Data treatment Experimental error

One possibility is that the curvature is an artifact introduced by a systematic error in the measurements. This is not unlikely, because rate constants may vary by orders of magnitude over a wide temperature range, necessitating different analytical methods or data treatments in different temperature regions. Careful experimental work should be able to identify such problems. 

It is important to note that the fitting according to eq. (1) requires zero intercept behavior i.e., F =. 00 for H (for which Oj = Or =. 00). While we recognize that the data for the unsubstituted (H) member of a set may be as subject to experimental error as any other member, such error is generally relatively small for a set of reliable data. Any constant error from this source will be distributed among all of the substituents in such a manner as to achieve best fit. Any loss in precision of fitting of the set which may result by such a procedure we believe is a small price to pay compared to the violence done by introduction in eq. (I) of a completely variable constant parameter. The latter procedure has been utilized by other authors both in treatments by the simple Hammett equation and by the dual substituent parameter equation. 

In the last section of the paper, we discuss a Bayesian approach to the treatment of experimental error variances, and its first limited implementation to obtain MaxEnt distributions from a fit to noisy data. 

A word about errors. I have used the phrase treatment of errors fairly liberally. A few of my colleagues take this phrase to mean the statistical manipulation of data once the latter have been obtained. I have followed a different tack, and mean here those errors and faults which can creep into an actual experimental measurement. Indeed, this book is not long enough to describe the actual manipulation of data. 

Data for the feed and copolymer compositions for each experiment with a given feed are substituted into Eq. 6-36 and r2 is plotted as a function of various assumed values of r. Each experiment yields a straight line and the intersection of the lines for different feeds gives the best values of r and r2. Any variations observed in the points of intersection of various lines are a measure of the experimental errors in the composition data and the limitations of the mathematical treatment (see below). The composition data can also be treated by linear least-squares regression analysis instead of the graphical analysis. 

The data from the method validation data should be analyzed as the data are obtained and processed to ensure a smooth flow of information. If an experimental error is detected, it should be resolved as soon as possible to reduce any impact it may have on later experiments. Analysis of the data includes visual examination of the numerical values of the data and chromatograms followed by statistical treatment of the data if required. 

The shift in the two tensors is expected to be effective for carbohydrate molecules bearing a number of polar groups and hydrogen-bonding centers. Hence, serious difficulty for quantitative analysis may arise if the molecule does not contain three or more nonequivalent C—H vectors that relax predominantly via the overall motion. If this fact is ignored, qualitative treatment may lead to an erroneous motional description. Thus, one should be very cautious in interpreting the relaxation data for overall motion, especially when discrepancies well outside the experimental error are observed for the T, values. When the relaxation times are nearly similar and within the experimental error, isotropic motion may be considered as a first approximation to the problem. 

The experimental error is also relevant to data treatment, and will also be considered in this section. The extent of the analytic error depends on various factors including the type of methodology adopted, operator training, and inoculum protocols. The errors are relatively high in biological systems for example, 10-30% for proteins concentration 7-10% for cells concentration and viability (especially at low viability) 2-5% for liquid chromatography measures (glucose, lactate, amino acids) (Portner and Schafer, 1996 Miller and Reddy, 1998). 

Data from two types of experiments have been used to calculate changes in thermodynamic properties of adsorption systems. The agreement is within experimental error and indicates that a complete thermodynamic treatment is as useful for adsorption systems as for solutions. 

Experimental procedures for quantitative mass spectrometric analysis usually involve several steps. The final error results from the accumulation of the errors in each step, some steps in the procedure being higher error sources than others. A separation can be made between the errors ascribable to the spectrometer and its data treatment on the one hand and the errors resulting from the sample handling on the other. 

The content and length of any given report will depend on the subject matter of the experiment and on the standards established by the instructor. It is om behef that at least in some cases the report should be quite complete and should include a quantitative analysis of the experimental uncertainties and a detailed discussion of the significance of the results (see the sample report given below). For many experiments a brief report with only a qualitative treatment of errors and a short discussion may be considered adequate. In either case, a clear presentation of the data, calculations, and results is essential to every report on experimental work. 

In the interpretation of the numerical results that can be extracted from Mdssbauer spectroscopic data, it is necessary to recognize three sources of errors that can affect the accuracy of the data. These three contributions to the experimental error, which may not always be distinguishable from each other, can be identified as (a) statistical, (b) systematic, and (c) model-dependent errors. The statistical error, which arises from the fact that a finite number of observations are made in order to evaluate a given parameter, is the most readily estimated from the conditions of the experiment, provided that a Gaussian error distribution is assumed. Systematic errors are those that arise from factors influencing the absolute value of an experimental parameter but not necessarily the internal consistency of the data. Hence, such errors are the most difficult to diagnose and their evaluation commonly involves measurements by entirely independent experimental procedures. Finally, the model errors arise from the application of a theoretical model that may have only limited applicability in the interpretation of the experimental data. The errors introduced in this manner can often be estimated by a careful analysis of the fundamental assumptions incorporated in the theoretical treatment. 

The accuracy of a crystal-structure analysis depends on (1) the magnitude and distribution of the experimental errors in the measurements of the x-ray diffraction spectra (2) the ratio of the observational data/ variable parameters and (3) the completeness of the computational treatment of the data. 

The results of the experimental SAM data treatment for the cases of ZnO and CaO are collected in Tables 3.7.7 and 3.7.8, respectively. As is seen, addition of the initial commercial powder to the saturated solution in contact with the partially dissolved oxide deposit leads to a reduction in the saturated solution s concentration by a factor of 1.5 for ZnO solutions, and approximately 1.25 for CaO solutions. Similar changes of the solubilities are observed if the CdO and PbO powders are examined by the SAM method. It should be noted especially that, in all the cases, the changes of e.m.f. (pO) are approximately 10 times as high as the experimental error of the determination of these parameters. 

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