Determinate error constant

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 a constant determinate error on the reported concentration of analyte. 

Effect of a Constant Determinate Error on the Value of k Calculated Using a Single-Point Standardization... 

Table 5.2 demonstrates how an uncorrected constant error affects our determination of k. The first three columns show the concentration of analyte, the true measured signal (no constant error) and the true value of k for five standards. As expected, the value of k is the same for each standard. In the fourth column a constant determinate error of +0.50 has been added to the measured signals. The corresponding values of k are shown in the last column. Note that a different value of k is obtained for each standard and that all values are greater than the true value. As we noted in Section 5B.2, this is a significant limitation to any single-point standardization. 

The results of Analyst-1 lie on either sides of the average value as shown by two cross-signs on each side which might have been caused due to random errors discussed earlier. It is quite evident that there exists a constant (determinate) error in the results obtained by the Analyst-2, and (/ / /) In case, Analyst-3 had performed the estimations on the very same day in quick succession i.e., one after the other, this type of analysis could be termed as repeatable analysis . If the estimations had been carried out on two separate days altogether, thereby facing different laboratory conditions then the results so obtained would be known as reproducible analysis . 

It should be mentioned that it is possible to have a high degree of correlation between two methods (r near unity) but to have a statistically significant difference between the results of each according to the t test. This would occur, for example, if there were a constant determinate error in one method. This would make the differences significant (not due to chance), but there would be a direct correlation between the results [r would be near unity, but the slope (m) may not be near unity or the intercept (b) not near zero]. In principle, an empirical correction factor (a constant) could be applied to make the results by each method the same over the concentration range analyzed. 

Constant determinate errors are independent of sample size, and therefore become less significant as the sample size is increased. For example, where a visual indicator is employed in a volumetric procedure, a small amount of titrant is required to change the color at the end-point, even in a blank solution (i.e. when the solution contains none of the species to be determined). This indicator blank (Topic C5) is the same regardless of the size of the titer when the species being determined is present. The relative error, therefore, decreases with the magnitude of the titer, as shown graphically in Figure 3. Thus, for an indicator blank of 0.02 cm, the relative error for a 1 cm titer is 2%, but this falls to only 0.08% for a 25 cm titer. 

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

In a single-point standardization, we assume that the reagent blank (the first row in Table 5.1) corrects for all constant sources of determinate error. If this is not the case, then the value of k determined by a singlepoint standardization will have a determinate error. 

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. 

A reagent blank corrects the measured signal for signals due to reagents other than the sample that are used in an analysis. The most common reagent blank is prepared by omitting the sample. When a simple reagent blank does not compensate for all constant sources of determinate error, other types of blanks, such as the total Youden blank, can be used. 

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

The rate of a reaction is temperature-dependent. To avoid a determinate error resulting from a systematic change in temperature or to minimize indeterminate errors due to fluctuations in temperature, the reaction cell must have a thermostat to maintain a constant temperature. 

Frequency factors arc often determined from data obtained within a narrow temperature window. For this reason, it has been recommended4 that when extrapolating rate constants less error might be introduced by adopting the standard values for frequency factors (above) than by using experimentally measured values. The standard values may also be used to estimate activation energies from rate constants measured at a single temperature. 

As to the computation of reaction enthalpies and entropies, AH and AS , the same arguments apply if they have been obtained from the temperature dependence of the equilibrium constant. A different situation arises vdien AH is determined directly from calorimetry, say with a constant relative error 6. The standard entropy AS then has the standard error... 

There are other important factors beyond the state of the surface that may lead to discrepancies between laboratory and field studies. Measurement error in the laboratory, first of all, is considerable. Brantley (1992) notes that rate constants determined by different laboratories generally agree to within only a factor of about 30. Agreement to better than a factor of 5, she reasons, might not be an attainable goal. 

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 association rate constants were the same within experimental error. The dissociation rate constant for 31 was however an order of magnitude larger than that for 32. The association rate constants determined with fluorescence correlation spectroscopy were similar to the rate constants determined using temperature jump experiments (see above). However, a significant difference was observed for the dissociation rate constants where, for the 1 1 complex, values of 2.6 x 104 and 1.5 x 104s 1 were determined in the temperature jump experiments for 31 and 32, respectively.181,182 The reasons for this difference were not discussed by the authors of the study with fluorescence correlation spectroscopy. One possibility is that the technique is not sensitive enough to detect the presence of higher-order complexes, such as the 1 2 (31 CD) complex observed in the temperature jump experiments. One other possibility is the fact that the temperature jump experiments were performed in the presence of 1.0 M NaCl. 

All of the methods calculate the critical temperature by di viding Ibc boiling point temperature by a constant. Vowtes. I.ydcrsen. and Riedel1 have proposed atomic contributions that can be summed to determine the constant. The error is... 

The rate constants determined in the kinetic studies described above were derived from relative rate constants. The rate constant for N-propylcyclobutylaminyl radical ring opening is the only absolute rate constant known for an aminyl radical. It is possible that this rate constant is only a minimum value and may be in error by up to a factor of 10. The rate constant for H-atom transfer from hydrogen donors to aminyl radicals and those for cyclization and ring opening of aminyl radicals all bear the uncertainty of this initial value. However, the ratios of rate constants... 

D Dielectric constant determined at a frequency of 105 (cycles/sec.) and at 25°C. unless otherwise noted. When reported as data of The Dow Chemical Co., error about 0.005. Where Reference 5 is noted it was obtained by squaring the refractive index at 20 °C. 

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]. 

These constants determine the titration exponents pH and the best indicators for the successive hydrions. The acid can be titrated as dibasic, using methyl yellow, methyl orange or bromophenol blue, and as tetrabasic using phenolphthalein, thymolphthalein or thymol blue in the presence of a moderate excess of soluble barium salt. The values of pH in the partly neutralised acid were corrected for the salt error, and the constants Kz and jfiT4 which prevail in solutions of low concentration were thus deduced —6... 

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