Data analysis procedure

By definition, the cake saturation (5) at any point on a capillary pressure curve is given by equation (4.30) 

Alternatively, if a filtration test has been performed and analysed according to the procedures in Section 4.1, and hence can be derived from equation (4.15). 

An experiment has been performed to determine the deliquoring characteristics of a filter cake formed to a depth of 6 cm. The data obtained over the pressure range 0-1140 kPa are shown in Columns (1) and (2) of Table 4.2. At the 

As the data were taken with an electronic balance it is necessary to convert the recorded masses to equivalent volumes by dividing each value by p, as shown in Column (3) of Table 4.2. Using equation (4.31) and converting to SI units as appropriate gives 

At the start of the test when 5 = 1, a rearranged version of equation (4.30) gives the initial volume of liquor in the cake 

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The Oliver-Pharr data analysis procedure [59] begins by fitting the unloading curve to the power-law relation... 

XPS Analysis. The ultrahigh vacuum (OHV) catalyst treatment-surface analysis system employed to characterize and treat the cobalt catalysts has been described previously ( 1, 2 The catalyst treatment and data analysis procedures have also been described (JJ. Briefly, the samples were treated in quartz reactors and then transferred under UHV into a modified Hewlett-Packard 5950A BSCA spectrometer for emalysis. Peak areas were normalized with theoretical cross-sections (Z) to obtain relative atomic compositions. 

The data analysis procedure for the case of constant heat flux is based on the theory describing the response of an infinite line source model (Ingersoll and Plass, 1948 Mogeson, 1983). Although this model is a simplification of the actual experiment, it can successfully be used to derive the geothermal properties (e.g. Kavenaugh, 1984 Austin,. 1998 Gehlin, 1998). 

In this section, the relationship between the measured quantity and the desired center-of-mass differential cross-section will be established and a brief description of the data analysis procedure will then be given. First, consider a Newton sphere with a single value of the product velocity v (see Fig. 4). From the Doppler-shift formula, at a given laser wavelength, the Doppler effect selectively ionizes those ions with vz = vcosO in the... 

The physico-chemical changes induced in polymers following exposure to radiation can be studied by a range of spectroscopic techniques. Recent developments in instrumentation and data analysis procedures in electronic, vibrational and magnetic resonance spectroscopies have provided considerable new insights into polymer structure and behaviour. The application of these spectroscopic methods in polymer studies are reviewed with emphasis on their utility in investigations of radiation effects on macromolecules. 

The variety of spectroscopic methods now available can be used to provide considerable information on radiation effects on polymeric materials. These applications are summarized in Table I. Improvements in instrumentation and data analysis procedures are continuing and the development of new spectroscopic techniques promise new insights into polymer structure and behaviour. 

The usual data analysis procedures for the linearizable models typified by Eq. (2) consist of (1) isolating a class of plausible rival models by means of plots of initial reaction-rate data as a function of total pressure, feed composition, conversion, or temperature (2) fitting the models passing the screening requirements of the initial rates by linear least squares, and further rejecting models based upon physical grounds. 

Experiments on the hydrolysis of 4-(p-chlorophenoxy) butyl bromide, (PCBB) which proceeds via an Sj 2 substitution mechanism (11) were similar in design and data analysis procedures to the chlorpyrifos experiments detailed above. Results from a study at 35°C using EPA-12 sediment with 80% of the compound in the sorbed state are illustrated in Figure 5. Calculated and observed values from this study, using the distilled water value for of (7.9 0.5xl0 ) min a... 

Data analysis procedures have developed substantially over the last few years. In particular, use of least square refinement methods have been developed. Recent progress with theoretical development for the treatment of multiple scattering has resulted in Ugand group refinement such as an imidazole. We can expect further development in this area which ought to lead us to restrained least square refinement procedures for EXAFS data analysis. This type of restrained refinement is commonly used for macromolecular crystallographic structure determination where a similar problem of imderdeterminancy exists... 

Ciosek, P., Brzozka, Z., Wroblewski, W., Martinelli, E., Di Natale, C., and D Amico, A. (2005). Direct and two-stage data analysis procedures based on PCA, PLS-DA and ANN for ISE-based electronic tongue-Effect of supervised feature extraction. Talanta 67(3), 590-596. 

Chu, B., Laser Light Scattering Basic Principles and Practice, 2nd ed., Academic Press, Boston, 1991. (Advanced level. A detailed manual of light scattering. Covers basic theory as well as hardware and data-analysis procedures.)... 

Meyer, S. L., Data Analysis for Scientists and Engineers, Wiley, New York, 1975. (This is a more detailed manual on statistics and contains very useful collections of tables, distribution functions, data analysis procedures, and graphical techniques.)... 

Computer programs accounted for the presence of oil drops below- the detection limit of the Coulter Counter. The data processing procedure, which assumed that the oil-drop size distribution was lognormal, yielded accurate estimates of the true mean and standard deviation describing the emulsion drop size distribution. The data-analysis procedure did not affect the actual measured drop populations which were used in the kinetic studies. The computer programs are described in detail by Bycscda.8... 

This work presented here covers the basic experimental techniques and data analysis procedures together with the analysis of the contribution of intracrystalline diffusion to the performance of AP catalysts. 

