Effect of experimental errors

In a comparison between surface area determination of ceramics by nitrogen adsorption and mercury porosimetry it was found that the results were similar in the surface area range 10-100 m2 g-1 but outside this range deviations were significant [78]. 

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It can be seen that k in Eq. (10) replaces the system-describing parameters L and Ah in Eq. (1). A direct test of the hypothesis is therefore to plot (j> against k for fixed values of P, G, and d, with L and Ah varying. For the hypothesis to be correct, the data points must all lie on a smooth curve. Experience shows, however, that plotting (f> against k often produces an undue amount of scatter which may obscure and distort any true relationship existing. This enhanced scatter is caused by the cumulative effect of experimental errors in the various terms in the heat-balance equation from which the quality k is derived. 

Used either as prelaboratory preparation for related laboratory activities or to expose students to additional laboratory activities not available in their program, these modules motivate students to learn by proposing real-life problems in a virtual environment. Students make decisions on experimental design, observe reactions, record data, interpret these data, perform calculations, and draw conclusions from their results. Following a summary of the module, students test their understanding by applying what they have learned to new situations or by analyzing the effect of experimental errors. 

Initial comparison of CFSTR runs with similar feed conditions indicates conditions for which the monomer conversion may be dependent on mixing speed. However, when the effects of experimental error in monomer conversion and differences in reaction temperature are considered, the monomer conversion is seen to be relatively independent of mixing speed for rpm equal to or greater than 500. Comparing Run 14 with Run 12 reveals a small decrease in monomer conversion in spite of a rise in reactor temperature of 2°C. This indicated the presence of a small amount of bypassing or dead volume at the lower mixing speed. This imperfect mixing pattern would also be present in Run 15. 

Usually, one plots the initial rate V against the initial amount X, which produces a hyperbolic curve, such as shown in Fig. 39.17a. The rate and amount at time 0 are larger than those at any later time. Hence, the effect of experimental error and of possible deviation from the proposed model are minimal when the initial values are used. The Michaelis-Menten equation can be linearized by taking reciprocals on both sides of eq. (39.114) (Section 8.2.13), which leads to the so-called Lineweaver-Burk form ... 

Yoshioka S, Aso Y, Takeda Y. Statistical evaluation of accelerated stability data obtained at a single temperature. I. Effect of experimental errors in evaluation of stability data obtained. Chem Pharm Bull 1990 38 1757-1759. 

The effect of experimental error on the efficiency of simplex optimization is reduced if the number of the factor increases. Caused by error of experiment, a simplex movement to optimum may turn into a circle, which is called simplex circling. In such cases we suggest a replication of experiment, and then the movement to optimum is either continued or terminated. The cause of simplex circling may be both error of experiment and achieved optimum, Fig. 2.53D. With a large number of factors, to get a more reliable estimate whether optimum has been reached, it is necessary to continue movement to optimum until the number of simplexes with the same vertex does not surpass the value ... 

Note that Vmax and Km may be estimated from data on steady state flux and substrate concentration based on a number of different ways of plotting J and [S], Cornish-Bowden illustrates that the Lineweaver-Burk plot (or double-reciprocal plot) is not recommended when one would like to minimize the effect of experimental error on parameter estimates. For a detailed discussion see Section 2.6 of [35]. 

This article presents a selected review of the main resnlts on pressnre drop and heat transfer coefficient measnrements with liqnid flows and underlines the discrepancies or the agreements with classical theories. The theoretical arguments set out by the authors to explain these discrepancies are also presented. To prevent ambignity, experimental results are presented wherein the evident effects of experimental errors have been removed. From these resnlts a tentative critical analysis is proposed to facilitate the choice of experiment interpretations and/or system designs. 

All are irreversible. Some laboratory data obtained under isothermal conditions are given below, where a is the initial concentration of NH3, yi the concentration of CH3NH2, yi that of (CH3)2NH, and the corresponding fraction NH3 unconverted a — x)ja. From these data determine the relative values ( 2/ 1) and ( 3/ 1)- How would you go about determining absolute values for ki and k l Note that there are maxima in the concentrations of both intermediates, as expected, but that 72 occurs at a high value of ammonia conversion. A prudent accounting for the possible effects of experimental error will be important in the analysis of these data. 

A different approach to a systematic study of the effects of experimental errors has also appeared. A computer program was developed which enabled ready calculation of the equilibrium constant from input experimental data. Beginning with synthetic data (no errors) small errors were deliberately introduced into the input data—for example, amounting to a weighing error of 0.3 mg in 20-500 mg, or an instrumental error of +0.003 absorbance units. Recalculation of the constant revealed that for certain concentration situations the determined equilibrium constant could be extremely sensitive to small experimental errors. The same conclusion was reached when K was determined by a graphical method with the same data. This again emphasizes the need for careful planning of experimental conditions. 

The Effect of Experimental Error on Standard Deviation of Calculated Stoichiometry Data Hydrochloric Acid-tri-n-Hexylamine (THA) Extraction to n-Octane... 

Coulter has discussed the effects of experimental errors on the precision of i.d.a. The most important factor is the extent of dilution, this having a larger effect than errors due to the statistics of counting, and should be carefully controlled. A nomogram is presented which enables optimum experimental parameters to be predicted for a particular analytical system, or allows an estimation of the precision of an actual system. Klas ° has more recently considered the optimization of experimental factors in i.d.a. with respect to the overall time of analysis. 

In most situations, there is no simple way to calculate the effect of experimental error on In CMD or In GSD. Nevertheless, confidence intervals for CMD and GSD can still be determined by making repeated size distribution measurements. The mean and standard deviation of the distribution of CMDs and GSDs are then calculated in the usual way, and confidence intervals for the CMD and GSD are calculated by... 

Pick next had to prove his hypothesis that diffusion and thermal conduction can be described by the same equations. He was by no means immediately successful. Pirst, he tried to integrate Eq. 2.1-2 for constant area, but he became discouraged by the numerical effort required. Second, he tried to measure the second derivative experimentally. Like many others, he found that second derivatives are difficult to measure the second difference increases exceptionally the effect of [experimental] errors. ... 

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