Analytical errors, positive

The reaction error is thus expressed as a percentage of the total ion concentration. Positive reaction errors indicate cation excess negative errors indicate anion excess. Reaction errors are caused by the analytical errors of the individual parameters and the fact that not all possible ions are commonly measured. 

Points 1 and 12 were assumed to correspond at their observed activities to the upper curve of run II, which had been evaluated as described in Improvements. The compositions so determined were used with the observed balance readings to establish the two calculation constants used in the evaluation of all other data in run I. Point 128 was confirmed within analytical error by a chemical analysis. The compositions associated with run III (Figure 2) could not be determined directly because of the unknown amount of oxide present. However, since the absolute composition-activity relationships for CeCd 6(4) are known approximately, an estimate of the composition was possible. The resulting calculated values for CeCd 4 5 were increased by 0.05%, in order to be consistent with the position of the upper structure in Figure 1. The resulting composition values should not be assumed to correspond precisely to those in Figure 1 however, it is not essential that the composition be known with greater precision. 

SSID for the elimination of analytical errors caused by possible interconversion of species. Absolute DL 12 pg of Hg (jniz 202). Methylation of inorganic mercury contained in the sample caused positive errors in the determination of MMM in sediment (54%) and plant materials (0.3-18.7%). No error was detected in the analyses of fish tissues... 

Spectral interferences also result from the presence of combustion products that exhibit broadband absorption or particulate products that scatter radiation. Both reduce the power of the iraiismillcd beam and lead to positive analytical errors. When the source of these products is Ihe fuel and oxidant mixture alone, the analytical data c in be corrected by making absorption measurements while a blank is aspirated into the flame. Note that this correction must be used with both double-beam and single-beam inslrilmcnls because Ihe reference beam of a double-beam instrument does not pass through Ihe Hamc (see Figure 9-13b). 

The average recovery by the flame AAS analytical technique of 17 spiked MCEF samples containing cadmium in the range of 0.5 to 2.0 times the TWA target concentration of 5 ng/m (assuming a 400 L air volume) was 104.0% with a pooled coefficient of variation (CV ) of 0.010. The flame analytical technique exhibited a positive bias of -h4.0% for the validated concentration range. The overall analytical error (OAE) for the flame AAS analytical technique was 6.0%. 

If the water from the sampler can be used without prior filtration, the desired sample volumes for manual analysis (generally about SO mL) may be poured into the final reaction bottles using the simple tool shown in Fig. 10-2. A hole of about 10 mm diameter is drilled into a lOOmL graduated cylinder of polypropylene just above the desired volume mark. The lower bend of the hole is adjusted (with a file) so that the cylinder in the vertical position retains the desired volume of seawater. The accuracy of 40 mL sample volumes thus collected was found to be better than 0.2mL causing analytical errors of less than 0.5 % (less than the method precision). 

Figure 5.2 Model of an averaged intensity spectrum, including a pixel error and a selection of background correction pixels (BCP) analyte wavelength position dashed line...

Effect of Constant Positive Determinate Error on Analysis of Sample Containing 50% Analyte (%w/w)... 

A proportional determinate error, in which the error s magnitude depends on the amount of sample, is more difficult to detect since the result of an analysis is independent of the amount of sample. Table 4.6 outlines an example showing the effect of a positive proportional error of 1.0% on the analysis of a sample that is 50.0% w/w in analyte. In terms of equations 4.4 and 4.5, the reagent blank, Sreag, is an example of a constant determinate error, and the sensitivity, k, may be affected by proportional errors. 

Note that a negative determinate error introduced by failing to recover all the analyte is partially offset by a positive determinate error due to a failure to remove all the interferent. 

Accuracy Under normal conditions relative errors of 1-5% are easily obtained with UV/Vis absorption. Accuracy is usually limited by the quality of the blank. Examples of the type of problems that may be encountered include the presence of particulates in a sample that scatter radiation and interferents that react with analytical reagents. In the latter case the interferant may react to form an absorbing species, giving rise to a positive determinate error. Interferents also may prevent the analyte from reacting, leading to a negative determinate error. With care, it maybe possible to improve the accuracy of an analysis by as much as an order of magnitude. 

If an analytical test results in a lower value x, < x0, then the customer may reject the product as to be defective. Due to the variation in the results of analyses and their evaluation by means of statistical tests, however, a product of good quality may be rejected or a defective product may be approved according to the facts shown in Table 4.2 (see Sect. 4.3.1). Therefore, manufacturer and customer have to agree upon statistical limits (critical values) which minimize false-negative decisions (errors of the first kind which characterize the manufacturer risk) and false-positive decisions (errors of the second kind which represent the customer risk) as well as test expenditure. In principle, analytical precision and statistical security can be increased almost to an unlimited extent but this would be reflected by high costs for both manufacturers and customers. 

Precision, accuracy and trueness are important performance characteristics in analytical chemistry. Each of them is well-defined in a positive sense ( closeness of agreement... ). However, their quantifying is done by means of unfavourable measures, namely by error quantities like, e.g., standard deviation and bias, respectively, which indeed do quantify imprecision and... 

Solution. The reconciled results in Table E16.4 are obtained by solving the optimization problem with the process model as the only set of constraints. Because all constraints are linear, an analytical solution exists to the problem, as given in Equation 16.11. This results in an 89.6% reduction in the sum of the absolute error. Note that all reconciled values are positive and hence feasible. It is not unusual for some reconciled flow rates to go negative, in which case it is necessary to solve the problem using a constrained minimization code such as QP. 

In actual practice, the concentration of chromate produces an intense yellow colour to such an extent that the end point is masked. Therefore, normally concentrations of 5 x 10 3 M are employed in analytical procedures. It suggests that [Ag+] shall be > 1.3 / 10 5 M at the end-point thereby introducing a positive determinate error. However, it has been proved experimentally that even with concentrations as low as 2 x 10 3 M, the extent of error caused is negligibly small. 

Systematic errors are peculiar to each particular method or system. They are constant in character and although they can be controlled to some extent, they cannot be assessed statistically. A major effect of the introduction of systematic error into an analytical method may be to shift the position of the mean of a set of readings relative to the original mean. It may not obviously affect... 

Now we want to have a closer look on the sitnation. We have to consider and avoid two different error possibilities. We want to exclude to think that the analyte is present where it is indeed not. This would be a false positive answer, a type I error. 

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