The nature of data

In the examples of descriptors and parameters given here, and in previous chapters, it may have been noticed that there are differences in the nature of the values used to express them. This is due to differences in their scales of measurement. It is necessary to consider four different scales of measurement nominal, ordinal, interval, and ratio. It is important to be 

This is the weakest level of measurement, i.e., has the lowest information content, and applies to the situation where a number or other symbol is used to assign membership to a class. The terms male and female, young and old, aromatic and non-aromatic are all descriptors based on nominal scales. These are dichotomous descriptors, in that the objects (people or compounds) belong to one class or another, but this is not the only type of nominal descriptor. Colour, subdivided into as many classes as desired, is a nominal descriptor as is the question which of the four halogens does the compound contain . 

An interval scale has the characteristics of a nominal scale, but in addition the distances between any two numbers on the scale are of known size. The zero point and the units of measurement of an interval scale are arbitrary a good example of an interval scale parameter is boiling point. This could be measured on either the Fahrenheit or Celsius temperature scales but the information content of the boiling point values is the same. 

A ratio scale is an interval scale which has a true zero point as its origin. Mass is an example of a parameter measured on a ratio scale, as are parameters which describe dimensions such as length, volume, etc. 

What is the significance of these different scales of measurement As was mentioned in Section 1.5, many of the well-known statistical methods are parametric, that is, they rely on assumptions concerning the distribution of the data. The computation of parametric tests involves arithmetic manipulation such as addition, multiplication, and division, and this should only be carried out on data measured on interval or ratio scales. When these procedures are used on data measured on other scales they introduce distortions into the data and thus cast doubt on any conclusions which may be drawn from the tests. Non-parametric or distribution-free methods, on the other hand, concentrate on an order or ranking of data and thus can be used with ordinal data. Some of the non-parametric techniques are also designed to operate with classified (nominal) data. Since interval and ratio scales of measurement have all the properties of ordinal scales it is possible to use non-parametric methods for data measured on these scales. Thus, the distribution-free techniques are the safest to use since they can be applied to most types of data. If, however, the data does conform to the distributional assumptions of the parametric techniques, these methods may well extract more information from the data. 

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Figure 32 is a summary of the nature of data that can be obtained in 2-D. Under conditions of trickle flow, this analysis shows that the liquid content of any given pixel remains constant, as evidenced by a low value of the standard deviation... 

No case study is exactly like another case. Each case study has its own features, defined by the natural setting and the nature of data obtained. The following case studies are an assortment of studies, heavily based on chemical data. 

Figure 1 The relative relationship between disciplines involved in research on the Earth s core and the nature of data and information that come from these various investigations. Studies listed in the upper row yield direct evidence on properties of the core. Those in the middle row yield indirect evidence on the composition of the Earth s core, whereas findings from disciplines listed on the bottom row provide descriptions of the state conditions for the core...

Several different correlation measures were proposed, depending on the nature of data. Pearson s correlation coeflBdent. It is the most known bivariate correlation measure estimating the degree of association between the two variables j and k, as follows ... 

Here, I provide a brief review of the methods developed in constructing RSDI. The point here is not to decide which approach techniques to use or to say which approach appears to be the best combinations of the indicators and weights or to say that the objective approaches are in some way meaningful methods or better than subjective approaches. Rather, to show the differences (uncertainty) of these RSDI results from all approaches. There are some special statistical tools used to measure the uncertainty and sensitivity of the input data in contribution to the output variance, for example the uncertainties analysis method (UA) and sensitivity analysis (SA) a review of these methods is available in Saisana et al. (2005). Due to the small sample size and the nature of data used in this study, a simple method in comparing the RSDI approaches and results is presented in Table 5.6 and Figure 5.9. 

This chapter is concerned with the pre-treatment of data and so far we have discussed the nature of data, the properties of the distribution of data, and means by which data may be scaled. All of these matters are important, in so far as they dictate what can be done with data, but perhaps the most important is to answer the question what information does the data contain . It is most unlikely that any given data set will contain as many pieces of information as it does variables. That is to say, most data sets suffer from a degree of redvmdancy and this section describes ways by which redundantgr may be identified and, to some extent at least, eliminated. This stage in data analysis is called data reduction in which selected variables are removed from a data set. It should not be confused with dimension... 

Traditional PHM extracts performance degradation pattern from real-time monitoring signal data or acquire degradation parameter data directly. Based on that information, life prediction model can be given according to the nature of data or the generalization capability of the selected models to... 

The relative efficiency of both unfold-PLS and N-PLS has been compared in order to understand how the nature of data, that is the different source of variability could influence the performance of a model. The use of N-PLS model led to a more parsimtMiious (1 LV) model and showed, in general, lower root mean square error in cross validation (RMSECV) values and a higher value of explained variance in prediction. 

Because of the nature of subsurface data, maps and sections are only models or approximations of reality, and always contain a degree of uncertainty. Reduction of these uncertainties is one of the tasks of the geoscientists, and will be further discussed in Section 6.2. 

A seemingly more stringent test would be to determine whether the ratios of areas for various solids as obtained by means of a given isotherm equation are independent of the nature of the adsorbate. The data summarized in Table XVII-3 were selected from the literature mainly because each author had obtained areas for two or more solids using two or more adsorbates. It is seen... 

