Error four sources

However, this convergence is not monotonic. Sometimes, the smallest calculation gives a very accurate result for a given property. There are four sources of error in ah initio calculations ... 

The external validity refers to applicability and generalization and is outlined in the section, Applying the Results. The remainder of this section focuses on critically appraising the quality— that is, the internal validity—of individual trials. The internal validity is determined by how well the trial ensures that the known and unknown risk factors are equally distributed between the treatment and control groups. To ensure validity, the conduct of the trial should minimize systematic bias and random error as much as possible to provide results that are as accurate and close to the truth as possible. Four sources of bias are possible in trials of health care interventions selection bias, performance bias, attrition bias, and detection bias. Bias can result in an overestimation or underestimation of the effectiveness of a drug therapy and mislead the reader. While it is beyond... 

The next four sources of error apply to capillary viscometers in par-t icular ... 

The four sources of error in ab initio molecular electronic calculations are (1) neglect of or incomplete treatment of electron correlation, (2) incompleteness of the basis set, (3) relativistic effects, and (4) deviations from the Bom-Oppenheimer approximation. Deviations from the Bom-Oppenheimer approximation are usually negligible for ground-state molecules. Relativistic effects will be discussed in Section 15.23. In calculations on molecules without heavy atoms, (1) and (2) are the main sources of error. 

To illustrate the proposed methodology, a gelation study of medicine was conducted in which two control factors of PEO (xi) and PEG (X2) were chosen. The time-oriented responses are gelation measurements of medicine collected from 0.5 hour to 5 hour (as described in Table 1). At each time, there are 6 experimental runs and four replications for each experimental run (as described in Table 2). In the Error Reference source not found, below, the data yi is the column of mean values and Si is the column of variance values of experimental runs. The main purpose of study is finding the optimal setting of control factors so that the mean responses y (gelation measurements) are near the targets and the variances s can be reduced as much as possible. For somewhat reasons, the experimental data cannot be published. 

That all four methods give a different result for the concentration of analyte underscores the importance of choosing a proper blank but does not tell us which of the methods is correct. In fact, the variation within each method for the reported concentration of analyte indicates that none of these four methods has adequately corrected for the blank. Since the three samples were drawn from the same source, they must have the same true concentration of analyte. Since all four methods predict concentrations of analyte that are dependent on the size of the sample, we can conclude that none of these blank corrections has accounted for an underlying constant source of determinate error. 

If, upon review of the patent, the patentee discovers that the claims contain a formal error, are too narrow, or are too broad in view of the prior art, the patentee may ask the U.S. PTO to correct this error. There are four administrative vehicles for correcting errors in issued patents. The appHcation of each of these mechanisms is dependent on the nature and severity of the error, as weU as the source of its creation. 

Exponential cost correlations have been developed for individual items of equipment. Care must be taken in determining whether the cost of the eqmpment has been expressed as free on Board (FOB), delivered (DEL), or installed (INST), as this is not always clearly stated. In many cases the cost must be correlated in terms of parameters related to capacity such as surface area for heat exchangers or power for grinding equipment. There are four main sources of error in such cost correlations ... 

The comparison of more than two means is a situation that often arises in analytical chemistry. It may be useful, for example, to compare (a) the mean results obtained from different spectrophotometers all using the same analytical sample (b) the performance of a number of analysts using the same titration method. In the latter example assume that three analysts, using the same solutions, each perform four replicate titrations. In this case there are two possible sources of error (a) the random error associated with replicate measurements and (b) the variation that may arise between the individual analysts. These variations may be calculated and their effects estimated by a statistical method known as the Analysis of Variance (ANOVA), where the... 

The electrolysis efficiency must be 100 per cent, i.e. the charge passed must be consumed only in the studied electrode reaction. There are four possible sources of error ... 

Figure 8.8 shows the resulting saturation indices for halite and anhydrite, calculated for the first four samples in Table 8.8. The Debye-Hiickel (B-dot) method, which of course is not intended to be used to model saline fluids, predicts that the minerals are significantly undersaturated in the brine samples. The Harvie-Mpller-Weare model, on the other hand, predicts that halite and anhydrite are near equilibrium with the brine, as we would expect. As usual, we cannot determine whether the remaining discrepancies result from the analytical error, error in the activity model, or error from other sources. 

In Chapters 3 and 4 we have shown that the vector of process variables can be partitioned into four different subsets (1) overmeasured, (2) just-measured, (3) determinable, and (4) indeterminable. It is clear from the previous developments that only the overmeasured (or overdetermined) process variables provide a spatial redundancy that can be exploited for the correction of their values. It was also shown that the general data reconciliation problem for the whole plant can be replaced by an equivalent two-problem formulation. This partitioning allows a significant reduction in the size of the constrained least squares problem. Accordingly, in order to identify the presence of gross (bias) errors in the measurements and to locate their sources, we need only to concentrate on the largely reduced set of balances... 

Next we consider the compact star in the low mass X-ray binary 4U 1728-34. In a very recent paper Shaposhnikov et al. (2003) (hereafter STH) have analyzed a set of 26 Type-I X-ray bursts for this source. The data were collected by the Proportional Counter Array on board of the Rossi X-ray Timing Explorer (RXTE) satellite. For the interpretation of these observational data Shaposhnikov et al. 2003 used a model of the X-ray burst spectral formation developed by Titarchuk (1994) and Shaposhnikov Titarchuk (2002). Within this model, STH were able to extract very stringent constrain on the radius and the mass of the compact star in this bursting source. The radius and mass for 4U 1728-34, extracted by STH for different best-fits of the burst data, are depicted in Fig. 6 by the filled squares. Each of the four MR points is relative to a different value of the distance to the source (d = 4.0, 4.25, 4.50, 4.75 kpc, for the fit which produces the smallest values of the mass, up to the one which gives the largest mass). The error bars on each point represent the error contour for 90% confidence level. It has been pointed out (Bombaci 2003) that the semi-empirical MR relation for the compact star in 4U 1728-34 obtained by STH is not compatible with models pure hadronic stars, while it is consistent with strange stars or hybrid stars. 

Fig. 13.8 Analysis of sterilized and unsterilized sediments from Hale Point, for methylmercury. Total mercury is 7.24 jg g 1. Results up to day 25 are the mean of eight determinations results beyond day 25 are the mean of four determinations. Error bars represent range limits for each analysis series. The samples were stored at room temperature (18°C), untreated o sterilized samples Source Reproduced with permission from McMillan Magazines [55]... 

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