Uncertainties in experimental data

The NONLINT-SIT program has been used to interpret the available experimental data in order to find the best chemical model, including the most important species and their equilibiinm constants based on the fixed valnes of the Gibbs energies of other participating species and values of the ion-interaction parameters. The latter were only varied in the optimisation in a few cases. The program provides imcertainty valnes for the fitted equilibrium constants based solely on the uncertainties in the experimental data. These are the values reported in the text of the review. 

The calculated uncertainties in A(.G° /RT will increase with the uncertainty in the interaction parameters and with increasing ionic strength. We have used the studies of [1963ALL/MCD] and the solubility investigations of many sulphate solids (see Section IX.1.3.3) to explore this effect, because the chemical system is simple, with Th(S04)3 as the dominant species. The solvent extraction data of [1963ALL/MCD], where the ionic strength varies from a very low value up to 4.5 m, were used as a first test of the impact of uncertainties in interaction parameters on the fitted values of AfG° /RT (Th(S04)3 ), as it is expected that this system will provide maximum variability in the calculated values. The values of all of the ion-interaction parameters involved in this system ate Usted in Table D-1 and the AjG° /RT values of all of the species considered in interpretation ate hsted in Table D-2. The fitted AfG° /RT (Th(S04)3 ) value was found to be -(1209.511 +0.086) when maximum values of all the ion interaction parameters, based on the uncertainties reported in Table D-1, were used and -(1209.348 + 0.088) when the minimum values were used. These compare with the value of A G° /RT (Th(S04)3 ) = -(1209.432 + 0.086) found when the mean values of the ion interaction parameters were used (see Section IX. 1.3.2). 

The mean and uncertainty based on the mean of the maximum and minimum 

Thus the optimised value is not significantly different from the value based on the mean epsilon values, but the uncertainty is slightly larger. The value including the uncertainty in the epsilon values would translate into log, K° (D.l) = (10.748 + 0.053) for Reaction (D.l) as compared to log, AT°(D.l) = (10.748 + 0.038) based only on the mean epsilon values (Table IX-6). 

Based on experimental data interpretations (see Section IX.1.3.2 for details). Assumed to be identical to that for Th - ClOt. 

---

Contrary to quantization, granulation allows us to capture relevant measurement uncertainties in experimental data. This implies that data based upon appropriate granulation are more accurate than the corresponding data based on the usual quantization. 

Kline and McClintock (1953) developed a method to estimate the uncertainty in experimental data [55]. In some cases, some primary measurements like temperature, pressure, and flow are combined to calculate another result ... 

Probability and statistics provide one useful set of tools to model the uncertainty in experimental data. It is appropriate to start with a brief re dew of the normal distribution, which plays a central role in analyzing data. The normal or Gaussian distribution is ubiquitous in applications. It is characterized by its mean, m, and variance, cr, and is given by... 

VII.29. The criticality safety analyst should consider three general sources of uncertainty uncertainty in the experimental data, uncertainty in the calculational method and uncertainty due to the particular analyst and calculational models. Examples of uncertainties in experimental data are uncertainties reported in material or fabrication data or uncertainties due to an inadequate description of the experimental layout or simply due to tolerances on equipment. Examples of uncertainties in the calculational method are uncertainties in the approximations... 

Calibration experiments with two nearly equal and well known calibration masses (mj ,m ) prior and after gravimetric adsorption experiments are recommended. This can avoid systematic uncertainties in experimental data due to (slow) shifts of the zero-point-position of the balance. 

The conformational dependence of the first hyperpolarizability has been addressed for a selection of four representative molecules at the DFT level using the BMK XC functional and the 6-31 -I- G basis set". For rotation of an heteroaromatic ring relative to the adjacent -(X=X)n- chain, the variations of p are small (less than 20%) and comparable to the uncertainty in experimental data, so that it was concluded that it is sufficient to consider only one representative conformation in the theory-assisted design. In contrast for the trans to cis conformational transition, p is reduced by about a factor of 2. It was further shown that the ampHtude of this conformation-induced change of p amounts to about twice the relative change in the distance between the donor and acceptor groups. 

Since all experimental data for vapor-liquid equilibrium have some experimental uncertainty, it follows that the parameters obtained from data reduction are not unique3. There are many sets of parameters that can represent the experimental data equally well, within experimental uncertainty. The experimental data used in data reduction are not sufficient to fix a unique set of best parameters. Realistic data reduction can determine only a region of parameters2. 

The objective of this test was to present and analyze suitable experimental results for verif ying quantitatively the use of the above-mentioned three corrections with the W-3 correlation for predicting the DNB heat flux in a rod bundle. Uncertainties in the data due to instrument errors and heater rod fabrication tolerances... 

Although results obtained by researches are sometimes contradictory, due also to the enormous variety of experimental conditions and the uncertainty in some data, and their indications are sometimes biased, there is enough solid ground on which is possible to work confidently. 