The existence of this situation (for nonporous solids) explains why the ratio test discussed above and exemplified by the data in Table XVII-3 works so well. Essentially, any isotherm fitting data in the multilayer region must contain a parameter that will be found to be proportional to surface area. In fact, this observation explains the success of Ae point B method (as in Fig. XVII-7) and other single-point methods, since for any P/P value in the characteristic isotherm region, the measured n is related to the surface area of the solid by a proportionality constant that is independent of the nature of the solid. 

As pointed out in Section XVII-8, agreement of a theoretical isotherm equation with data at one temperature is a necessary but quite insufficient test of the validity of the premises on which it was derived. Quite differently based models may yield equations that are experimentally indistinguishable and even algebraically identical. In the multilayer region, it turns out that in a number of cases the isotherm shape is relatively independent of the nature of the solid and that any equation fitting it can be used to obtain essentially the same relative surface areas for different solids, so that consistency of surface area determination does not provide a sensitive criterion either. 

Sequences such as the above allow the formulation of rate laws but do not reveal molecular details such as the nature of the transition states involved. Molecular orbital analyses can help, as in Ref. 270 it is expected, for example, that increased strength of the metal—CO bond means decreased C=0 bond strength, which should facilitate process XVIII-55. The complexity of the situation is indicated in Fig. XVIII-24, however, which shows catalytic activity to go through a maximum with increasing heat of chemisorption of CO. Temperature-programmed reaction studies show the presence of more than one kind of site [99,1(K),283], and ESDIAD data show both the location and the orientation of adsorbed CO (on Pt) to vary with coverage [284]. 

This also illustrates the use of different wavelengths of light to obtain much more infomration on the nature of the film. Here A and T are plotted versus the wavelength of light ( ) and the line drawn tln-ough these data represents a fit calculated for the various fihns of yttrium oxide deposited on silica as shown at tire bottom of the figure [40],... 

Chemists are interested not only in the thermodynamics of a process (the relative stability o the various species) but also in its kinetics (the rate of conversion from one structure tc another). Knowledge of the minimum points on an energy surface enables thermodynamic data to be interpreted, but for the kinetics it is necessary to investigate the nature of the... 

Many molecules are obtained and used in a crystalline form, the nature of which can have e significant impact on their properties and behaviour. Moreover, it is sometimes possible foi a given material to exist in more than one crystalline form, depending upon the conditions under which it was prepared. This is the phenomenon of polymorphism. This can be important because the various polymorphs may themselves have different properties. It is Iberefore of interest to be able to predict the three-dimensional atomic structure(s) that a gi en molecule may adopt, for those cases where it is difficult to obtain experimental data and also where one might wish to prioritise molecules not yet synthesised. 

To meet the point that the amount of resonance interaction in the transition state will be dependent upon the nature of the electrophile, Yukawa and Tsuno have put forward a modified equation with three parameters. The physical interpretation of such an equation is interesting, but it is not surprising that it correlates experimental data better than does the equation with two parameters. ... 

The interest attaching to the nitration of pyridine i-oxide and its derivatives has already been mentioned ( 8.2.5). Some data for these reactions are given in tables 8.1, 8.2 and 8.4. The 4-nitration of pyridine I-oxide is shown to occur through the free base by comparison with the case of i-methoxypyridinium cation ( 8.2.2), by the nature of the rate profile ( 8.2.1), and by consideration of the encounter rate ( 8.2.3). - Some of these criteria have been used to show that the same is true for... 

Recently kinetic data have become available for the nitration in sulphuric acid of some of these hydroxy compounds (table 10.3). For 4-hydroxyquinoline and 4-methoxyquinoline the results verify the early conclusions regarding the nature of the substrate being nitrated in sulphuric acid. Plots of log Q against — (Lf + logioflHao) fo " these compounds and for i-methyl-4-quinolone have slopes of i-o, i-o and 0-97 at 25 C respectively, in accord with nitration via the majority species ( 8.2) which is in each case the corresponding cation of the type (iv). At a given acidity the similarity of the observed second-order rate constants for the nitrations of the quinolones and 4-methoxy-quinoline at 25 °C supports the view that similarly constructed cations are involved. Application of the encounter criterion eliminates the possibilities of a... 

A vast amount of research has been undertaken on adsorption phenomena and the nature of solid surfaces over the fifteen years since the first edition was published, but for the most part this work has resulted in the refinement of existing theoretical principles and experimental procedures rather than in the formulation of entirely new concepts. In spite of the acknowledged weakness of its theoretical foundations, the Brunauer-Emmett-Teller (BET) method still remains the most widely used procedure for the determination of surface area similarly, methods based on the Kelvin equation are still generally applied for the computation of mesopore size distribution from gas adsorption data. However, the more recent studies, especially those carried out on well defined surfaces, have led to a clearer understanding of the scope and limitations of these methods furthermore, the growing awareness of the importance of molecular sieve carbons and zeolites has generated considerable interest in the properties of microporous solids and the mechanism of micropore filling. 

We therefore felt it timely to attempt a critical exposition and assessment of the common methods for the evaluation of the surface area and pore size distribution of solids from adsorption measurements. Our main concern has therefore been with the use of adsorption data for these purposes rather than with adsorption per se and it is for this reason that our treatment of theoretical matters, whilst sufficiently detailed to bring out the nature of the assumptions underlying the various methods, is not exhaustive we have not set out to write a text-book or a treatise on adsorption, and our choice of material from the literature has been dictated solely by its seeming suitability for the explanation or illustration of the topic under discussion. 

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