As an example, a recent intercomparison (37) included three N02 measurement techniques aTDLAS-based system and two chemical-based systems— the photolysis-ozone chemiluminescence system diagramed in Figure 7 and an instrument based on N02 plus luminol chemiluminescence. Above 2 ppbv the three instruments gave similar results, but at sub-ppbv the results from the three techniques became dissimilar. Tests on the prepared mixtures showed that the luminol results were affected by expected interferences from 03 and PAN. No interferences were found in the TDLAS system, but near the detection limit the data analysis procedures calculated levels of N02 that were too high. The outcome of this intercomparison was close to the ideal the sensitivity, specificity, accuracy, and precision of each instrument were objectively analyzed previous data sets taken by different systems can now be reliably evaluated and each investigator was able to perceive areas in which the technique could be improved. 

A — 1.064 /xm using the instrumentation and data analysis procedures described above. Typical d33 values at zero time were found to be in the range 0.1 -1.0 x 10 esu. These magnitudes agree well with those expected for the chromophore number densities employed (N = 0.4-1.9 x 10 /cm ), assuming literature Mz zzz values for the chromophore and the applicability of an isolated chromophore, molecular gas description of the field-induced chromophore orientation process (7,8). 

In many respects, the held of chemometrics is the child of statistics, computers, and the information age. Rapid technological advances, especially in the area of computerized instruments for analytical chemistry, have enabled and necessitated phenomenal growth in the held of chemometrics over the past 30 years. For most of this period, developments have focused on multivariate methods. Since the world around us is inherently multivariate, it makes sense to treat multiple measurements simultaneously in any data analysis procedure. For example, when we measure the ultraviolet (UV) absorbance of a solution, it is easy to measure its entire spectrum... 

Pyrolysis of food samples provides a large number of products, which, after detection by MS and analysis by advanced statistical treatment, can be used to compare different samples. The method is very rapid and does not require chromatographic separation or MS identification of the pyrolysis products. Pyrolysis MS, coupled with multivariate data analysis procedures, has been used to discriminate between cocoa butters of three different continental areas (Radovic et al., 1998). The technique could in some cases separate deodorized from non-deodorized cocoa butters and also show those that have had alkali treatment. The presence of non-cocoa fats did not affect the assay. 

Probably the commonest way to collect data and perform simple manipulations is within a Microsoft XL spread-sheet. Consequently, the most obvious way to carry out statistical analyses of such data would seem to lie within XL itself. Let me give you my first piece of advice. Do not even consider it The data analysis procedures within XL are rubbish - a very poor selection of procedures, badly implemented (apart from that, they are OK). If anybody in the Microsoft Corporation had a clue, they could have cleaned up in this area years ago. The opposition is pretty feeble and a decent statistical analysis package built into XL would have been unstoppable. 

Figure 3.3 Data analysis procedures available for sampling...

The imaginary FT spectra in Figure 1 (b) show the separate Co-S and Co-Co(1) coordinations which cannot be discerned in the absolute FT spectra. It appears that the Co-S peak amplitude increases in the order COgSg Co/C Co-Mo/C, whereas the Co-Co(1) peak amplitude decreases in the same order. Data analysis was carried out by isolating the first and second peak in the absolute FT spectra and fitting the resulting EXAFS functions using Co-S and Co-Co EXAFS contributions. For a detailed description of the data analysis procedure we refer to (16). The structural parameters (N,R and A ) obtained in this way are collected in Table I. 

Time-resolved fluorescence depolarization studies have, over the past decade, provided an interesting method for monitoring molecular reorientational motions in solution. The technique has been applied to investigations of both nthetic polymers and macromolecules of biological interest, and a selection of the results of these are discussed here. However, until recently, the relatively pc r quality of much of the data available from these measurements has precluded detafled quantitative interpretations of the results. With the advent of improved experimental techniques for fluorescence decay time determinations due in part to the availability of pulsed lasers for sample excitation and more accurate data analysis procedures, it is envisaged that interest in the technique may be revived. We will present here a short recapitulation of the background to these experiments, following from Sect. A. V. 

The whole data analysis procedure can then be summarized as follows (see Fig. 10). Based on a nuclear electric quadrupolar coupling constant of the I spins known from experiment, a universal S I REDOR curve is computed via SIMPSON, at the precise conditions that were applied to obtain the experimental data. This simulation curve is fitted to a parabola, resulting in the appropriate fj value, which is then applicable to the analysis of the experimental... 

Another form of random matrix-related interference is more rarely occurring gross errors, which typically are seen in the context of immunoassays and relate to unexpected antibody interactions (see interference section) Such an error will usually show up as an outlier in method comparison studies. A weU-known source is the occurrence of heterophilic antibodies. This is the background for the fact that outliers should be carefuUy considered and not just discarded from the data analysis procedure. Supplementary studies may help clarify such random matrix-related interferences and may provide specifications for the assay that limit its application in certain contexts (e.g., with regard to samples from certain patient categories). 

The investigator should consider whether the study design is likely to disclose critical differences of clinical relevance. Important factors in this context are the range of measurements, the SDs of the random errors of the involved methods, and the number of samples. These factors determine the statistical power of a method comparison study (i.e., the ability of the data analysis procedure to verify the presence of a given systematic difference). 

In the first experimental paper entitled Anomalous neutron inelastic cross sections at eV energy transfers J. Mayers and T. Abdul-Redah give an overview of the NCS technique and a full description of the data analysis procedure followed to extract the required information about the scattering cross sections. Due to the various criticisms [Blostein 2001 Blostein 2003 (a) Blostein 2003... 

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