Systematic errors definition

For exposure of reasons of observable discrepancy of results of the analysis simulated experiment with application synthetic reference samples of aerosols [1]. The models have demonstrated absence of significant systematic errors in results XRF. While results AAA and FMA depend on sort of chemical combination of an elements, method of an ashing of a material and mass of silicic acid remaining after an ashing of samples. The investigations performed have shown that silicic acid adsorbs up to 40 % (rel.) ions of metals. The coefficient of a variation V, describing effect of the indicated factors on results of the analysis, varies %) for Mn and Fe from 5 up to 20, for Cu - from 10 up to 40, for Pb - from 10 up to 70, for Co the ambassador of a dry ashing of samples - exceeds 50. At definition Cr by a method AAA the value V reaches 70 %, if element presences an atmosphere in the form of Cr O. At photometric definition Cr (VI) the value V is equal 40%, when the element is present at aerosols in the form of chromates of heavy metals. 

The term definitive method is applied to an analytical or measurement method that has a valid and well described theoretical foundation, is based on sound theoretical principles ( first principles ), and has been experimentally demonstrated to have negligible systematic errors and a high level of precision. While a technique may be conceptually definitive, a complete method based on such a technique must be properly applied and must be demonstrated to deserve such a status for each individual application. A definitive method is one in which all major significant parameters have been related by a direct chain of evidence to the base or derived SI units. The property in question is either directly measured in terms of base units of... 

The advantage of the measures as suggested here is that they point into the same direction as it is done by the verbal definitions. High precision and a high degree of accuracy, respectively, are characterized by high numerical values of the measures which approximate to 1 in the ideal case (absence of random and systematic deviations, respectively) and approximate to 0 if the deviations approach to 100%. In the worst cases, the numerical values prec(x) and acc(x) become negative which indicates that the relative random or systematic error exceeds 100%. 

Accuracy is often used to describe the overall doubt about a measurement result. It is made up of contributions from both bias and precision. There are a number of definitions in the Standards dealing with quality of measurements [3-5]. They are only different in the detail. The definition of accuracy in ISO 5725-1 1994, is The closeness of agreement between a test result and the accepted reference value . This means it is only appropriate to use this term when discussing a single result. The term accuracy , when applied to a set of observed values, describes the consequence of a combination of random variations and a common systematic error or bias component. It is preferable to express the quality of a result as its uncertainty, which is an estimate of the range of values within which, with a specified degree of confidence, the true value is estimated to lie. For example, the concentration of cadmium in river water is quoted as 83.2 2.2 nmol l-1 this indicates the interval bracketing the best estimate of the true value. Measurement uncertainty is discussed in detail in Chapter 6. 

Certification using one definitive method. This option is employed when a highly established, internationally accepted scientific primary method is available. The method must be shown to have negligible systematic errors and to provide sufficient measurement accuracy. An example of such a method is isotope dilution mass spectrometry. 

To solve a crystal structure by direct methods, difficult data are those which are incomplete in the sampling of reciprocal space, have non-atomic i.e. < 1.3A resolution) and are noisy with large (systematic) errors in the data measurements. As we have seen, this definition spans many electron diffraction data sets, but there are some of sufficient quality that they can be solved routinely using conventional direct methods packages. Often these are of inorganic materials or intermetallic compounds that are relatively resistant to radiation damage. 

Figure 9) The magnitude of the systematic error contribution changes continuously with time, but it follows a definite cyclic pattern that repeats itself periodically. (This case is simulated here as a sine wave.)... 

This is essentially the multi-dimensional definition of slope. It describes how changes in u depend on changes in x, y, and z. Note that we use du to examine systematic errors but (du) to examine random errors. 

Errors of type 3 include systematic errors, such as spectroscopic errors or errors due to imperfect knowledge of the VMR profiles of non-target species. These errors are taken into account in the definition of the optimum size of each microwindow and for the selection of the optimal set of microwindows that should be used for the retrieval. The quantifiers that are calculated for these operations can also be used for the determination of the total error budget. 

Systematic Errors in Accurate Mass Measurements. 1. Problem Definitions The value of high resolution mass spectrometry is diminished if the mass measurements do not give unambiguous elemental compositions. Accurate mass measurements in FTMS require a precise measurement of ion frequencies and an accurate calibration law for converting ions frequencies to mass. The ion frequencies can be measured to nine significant figures with modern electronics however, the relationship between ion frequencies in the cubic cell and mass still requires further development. 

