig. 5.3). Control sample results can then be subjected to a number of statistical and plotting procedures that determine the accuracy and precision of results. These processes give an indication of the levels of uncertainty that are associated with the results, information that is essential to interpret the data and present it in a meaningful manner. 

Repeatability, measurement precision under a set of repeatable conditions of measurement [3] precision of results obtained under the same measurement conditions (a given laboratory, analyst, measuring instrument, reagents, etc.). 

Intermediate precision precision of results obtained in a given laboratory over a long-term process of measuring. Intermediate precision is a more general notion (due to the possibility of changes in the greater number of determination parameters) than repeatability [3]. 

Reproducibility precision of results obtained by different analysts in different laboratories using a given measurement method [3]. 

The expansions in even powers of normal frequencies are of special interest, because they provide means for obtaining explicit relations between the equations of motion and the thermodynamic quantities, through the use of the method of moments The sum of over all the normal vibrations can be expressed as the trace, or the sum of all the diagonal elements, of a matrix H" obtained by multiplying the Hamiltonian matrix H of the system by itself (n — 1) times. Such expansions thus enable us to estimate the thermodynamic functions and their isotope effects from known force fields and structures without solving the secular equations, or alternatively, to estimate the force fields from experimental data on the thermodynamic quantities and their isotope effects. The expansions explicitly correlate the motions of particles with the thermodynamic quantities. They can also be used to evaluate analytically a characteristic temperature associated with the system, such as the cross-over temperature of an isotope exchange equilibrium. Such possible applications, however, are useful only if the expansion yields a sufficiently close approximation. The precision of results obtainable with orthogonal polynomial expansions will be explored later. 

Reliability of results is a function of precision (reproducibility) and accuracy (true value). The precision of results can easily be determined by internal measurement. The determination of accuracy in most cases, however, requires more detailed procedures such as the following ... 

Will POCT provide the required accuracy and precision of result Is there staff available to perform the test ... 

The technique improves the analysis for most metals in most sample solutions in terms of precision of results, ease of sample handling, less physical interference, higher sample throughput and versatility towards physical and chemical properties of reagents. The technique allows several elements to be measured at the same time using a simultaneous CCD. Disadvantages are loss of sensitivity compared with continuous nebulisation and may not be suitable where high salt contents are present in solutions. 

Optimization with the goal to maximize precision of results, to determine optimum assay conditions, and to assess the effect of changes on the assay requires a rigid statistical evaluation of the error structure of the assay. The approach of Ekins (1979) for RIA is valid for EIA as well and is based on rather simple concepts. Rodbard (1978) used a much more complex approach to analyze the error structure of EIA. 

There are other supports used in torsional braid (or perhaps, more strictly termed, supported dynamic mechanical) measurements. These include solid substrates (solids that are free of mechanical transitions under the testing conditions), which have been shown to improve the precision of results over those obtained using conventional glass braids (Wetton, 1986). However, these solid substrates generally require thick coatings. Also wire-mesh... 

Various analytical techniques for the determination of different levels of total iodine or iodine species in foodstuffs and related materials are presently available. They differ in principles, equipment needed, detection limits, reliability, i.e., accuracy and precision of results, the ease of performance, sample throughput, and analysis cost. The choice of the most appropriate method largely depends on the purpose of the analysis, e.g., whether it concerns routine monitoring and/or screening or whether delicate certification of a foodstuff reference material is to be carried out. Obviously, one of the decisive parameters is whether the method s detection limit is sufficiently low for the given purpose. For this reason, it appears useful to give the typical iodine levels in various foods to facilitate the choice of the appropriate method(s). Table 2.5 lists the average iodine content of foods (fresh and dry basis), which was adapted from the data reported by Koutras et al. (1985). 

Partly because of the complexity of the sample and problems relating to specificity, few standards are available. An expanding number of pertinent Standard Reference Materials is becoming available from the National Bureau of Standards. Even when available, cost dictates that these be used only to calibrate other reference materials. The latter include so-called standards purchased from reagent suppliers and control samples that are frequently derived from a carefully stored pool of blood samples. The precision of results can be assured by good instruments,... 

