Presentation of Analytical Results

If it can be supposed that the measured values, y, obtained in the course of the analytical process, are both precise and accurate, then the analytical results, x, do not have automatically the same quality. For this, some preconditions must be fulfilled, namely 

It is in the nature of people to present results - whatever kind - with the highest possible precision. From this point of view it seems to be unnatural and absurd to collect facts which may decrease the precision and, therefore, the quality of the measured data. However, that is asked of the analyst, not only for the sake of truthfulness but also for responsible comparisons of analytical results with reference values, as will be shown in Sect. 8.2. 

Analytical results should be given always in the form 

In each case, the number of digits should be rounded in such a way that no insignificant precision is feigned. 

Results of ultra trace analyses are sometimes characterized by relatively high uncertainties up to more than 100%. In such cases it is not allowed that the lower uncertainty limit falls below zero. Results like, e.g., (0.07 0.10) must be replaced by such as (0.07 + 0.10/ — 0.07) or (0.07/q o°), respectively. That means, the total uncertainty interval (confidence interval, prediction interval is 0...0.17). In general, when the confidence interval includes a negative content (concentration), the result has to be given in the form 

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The problematic nature of the presentation of analytical results will be illustrated by examples of results of the Mo determination in several wine samples (fictional, but on the basis of own studies see Thiel et al. [2004] Geisler [1999]) by means of ICP-MS (nuclide Mo 95) ... 

The EPA clearly needed to develop technical guidelines for environmental monitoring this included the implementation of sampling and analytical protocols, and the establishment of acceptable techiuques for the documentation and presentation of analytical results. The alternative was to continue to produce results that were indefensible and expensive. The EPA realized that protocols were lacking, and published some interim guidelines on QA (EPA, 1980b), but these had not yet been widely implemented by the time the Love Canal situation came to light. 

R. W. G. Wyckoff, "The Analytical Presentation of the Results of the Theory of Space-Groups , Publ. Carnegie Institution No. 318, 1922. 

Information from the summary table in each workbook was directly imported into a master compilation of analytical results. The compilation could then be manipulated as desired to present the data in various ways. For example, the compilation could be searched for the number of apple samples that contained no detectable residues of any analyte or for the number of tomato samples that required dilution and reanalysis. 

The initial condition is C(0) = Cjs, where Cjs is the value of the steady state solution. The inlet concentration is a function of time, Cin = Cm(t), and will become our input. We present the analytical results here and will do the simulations with MATLAB in the Review Problems. 

Analytic solutions for flow around and transfer from rigid and fluid spheres are effectively limited to Re < 1 as discussed in Chapter 3. Phenomena occurring at Reynolds numbers beyond this range are discussed in the present chapter. In the absence of analytic results, sources of information include experimental observations, numerical solutions, and boundary-layer approximations. At intermediate Reynolds numbers when flow is steady and axisym-metric, numerical solutions give more information than can be obtained experimentally. Once flow becomes unsteady, complete calculation of the flow field and of the resistance to heat and mass transfer is no longer feasible. Description is then based primarily on experimental results, with additional information from boundary layer theory. 

The process of providing an answer to a particular analytical problem is presented in Figure 2. The analytical system—which is a defined method protocol, applicable to a specified type of test material and to a defined concentration rate of the analyte —must be fit for a particular analytical purpose [4]. This analytical purpose reflects the achievement of analytical results with an acceptable standard of accuracy. Without a statement of uncertainty, a result cannot be interpreted and, as such, has no value [8]. A result must be expressed with its expanded uncertainty, which in general represents a 95% confidence interval around the result. The probability that the mean measurement value is included in the expanded uncertainty is 95%, provided that it is an unbiased value which is made traceable to an internationally recognized reference or standard. In this way, the establishment of trace-ability and the calculation of MU are linked to each other. Before MU is estimated, it must be demonstrated that the result is traceable to a reference or standard which is assumed to represent the truth [9,10]. 

Abstract In this article the role of reference materials is confined to chemical measurements only. Recognized reference materials are one of the tools to obtain comparability of analytical results. Recognition demands confidence in the reference materials and in the reference material producers. A reference material producer is a technical competent body that is fully responsible for the certified or other property values of the reference material. The analyte has to be specified in relation to the selectivity of analytical procedure. The full range of reference materials can be presented as a three-dimensional space of the coordinates analyte,... 

Most of the present approximations to EJn] give relatively good results for EJn] but the shapes of the corresponding correlation potentials are not quite satisfactory. With this in mind, for comparison purposes, we introduce the first known closed-form expression connecting a component of the correlation potential to the correlation energy functional from which the potential is obtained by taking a functional derivative [29]. In particular, the closed-form expression connects Ec(2)[n] with its functional derivative, vc(2)([n] r). We will present our analytical results for spherically symmetric two-electron spin-nonpolarized densities. 

In reality however, situations also exist where a more complex form of the rate expression has to be applied. Among the numerous possible types of kinetic expressions two important cases will be discussed here in more detail, namely rate laws for reversible reactions and rate laws of the Langmuir-Hinshelwood type. Basically, the purpose of this is to point out additional effects concerning the dependence of the effectiveness factor upon the operating conditions which result from a more complex form of the rate expression. Moreover, without going too much into the details, it is intended at least to demonstrate to what extent the mathematical effort required for an analytical solution of the governing mass and enthalpy conservation equations is increased, and how much a clear presentation of the results is hindered whenever complex kinetic expressions are necessary. 

Suspended particulate matter and marine organisms are present in seawater. In seawater analysis, it is desirable to separate the particulate and dissolved fractions, and to analyse them separately. A comparison of analytical results for filtered and unfiltered seawater is shown in Table 3 [15], where upper and lower limits of particulate metal concentrations are also given. As can be seen in Table 3, the contents of particulate trace metals are less than 1% of the total metal concentration, which is generally within... 

There is one more, very important and relatively simple method to use when an interference effect is difficult to explore but its occurrence is probable and poses a threat to the reliability of analytical results. This refers to the case when an analyzed series of samples have similar chemical composition (at least in terms of the composition of interferents) and the determined component is present in all samples in a similar quantity. In this situation, the standard addition method can be used for analysis of one selected sample and the constructed calibration graph employed for interpolative determination of analyte in the remaining samples. This combined procedure is depicted in Fig. 3.16. Thus obtained results are, as a mle, more accurate than those obtained after application of the set of standards method to all the samples. In addition, the analyses are conducted faster than when all the samples are analyzed using the standard addition method. 

Table 41.4 presents the analytical results obtained for one of the days of operation, using the Toray and Osmonics membranes. It can be seen that both membranes provided a permeate stream that fulfilled the dumping specifications. 

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