Proportional determinate errors

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. 

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

The method of standard additions can be used to check the validity of an external standardization when matrix matching is not feasible. To do this, a normal calibration curve of Sjtand versus Cs is constructed, and the value of k is determined from its slope. A standard additions calibration curve is then constructed using equation 5.6, plotting the data as shown in Figure 5.7(b). The slope of this standard additions calibration curve gives an independent determination of k. If the two values of k are identical, then any difference between the sample s matrix and that of the external standards can be ignored. When the values of k are different, a proportional determinate error is introduced if the normal calibration curve is used. 

Is the failure to correct for buoyancy a constant or proportional source of determinate error ... 

Determinate errors may be constant or proportional. The former have a fixed value and the latter increase with the magnitude of the measurement. Thus their overall effects on the results will differ. These effects are summarized in Figure 2.1. The errors usually originate from one of three major sources operator error instrument error method error. They may be detected by blank determinations, the analysis of standard samples, and independent analyses by alternative and dissimilar methods. Proportional variation in error will be revealed by the analysis of samples of varying sizes. Proper training should ensure that operator errors are eliminated. However, it may not always be possible to eliminate instrument and method errors entirely and in these circumstances the error must be assessed and a correction applied. 

The problem of chemical composition was directly related to that of chemical combination. Combining chemicals to produce new substances had been a goal of individuals throughout history. Lavoisier s work emphasized the quantitative study of chemical combination. Chemists sought to determine the proportion in which chemicals combined, and how much of one substance it took to react with another. Rather than combining substances using the alchemist s trial and error method, chemists sought to determine the specific ratio of chemicals involved in chemical reactions. 

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 contending scientist, Joseph Louis Proust, was at that time teaching chemistry in Spain. He had made numerous experiments to determine the proportions in which various compounds were formed, and had arrived at the conclusion that Berthollet was entirely mistaken. Proust repeated the experiments of his countryman. He used the purest of chemicals and the most accurate apparatus. He took every precaution to avoid error, and found mistakes in Berthollet s determination. Besides, Berthollet had used substances like glass, alloys, and mixtures of various liquids, all of which were not true compounds. For eight years Proust tried to persuade the scientific world, and especially the followers of Berthollet, that when elements combined to form chemical compounds, the elements united in definite proportions by weight—a theory advanced... 

Is a determinate error fixed or proportional I Graphical plot of results against sample weight (figure 2.1)... 

Fig. 2. Selective toxicity of EF13 for C8166 cells chronically infected with HIV-1. Uninfected (H9) and chronically HIV-infected (H9RF) cells were cultured for 4 d in the presence of EF13, a potential anti-HIV compound. Cell samples were taken daily and counted in the presence of Trypan blue to determine the proportion of cells that were live and dead. The data points represent the mean of 5 counts plus error bars of one standard deviation.

The determination error is smaller if the absorption of radiation is a consequence of the nature of the analyte itself, as with the coloured ions of transition metals. Conversion of the analyte into a form capable of absorbing radiation in proportion to its concentration requires some additional procedures (such as the use of a chromogenic reagent, pH adjustment, or addition of masking agents), that must be identical in the treatment of standard solutions and of the sample solution. 

That is, a summary measure of the amount of information in the information matrix (given by the normalized determinant) is proportional to the number of individuals in the study, where det denotes the determinant and is a scalar measure of the informativeness of the information matrix. Therefore, it follows that the standard error will be proportional to the inverse of the square root of sample size (Eq. (5.20)), and incorporating Eq. (5.15) provides the approximation... 

The error can be proportional to sample size or may change in a more complex manner. More often than not, the variation is unidirectional, as in the case of solubility loss of a precipitate (negative error). It can, however, be random in sign. Such an example is the change in solution volume and concentration occurring with changes in temperature. This can be corrected for by measuring the solution temperature. Such measurable determinate errors are classed as systematic errors. 

An analyst working at a different hospital with different instrumentation obtains the results shown in Table 1.8. Examination of these analytical results shows they are all 20% greater than the true answer. The error is proportional to the true concentration of the analyte. Such information as to the nature of the error is useful in the diagnosis of the source of the determinate error. 

A few words of caution are required, however. The estimate in vitro of brain/ blood concentration ratios is subject to many errors and has to be regarded as a gross approximatioa Although compounds are administered intravenously by infusion over an extended period (2-3 h) so that near steady state equilibrium is produced, they are subject to different rates of metabolism, elimination (excretion) and protein binding. All these factors will affect the concentration of drag available for brain penetration and will operate differently for each compound. In each case a check was made to determine the proportion of parent drag in the peripheral blood and in the brain by thin-layer chromatography. In most cases, the parent compound was still present at 90% for a few compounds, the proportion of parent present in the blood had decreased to 50%, so that the ratios for these could be underestimated by a factor of up to twofold with respect to metabohsm. 

Determinate errors can be proportional to the size of sample taken for analysis. If so, they will have the same effect on the magnitude of a result regardless of the size of the sample, and their presence can thus be difficult to detect. For example, copper(II) can be determined by titration after reaction with potassium iodide to release iodine according to the equation... 

The proportionality constant determines the proportional band. One of the important characteristics of proportional control is that it produces a permanent residual error in the operating point of the controlled variable when a change in system conditions occurs. This error is referred to as offset. This error limits the use of proportional control to processes with moderate to small process lag times, where large changes in conditions are unlikely to happen. 

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