One possibility is to classify the methods used in the various steps of the analytical process (see also Section 1.5). Note that the analytical process usually starts with the definition or selection of the matter to be investigated. Here it is very important to realize that every sample or object of investigation has a history. Because this history may cause severe systematic errors, THIERS [1957] explains Unless the complete history of any sample is known with certainty, the analyst is well advised not to spend his time in analyzing it. Clearly, in such circumstances one should be extremely cautious about drawing conclusions from chemometric interpretations even where data are available. 

Obviously, even if CIHRM j and CCRM j have an additive systematic error, Ej is free from this error by definition. Additivity of bias is a reasonable approximation for nearly iden-... 

A definitive method is one that, after exhaustive investigation, provides analytical results that are accurate, i.e., are free of systematic errors, to the extent required for the intended end-use(s) (Cali et al., 1977). The resulting accuracy can be specified and proved on theoretical and experimental grounds, usually from first principles. The result obtained is termed the definitive value and is the best approximation to the true value. ... 

Definitions 2 and 3 allow an evolution in the different techniques and methods as definitive methods for the same analyte (Leijnse, 1982). Indeed, even though systematic errors were investigated during the initial research work, later technical advances may uncover errors that were undetected during the original measurements. The end use and end purposes of the definitive method include the evaluation of the accuracy of reference methods and its application to the quantitation of analytes in certified reference materials present in a biological matrix. 

A reference method is one which after exhaustive investigation has been shown to have negligible inaccuracy in comparison with its imprecision [International Federation of Clinical Chemistry (IFCC), 1979]. With its comparison of inaccuracy and imprecision this definition clearly refers to the principles of quality control in clinical chemistry. Indeed, statistical models such as Youden plots are used to find out whether the error in a pair of results happens by chance (imprecision of the method) or is systematic (inaccuracy) (Youden, 1967). If the results are close to the true values, inaccuracy is negligible in comparison with imprecision. As demonstrated earlier, each analytical procedure has a certain degree of imprecision consequently, the total absence of systematic error can never be proved. Only as the influence of a systematic error is evident in comparison with the influence of chance or random error can the systematic error be demonstrated. 

Systematic error — A kind of -> error that can be ascribed to a definite cause and even predicted if all the aspects of the measurement are known. It is also named determinate error. Systematic errors are usually related to the -> accuracy of a measurement since their deviations are generally of the same magnitude and unidirectional with respect to the true value. There are basically three sources of systematic errors instrumental errors, -> methodic errors, and operative errors [iii]. In addition, systematic errors can be classified as constant errors and - proportional errors [iv]. 

The systematic error caused by the definition of the zeroth order Hamiltonian, as described above, leads to too low relative energies for systems with open shells. A consequence is that dissociation and excitation energies will be too low because the dissociated or excited state has usually more open shell character than the reference state. Is there a way we can remedy this systematic error The diagonal elements of the generalized Fock operator can for an active orbitals be estimated as ... 

Some of the concepts used in defining confidence limits are extended to the estimation of uncertainty. The uncertainty of an analytical result is a range within which the true value of the analyte concentration is expected to lie, with a given degree of confidence, often 95%. This definition shows that an uncertainty estimate should include the contributions from all the identifiable sources in the measurement process, i.e. including systematic errors as well as the random errors that are described by confidence limits. In principle, uncertainty estimates can be obtained by a painstaking evaluation of each of the steps in an analysis and a summation, in accord with the principle of the additivity of variances (see above) of all the estimated error contributions any systematic errors identified... 

Bias errors are systematic errors that do not have a mean value of zero and that cannot be attributed to an inadequate descriptive model of the system. Bias errors can arise from instrument artifacts, parts of the measured system that are not part of the system under investigation, and nonstationary behavior of the system. Some types of bias errors lead the data to be inconsistent with the Kramers-Kronig relations. In those cases, bias errors can be identified by checking the impedance data for inconsistencies with the Kramers-Kronig relations. As some bias errors are themselves consistent with the Kramers-Kronig relations, the Kramers-Kronig relations cannot be viewed as providing a definitive tool for identification of bias errors. 

Accuracy has been conventionally defined as the sum of absolute value of the systematic error and the standard deviation of the meter (MiUer, 1996). Since in the absence of hardware or software redundancy the systematic errors cannot be detected, this conventional definition is not practical. Bagajewicz, (2005) defined accuracy with... 

The accuracy of a method is affected by systematic (bias) as well as random (precision) error components [3, 9] This fact has been taken into account in the definition of accuracy as established by the International Organization for Standardization (ISO) [17]. However, it must be mentioned that accuracy is often used to describe only the systematic error component, i.e. in the sense of bias [1, 2, 6-8,10,12, 13]. In the following, the term accuracy will be used in the sense of bias, which will be indicated in brackets. 

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