Significant Systematic Error

Systematic error in an analytical method must be determined and corrected for. We have seen that systematic error is assessed by making a measurement on a certified reference material (sometimes just referred to as a CRM). The mean of a number of determinations, x, can be used to decide if the systematic error is significant by using the equation for a confidence interval of the mean 

Taking xCRM as the quantity value of the CRM (it is possible to extend the analysis if the value has its own uncertainty), then equation 3.3 can be used to calculate a t-value simply by setting /i = acrm  

As in all such testing if the probability falls below the limit decided (p a) then the null hypothesis, that there is no systematic error, is rejected, and we conclude that there is systematic error. 

The fluoride content in toothpaste is measured using a fluoride ion-selective electrode. To perform the measurement requires the sample to be prepared by extraction of the fluoride from the toothpaste. To determine whether the extraction and measurement procedure are free of systematic error a number of analysts measured the fluoride content of a test toothpaste sample with assigned mass fraction of 0.033 m/m%. The measured mass fractions of fluoride expressed as a percentage determined by the nine analysts were 0.042, 0.040, 0.028, 0.035, 0.044, 0.035, 0.041, 

Determine whether there is a systematic error in the method with 95% probability. 

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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. 

Table 35-3 illustrates the ANOVA results comparing laboratories (i.e., different locations) performing the same METHOD A for analysis. This statistical test indicates that for the mid-level concentration spiked samples (i.e. 4 and 4 at 3.40 and 3.61% levels, respectively) difference in reported average values occurred. However, this trend did not continue for the highest concentration sample (i.e., Sample No. 6) with a concentration of 3.80%. The Lab 1 was slightly lower in reported value for Samples 4 and 5. There is no significant systematic error observed between laboratories using the METHOD A. 

The score values are compared to a statistical table of values found in reference [1], This table is partially reproduced as Table 37-lc. If an individual laboratory score is equal to or outside of the limit boundaries, then we conclude that there is a pronounced systematic error present between the laboratory, or laboratories, with the extreme score. In this particular case the limits are 8 to 22, therefore there is no significant systematic error in the methods as determined using this test. 

The section following shows a statistical test (text for the Comp Meth MathCad Worksheet) for the efficient comparison of two analytical methods. This test requires that replicate measurements be made on two different samples using two different analytical methods. The test will determine whether there is a significant difference in the precision and accuracy for the two methods. It will also determine whether there is significant systematic error between the methods, and calculate the magnitude of that error (as bias). 

The chemical or biological basis of an analytical method may not permit a simple, direct relationship between the reading and the concentration of the analyte and failure to appreciate the limitations and constraints of a method can lead to significant systematic error. Carbohydrates may be quantified, for instance, using a method based on their reducing properties but results will tend to be higher than they should be if non-carbohydrate reducing substances are also present in the samples. 

In any experiment, therefore, all significant systematic errors should be measured and corrected for, and the random errors, including those pertaining to the bias corrections, estimated and combined in the measurement uncertainty. 

Demonstration of the absence of significant systematic error after corrections have been made for bias and/or recovery... 

The variation of the cathodic peak potential with the scan rate (0.3-0.4 mV precision on each determination, 1 mV reproducibility over the whole set of experiments) allows the determination of the rate constant with a relative error of 3-11%. The results are consistent with those derived from anodic-to-cathodic peak current ratios. Simulation of the whole voltammogram confirms the absence of significant systematic errors that could arise from the assumptions underlying the analysis of kinetic data. Activation parameters derived from weighted regression Arrhenius plots of the data points taken at 5 or 6 tern-... 

The key to a successful indexing is not a complete absence of impurity peaks (a few may be present) but it is the accuracy with which peak positions have been determined and the absence of significant systematic errors. Yet another important piece of advice, given in the manual, should always be followed do not waste computer time on bad data. Since the cost of computer time continuously lowers, but the cost of labor continuously rises, this statement could be rephrased do not waste your time on bad data. The latter is indeed applicable to any type of data analysis. 

FIGURE 1 Velocity calibration of a M ssbauer spectrometer. The spectrum shown (a) is of metallic iron at room temperature. Line positions are given in channels and line widths in mm/s. The velocity calibration constant (b) is derived from the known energy differences between various components of the magnetic hyper fine spectrum. In the present data a differential nonlinearity of about 1 percent is observed. Such spectrometer nonlinearity may become a source for significant systematic errors in high-resohition experiments. 

Systematic error A deviation from the true value that is always of the same magnitude and in the same direction from the mean. It should be estimated from measurement of certified reference materials and corrected for in a chemical analysis. Significant systematic error can be tested using t = ( assigned — x, fn/s,) where n independent... 

Consider what the consequences of setting the probability level for acceptance of H0 at 90, 95, and 99% might be. As an example suppose an analytical method has been used to analyze a certified reference material for the element zinc, that is, a material whose amount of substance of zinc has been established to a high metrological standard with low measurement uncertainty, with a view to deciding if there is any significant systematic error in the method. The mean of n measurement results has been determined and suppose that the population standard deviation (a), and therefore the standard deviation of the... 

Less than complete isotopic equilibration will lead to significant systematic errors... 

The data of Knets [1978] on human tibia are difficult to analyze. This could be due to the possibility of significant systematic errors due to mechanical testing on a large number of small specimens from a multitude of different positions in the tibia. 

Z < 118 have been obtained there is good overall agreement with known values, though the breakdown of the energies indicates the presence of significant systematic errors. Dynamical effects of electron correlation can also be studied through analysis of the correlation-induced changes in the subhamiltonian interelectron distances. 

The use of CRMs for validation purposes is, however, not limited to the above intralaboratory verification of trueness (checking the absence of significant systematic errors). They also enable the user to estimate the precision of a method (repeatability and reproducibility), which should actually represent one of the first steps of the method validation. In this respect, the evaluation will have to take into account specific characteristics of the CRM, in particular, possible sources of uncertainties linked to the material heterogeneity which should in principle be considered for the calculation of the uncertainty of the certified values. 

Correct identification of indicator isotopes and conversion of photopeak areas to exact quantities of the corresponding element are computationally simple, but crucial, steps of the analysis. Significant systematic errors may result from incorrect assignments or from the use of single-element comparators or Icq values under variable irradiation conditions. 

A further check on the occurrence of systematic errors in a method is to compare the results with those obtained from a different method, if two unrelated methods are used to perform one analysis, and if they consistently yield results showing only random differences, it is a reasonable presumption that no significant systematic errors are present. For this approach to be valid, each step of the two experiments has to be independent. Thus in the case of serum chromium determinations, it would not be sufficient to replace the atomic-absorption spectrometry step by a colorimetric method or by plasma spectrometry. The systematic errors would only be revealed by altering the sampling methods also, e.g. by minimizing or eliminating the use of stainless-steel equipment. A further important point is that comparisons must be made over the whole of the concentration range for which an analytical procedure is... 

The imcertainties have sometimes been re-estimated, and explicit remarks to this effect have then been made. Sometimes attention is drawn to a potential soiuce of significant systematic error, such as the presence of sample impurity, implicit assrunptions in the analysis such as the neglect of significant shrinkage effects, or strong correlation among the parameters. For some of the geometric parameters... 

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