Possible systematic error

In all these processes, however, when manipulating samples, there may be the risk of the operator introducing some spurious carbon. To take this effect into account, samples of certified 14C concentration [65] and of dead carbon are also prepared and then measured together with the unknown samples, hence making it possible to evaluate and correct for possible systematic errors due to unwanted carbon contamination during sample preparation. 

A large number of techniques have been used to investigate the thermodynamic properties of solids, and in this section an overview is given that covers all the major experimental methods. Most of these techniques have been treated in specialized reviews and references to these are given. This section will focus on the main principles of the different techniques, the main precautions to be taken and the main sources of possible systematic errors. The experimental methods are rather well developed and the main problem is to apply the different techniques to systems with various chemical and physical properties. For example, the thermal stability of the material to be studied may restrict the experimental approach to be used. 

The root-mean-square error of the model with only nearest-neighbor and next-nearest-neighbor interactions is 3.9 kJ/mol. The one of the model that also includes the linear 3-particle interaction is 2.9 kJ/mol. Using these errors as estimates for the errors in DFT calculations gives the error estimates of the lateral interactions in table 2. These should be regarded as lower estimates. If we would use a larger estimate for the errors in DFT then the errors of the lateral interactions would increase proportionally. Note that, because the term is always the same in the expressions for independent of the adlayer structure, possible systematic errors in DFT (cr in Section 3.4.2) only affect E 2 and not the lateral interactions. 

Shuman, M. S. (1990). Carboxyl acidity of aquatic organic matter possible systematic errors introduced by XAD extraction. In Organic Acids in Aquatic Ecosystems, Perdue, E. M., and Gjessing, E. T., eds., John Wiley Sons, New York, pp. 97-109. 

When bond lengths with different chemical sorrounding are compared to each other, the experimental error limits for the individual values are of great importance. It has become common practice in ED studies to report estimated uncertainties, which usually are 2 to 3 times the standard deviation of the least-squares refinement. It is assumed that such uncertainties account for possible systematic errors. Most MW studies also report estimated uncertainties, which may be considerably larger than the standard deviations derived from fitting the rotational constants. In X-ray crystallography it is common use to cite standard deviations from the least-squares analysis of the structure factors. 

A very limited number of compounds which contain C(sp)—F bonds has been studied in the gas phase (Table 18). In the MW analyses for bromo- and chlorofluoroacetylene, the length of the C=C bond had to be assumed, because only two rotational constants were measured. This bond length was varied within a reasonable range and the experimental uncertainties for the C—F bond distances include a possible systematic error due to this assumption. The C—F bond lengths in the four acetylenes are equal within their experimental error limits. The value derived for FCN is somewhat shorter, that for FCP slightly longer, but the differences are within the experimental uncertainties which are rather large for molecules of this size. 

The statistical error in our result is now small and so our attention must turn to possible systematic errors. The work [20] considers this aspect of the problem in great detail and so we present only the main points here. 

Do the values obtained for AZo agree satisfactorily If not, check the calculations and/or consider possible systematic errors. Plot the LHS of Eq. (34) against 1/7) and determine both AZo and the constant term graphically or by least squares. Does this value of A o agree with the average of the values obtained by direct application of Eq. (34)7 Does the constant term agree with the theoretical value ... 

It must be kept in mind that the treatment of uncertainties given in this chapter is concerned with uncertainty in the data caused by random errors and not with that due to possible systematic errors. For a discussion of the latter, see Chapter 11. 

This requirement is based on an assumption that the possible systematic errors, if any, as a result of matrix effects, spectral interferences, etc. are the same or at least similar in the CRM and in the analyzed samples. 

A commonly recommended and accepted way of checking accuracy is the analysis of CRMs along with routinely analyzed samples. The RM(s) applied for this purpose should obviously be as similar as possible in both the type of matrix and content of determined element(s). In this case, it can be assumed that the possible systematic errors resulting from matrix effects, spectral interferences, etc. are the same or at least similar in the CRM and in the analyzed samples. The result of measurement of f/m can be then compared with the certified value Aj-ef Cref, where f/m and (/ref expanded uncertainties of the measurement result and certified value, respectively. Good agreement of the result of measurement and the certified value confirms correctness of analysis. Taking into account numerical values, the following condition should be fulfilled [60] ... 

Tables 2—4 (see Appendix, p. 95) list what the author believes are the most accurate values of the dielectric virial coefiBdents obtained to date. The values of the coefiSdents for a particular gas are all taken from a angle paper, except in the case of a few dipolar gases where the authors published values of Ae and B, in separate papers. Emphasis has been placed on accmate values of Be, and for some gases, particularly non-dipolar ones, more accurate values of Ae can be found elsewhere in the literature (e.g. Table II of ref. 61). The uncertainty limits listed are those given by the authors. In most cases involving expansion techniques these reflect deviations of the experimental points from the computed least-squares curve, and contain no estimate of possible systematic errors. The papers listed under other references contain data which will lead to values of the virial coefiSdents considered less accurate than those given in the tables. In many cases these papers contain no actual values of the coefiSdents, but rather data from which values can be obtained.

For all antimony and bismuth analyses, standard addition as well as a calibration graph were applied to check for possible systematic errors. The results, obtained by the two methods, agreed within 10%. 

By default, TREOR adjusts the data for possible systematic errors in the first seven peaks by using higher order peaks. Sometimes this procedure may be not quite right, and when no solution has been found, it is recommended to suppress this correction by adding the instruction IDIV = 0. 

Where we do present geometrical parameters, we follow our usual practice of quoting them for the structural type (re, ra, rg, r l, etc.) reported in the original papers and with the same uncertainties, quoted in parentheses after numerical values. Such uncertainties may be estimated standard deviations, or multiplied by two or three to reflect supposed inadequacies in the modelling of the structures, or with additions for possible systematic errors. It is our view that systematic errors should be largely avoidable, that models should not be inadequate, and that an estimated standard deviation is a perfectly good and well understood quantity, and therefore that it should be left to readers to multiply it by whatever number they choose. 

Other indirect determinations can be performed by making use of chemical interferences. Based on the calcium phosphate interference in flame AAS for example, phosphate can be determined by measuring the decrease in the absorption signal obtained for calcium. However, for real samples such indirect techniques should be used very carefully in view of possible systematic errors. 

When the operator has determined the totality of the uncertainty budget within the possibilities offered by his laboratory, the uncertainty due to the presence of (a) possible systematic error(s) or bias remains. Only one possibility exists to detect such a bias. It lies in external help. Comparing the results of the test method to another method developed in-house involves the risk of having an unknown laboratory bias, e g. biased primary calibrants etc. Therefore, it is more appropriate to look for external help. This can come from the comparison of results obtained on a reference sample with those obtained on the same sample by another laboratory or by analysing a certified reference material. Both possibilities will be dealt with in the next two chapters of this book. 

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