Systematic errors for methods

Figure 38-1 Two-sample charts illustrating systematic errors for Methods A vs. B.

Ho If Fs is less than or equal to Ft, then there is NO DIFFERENCE in systematic error for methods. 

The overall uncertainty of an experimental result maybe given as a function of the random and systematic errors. For methods of estimating individual bias components and propagated errors to predict the total systematic error, the reader is referred to Currie and DeVoe (1977) or Peters et al. (1974). Methods for estimating propagation of errors in products, quotients, sums, or differences are provided in Cans (1992), Kline (1985), and Topping (1962). Statistical methods for addressing measurements that appear to be outliers (i.e., extreme values that are not part of the population) are presented in McCuen (1992). 

Our calculations show that the systematic errors for the evaluation of the triangle height are lower then for the peak height and peak ar ea. It is to be noted that tangent method allows estimating of the latent peak in the overlapped signals when peak area and peak maximum determination is impossible. 

XRF nowadays provides accurate concentration data at major and low trace levels for nearly all the elements in a wide variety of materials. Hardware and software advances enable on-line application of the fundamental approach in either classical or influence coefficient algorithms for the correction of absorption and enhancement effects. Vendors software packages, such as QuantAS (ARL), SSQ (Siemens), X40, IQ+ and SuperQ (Philips), are precalibrated analytical programs, allowing semiquantitative to quantitative analysis for elements in any type of (unknown) material measured on a specific X-ray spectrometer without standards or specific calibrations. The basis is the fundamental parameter method for calculation of correction coefficients for matrix elements (inter-element influences) from fundamental physical values such as absorption and secondary fluorescence. UniQuant (ODS) calibrates instrumental sensitivity factors (k values) for 79 elements with a set of standards of the pure element. In this approach to inter-element effects, it is not necessary to determine a calibration curve for each element in a matrix. Calibration of k values with pure standards may still lead to systematic errors for unknown polymer samples. UniQuant provides semiquantitative XRF analysis [242]. 

The analytical results for each sample can again be pooled into a table of precision and accuracy estimates for all values reported for any individual sample. The pooled results for Tables 34-7 and 34-8 are calculated using equations 34-1 and 34-2 where precision is the root mean square deviation of all replicate analyses for any particular sample, and where accuracy is determined as the root mean square deviation between individual results and the Grand Mean of all the individual sample results (Table 34-7) or as the root mean square deviation between individual results and the True (Spiked) value for all the individual sample results (Table 34-8). The use of spiked samples allows a better comparison of precision to accuracy, as the spiked samples include the effects of systematic errors, whereas use of the Grand Mean averages the systematic errors across methods and shifts the apparent true value to include the systematic error. Table 34-8 yields a better estimate of the true precision and accuracy for the methods tested. 

This indicates that the deviations are due to systematic errors, for example deficiencies of the applied methods and basis sets. DFT-based methods, such as GIAO/DFT calculations are known to overestimate paramagnetic contributions to the chemical shielding. This results, for critical cases with small HOMO/LUMO separations, in overly deshielded competed chemical shifts. Notorious examples for these deficiencies are 29Si or 13C NMR chemical shift computations of silylenes, silylium ions or dienyl cation .(5/-54) Taking into account the deficiencies of the applied method, and bearing in mind very reasonable correlations shown in Figures 4 and 5, the computational results do support the structural characterization of the synthesized vinyl cations. 

Many possibilities to search for systematic errors. For example, we can exclude any line or atom to avoid possible effects of unknown line blending, calibration errors, etc. The opposite signs and different values of the relativistic shifts for different lines give us a very efficient method to control the systematic effects. 

Two power function graphs are necessary, one to describe the performance for random error (RE) and the other for the performance for systematic error. For RE, as shown in Figure 19-10, A, the x-axis is labeled ARE. A value of 1.0 corresponds with the original standard deviation of the analytical method, a value of 2.0 to a doubling of that standard deviation, 3.0 to a tripling, and so on. For systematic error (SE), the x-axis is labeled ASE (see Figure 19-10, B). A value of 1.0s corresponds to a systematic shift equivalent to the size of the standard deviation, a value of 2.0 s to a shift equivalent to two times s, and so on. 

The solubilities reported for anthracene are clustered about two values. A possible reason for this phenomenon is that most commercial preparations of anthracene contain at least 2% phenanthrene. Though the two compounds are structural isomers, phenanthrene is approximately 20 times more water-soluble than anthracene. The presence of phenanthrene in solution would contribute a positive systematic error to methods that employ nonspecific analytical measurement techniques, such as UV spectroscopy (29) and nephelometry (24), The value reported by Schwarz (31), who employed a more selective analytical technique (fluorescence), agrees with that determined by DCCLC. 

Table I lists the data obtained by our four methods for the reactivities of various organic compounds (relative to hexane) and also some of the previous data collected by radiolysis techniques. All of the data agree well with the exception of the reactivities of the alcohols as measured by aqueous radiolysis and the more reactive hydrocarbons as measured by radiolysis. The disagreement between our work and radiolysis for ethanol and 2-propanol cannot be attributed to experimental error since numerous laboratories have studied the radiolysis of these alcohols. The reason for this discrepancy is unknown at present. However, we feel that two arguments suggest that our data may be correct and that the radiolysis results may contain some subtle systematic error for ethanol and 2-propanol. The first is discussed below in connection with Table II. The second is the lack of internal consistency of the radiolysis data themselves. When compared with other compounds studied by radiolysis which contain RCH2OH or R2CHOH groups, ethanol and 2-propanol stand out as unusually reactive. This point is discussed by Pryor and Stanley (Table IV of Reference 4).

Systematic error is under the control of the analyst. It is the analyst s responsibility to recognize and correct for these systematic errors that cause results to be biased, that is, offset in the average measured value from the true value. How are determinate errors identified and corrected Two methods are commonly used to identify the existence of systematic errors. One is to analyze the sample by a completely different analytical procedure that is known to involve no systematic errors. Such methods are often called standard methods they have been evaluated extensively by many laboratories and shown to be accurate and precise. If the results from the two analytical methods agree, it is reasonable to assume that both analytical procedures are free of determinate errors. The second method is to run several analyses of a reference material of known. 

The common spectrophotometric method for creatinine detection is based on the Jaffe reaction between creatinine and picric acid in alkaline solution to form a red-yellow complex. However, substances of endogenous and exogenous origin usually cause interference. In spite of these problems, the colorimetric method of Jaffe is still used today for the determination of creatinine in biological samples.A batchwise kinetic procedure and flow injection analysis have shown the possibility to determine creatinine in human urine samples by this reaction, free from any systematic error.Enzymatic methods have been reported to increase specificity/selectivity but still suffer from interferences. To avoid these problems, new analytical methods were developed. Several electtoanalytical techniques, based on potentiometric or amperometric detection, are available. Potentiometric methods using several sensors and biosensors were known for the... 

Under optimum conditions a precision of 0.002 pH can be obtained with glass electrodes, compared with 0.0005 pH or better for spectrophotometry with a 100 mm path length. Systematic errors are currently estimated to be similar for both techniques, of the order of 0.004 pH. The systematic errors for spectrophotometric measurements are likely to decrease in the near future as further indicator pK determinations become available and as more accurate methods of correcting for the added indicator are developed. Spectrophotometry is therefore expected to become the method of choice for the most accurate and precise measurements of seawater pH. 

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