Day-to-day consistency and precision of results Data reliability and accuracy of results Potential errors... 

It is worth noting that within the PI implementation, we are mainly interested in evaluating the trace of the density matrix, as it is directly related to the partition function. Also when using the primitive approximation, we neglect terms that are of the order x. To improve the precision of results in MC simulations and to achieve faster convergence as P increases, higher order corrections (or propagators of the density matrix) have been developed. 

The tantalum boat atomization technique provides very low detection limits coupled with small sample size. The reproducibility of the sample size is apparently the limiting factor on precision of results. Figure 10-25 shows results obtained on replications of zinc samples. Relative standard deviations of between 2.8 and 3.4% were obtained for zinc concentrations between 1 X 10 and 5 x 10 g. Some typical absolute detection limits with the tantalum boat systems are given in Table 10-4. They range from 10 to... 

Two groups of values are presented obtained from isothermal saturation and potentiometric results. The precision of results from isothermal saturation is worse. The potentiometric results should give lower values than isothermal saturation because it includes molecular oxide concentration. Figure 21.3.1 shows that results have opposite trend to [21.3.10]. 

The differentiation between sources of lead organometallic compounds was recently accomplished using quadrupole ICP-MS. The measurement of lead isotope ratios by GC-ICP-MS of organolead standards allowed the differentiation between lead sources. The excellent precision of results obtained using a multicollector ICP-MS for lead isotope ratio... 

The CV or RSD, the units of which are obviously per cent, is an example of a relative error, i.e. an error estimate divided by an estimate of the absolute value of the measured quantity. Relative errors are frequently used in the comparison of the precision of results which have different units or magnitudes, and are again important in calculations of error propagation. 

Assume that c is the true value of some analytical quantity to be determined. For a given measurement series as in Example 2.1. the error is Lf-cl. We already know that x-> E(x) for A->- 00. In the ideal case, where there is no bias, E(x) = c hence, the error will become zero with increasing sample size. Otherwise, the determination has some bias i (.v) - c >0. and the error can only be reduced to the value of this bias. A statistical test for presence of bias is discussed in Section 3.3.2. The concept of precision refers to the scattering of measurements and is given by the (empirical) standard deviation of a measurement series. As long as precision refers to the results of a. single laboratory, it is identified with the concept of repeatability. Precision of results provided by different laboratories is identified with the concept of reproducibility. For a quantification of both concepts, see Chapter 3.4. 

Another point to be respected in measurement design is the precision of results. As an example, consider the objective function representing mean square error of the result... 

Much more difficult is the situation in the case of a nonlinear objective function of the type (12.2.3). Numerous case studies have shown that the optimum solution according to the objective function (12.2.2), i.e. optimisation as the cost of the measurement concerns, yields a solution that is unacceptable from the point of view of the precision of results. It means that the solution with minimum costs is, at the same time, the solution with some unmeasured quantities that are theoretically observable, but with unacceptably low precision (for example, the confidence interval wider than the value of the quantity). In this case, the following optimisation method can be recommended. The method is analogous to the direct search in graphs that proved efficient for optimisation of measurement designs in single-component mass balancing see Subsection 12.1.2. 

For optimization of the spike addition, it is necessary to know the approximate element concentration in the sample. As the precision of results is not significantly influenced over a wide range of analyte to spike mixing ratios, preanalysis via a semiquantitative method is typically sufficient. If the expected amount of analyte is very low, it can also be advantageous to work with a distinct excess of spike to make chemical isolation of the isotope-diluted sample easier. This means that conditions to the left of the minimum in Figures 8.5 and 8.6 are used. Under extreme conditions of analyte to spike ratio, not only the enhanced error multiplication factor has to be taken into account, but also the deteriorating... 

The precision of the spectral data is usually more reliable than that of the results obtained by prediction of constituents in the check samples because the results are susceptible to the error of the calibration models. Table 7.1.12 compares the precision of results for prediction of constituents in check samples of some commodities with that of spectral data (average taken at 5 wavelength points). 

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