Thermodynamic calculations based on the compositional dependence of the equilibrium constant are applied to solubility data in the KCl-KBr-H20 system at 25°C. The experimental distribution coefficient and activity ratio of Br /Cl in solution is within a factor of two of the calculated equilibrium values for compositions containing 19 to 73 mole percent KBr, but based on an assessment of uncertainties in the data, the solid solution system is clearly not at equilibrium after 3-4 weeks of recrystallization. Solid solutions containing less than 19 and more than 73 mole percent KBr are significantly farther from equilibrium. As the highly soluble salts are expected to reach equilibrium most easily, considerable caution should be exercised before reaching the conclusion that equilibrium is established in other low-temperature solid solution-aqueous solution systems. 

Now, the numerical integration involved in Eqs. (67) and (69) may be troublesome because of the uncertainties affecting experimental data points. In order to alleviate this problem, Halle et al. (53) proposed to model the observed dispersion curve according to the following expansion... 

A more extensive comparison of DFT-predicted adsorption energies with experimental data for CO adsorption on metal surfaces was made using data from 16 different metal surfaces by Abild-Pedersen and Andersson.13 Unlike the earlier comparison by Hammer et al., this study included information on the uncertainties in experimentally measured adsorption energies by comparing multiple experiments for individual surfaces when possible. These uncertainties were estimated to be on the order of 0.1 eV for most surfaces. In situations where multiple experimental results were available, the mean of the reported experimental results was used for comparison with DFT results. For calculations with the PW91 GGA functional, the mean absolute deviation between the DFT and experimental adsorption... 

Inspection of Table 5.7 shows that our conclusion drawn above from our simple picture of the salting effect, which is that smaller and/or polar compounds should exhibit smaller Kf values as compared to larger, nonpolar compounds, is more or less confirmed by the experimental data. When considering the rather limited experimental data set, and the relatively large uncertainty in the data, it is, however, presently not feasible to derive any reliable quantitative relationship using molecular descriptors that would allow prediction of Kf values of other compounds. One... 

It is not often that proper estimates can be made of uncertainties of all the parameters that influence the performance or required size of particular equipment, but sometimes one particular parameter is dominant. All experimental data scatter to some extent, for example, heat transfer coefficients and various correlations of particular phenomena disagree, for example, equations of state of liquids and gases. The sensitivity of equipment sizing to uncertainties in such data has been the subject of some published information, of which a review article is by Zudkevich Encycl. Chem. Proc. Des. 14, 431-483 (1982)] some of his cases are ... 

Sources of Uncertainty in Reactivity Data. The experimental conditions employed to obtain the data assembled in Tables IV through IX varied considerably among, and sometimes within the individual studies. Most notable among the parameters whose values showed substantial variability were solvent composition and temperature. Additional uncertainty is introduced when correlation equations are used to estimate log(ks/kH2o) values for those reactions where actual laboratory data are lacking (1 22). 

The experimentally determined value of the spray cabinet corrosivity (in 96 h) 111 3 g/m2 covers the value interval 140 40 g/m2 indicated in the standard method. The standard deviation in experimental data scattering is rather small (5=4.1 g/m2) the calculated expanded uncertainty ( 215 g/m2), however, exceeds interval indicated in the standard method. 

Uncertainty is classified in two major groups Random error is always present in experimental data and can never be completely eliminated. It can result from the random nature of collisions that lead to chemical or biochemical reactions, or may be caused by small voltage fluctuations in measurement instrumentation. Random error causes positive and negative deviations from the true value, and affects the precision of the results. Precision is usually discussed in terms of standard deviation (,v) and relative standard deviation (RSD), both defined later in this chapter. Systematic error is produced by a more or less constant mistake, and results in a... 

Note on collision strengths the vast majority of these values are computed, not experimental. This does not mean that they have zero uncertainty A recent example is given by the case of [S III] (Tayal Gupta 1999). This new 27-state R-matrix calculation resulted in changes of approximately 30% in the collision strengths for optical and IR forbidden transitions from earlier calculations. This shows that even for commonly-observed ions the atomic data is still in a state of flux. Observers should take into account the probable uncertainty in atomic data when estimating errors in abundances. 

Minimize Uncertainty in Input Data through Experimentation Principles... 

This procedure proved viable for Fe(II) concentrations from 0.02 to 25 mM, initial Fe(III) between 0.1 and 25 mM, and ionic strengths (Ps) from 0.005 to 0.150 M. Practical limitations in the technique resulted when Fe(III) levels were sufficiently low that precipitation produced a pH change so small as to magnify experimental uncertainties in concentration data to the point that they were of the same order as the charge imbalance. Ionic strengths below about 0.005 M posed no additional calculation problems, but measurements of pH, redox, and reference potentials became erratic (48). Fe(II) concentrations below 0.02 mM were not investigated. 

---