Data analysis methods differential method

There are many different ways how research is carried out. Here, we differentiate the general research design from more detailed-level data analysis methods. 

Hoffarth and Zesiger (2000) differentiate headspace vapours of perfumes using PCA and other multivariate data analysis methods by using a high-sensitivity quadrupole mass spectrometer-based electronic nose. 

This focus in this chapter is on analytical methods for measuring action spectra, with emphasis on those derived from fluence-response data. For a set of examples, the reader can consult studies of Phycomyces, not only studies of its phototropism but also of the light-growth response, carotene synthesis, and differentiation," as well as studies of other blue-light systems.The later studies on Phycomyces employed formal data analysis methods — including error analysis (and error propagation )... 

Integrating the rate equation is often diffieult for orders greater than 1 or 2. Therefore, the differential method of analysis is used to seareh the form of the rate equation. If a eomplex equation of the type below fits the data, the rate equation is ... 

Figure 3-17. Sohematios of the differential method for data analysis.

Modern instruments capable of obtaining excitation-emission matrices (EEMs) allow use of new data-analysis techniques to resolve overlapped spectra. Resolution techniques such as the ratio method (28) and others (29,30) may provide further differentiation of the components present in the phases separated by solvent extraction. 

Since data are almost invariably taken under isothermal conditions to eliminate the temperature dependence of reaction rate constants, one is primarily concerned with determining the concentration dependence of the rate expression [0(Ct)] and the rate constant at the temperature in question. We will now consider two differential methods that can be used in data analysis. 

The following example illustrates the use of the differential method for the analysis of kinetic data. It also exemplifies some of the problems... 

Techniques for the Analysis of Reaction Rate Data that are Suitable for Use with Either Integral or Differential Methods... 

These concentrations may be used in the various integral and differential methods for the analysis of kinetic data that have been described in previous sections. An example of the use of this approach is given in Illustration 3.5. 

Consideration of the white blood cell (WBC) and differential counts leads to another problem. The total WBC is, typically, a normal population amenable to parametric analysis, but differential counts are normally determined by counting, manually, one or more sets of one hundred cells each. The resulting relative percentages of neutrophils are then reported as either percentages or are multiplied by the total WBC count with the resulting count being reported as the absolute differential WBC. Such data, particularly in the case of eosinophils (where the distribution does not approach normality), should usually be analyzed by nonpara-metric methods. It is widely believed that relative (%) differential data should not be reported because they are likely to be misleading. 

The root time method of data analysis for diffusion coefficient determination was developed by Mohamed and Yong [142] and Mohamed et al. [153]. The procedure used for computing the diffusion coefficient utilizes the analytical solution of the differential equation of solute transport in soil-solids (i.e., the diffusion-dispersion equation) ... 

Whatever the application, MS-based analyses of FAC effluent will always be faced with the need to support a wide range of buffer components, ranging from variable ionic strength, surfactant levels to required cofactors. In select situations such as indicator analyses, online methods may be appropriate but it is clear that the insertion of an intermediate LC step offers sigmficantly improved performance. This changes the nature of the data analysis, from the detection of sigmoidal breakthrough curves to peak detection and differential analysis across multiple fractions. 

Table I. Means and Standard Deviations of the Data for 23 Differentially Substituted Pyridazinones Before and After Analysis by Ward s Method.

There are two procedures for analyzing kinetic data, the integral and the differential methods. In the integral method of analysis we guess a particular form of rate equation and, after appropriate integration and mathematical manipulation, predict that the plot of a certain concentration function versus time... 

In the differential method of analysis we test the fit of the rate expression to the data directly and without any integration. However, since the rate expression is a differential equation, we must first find llV) dNldt) from the data before attempting the fitting procedure. 

Chemometric evaluation methods can be applied to the signal from a single sensor by feeding the whole data set into an evaluation program [133,135]. Both principle component analysis (PCA) and partial least square (PLS) models were used to evaluate the data. These are chemometric methods that may be used for extracting information from a multivariate data set (e.g., from sensor arrays) [135]. The PCA analysis shows that the MISiC-FET sensor differentiates very well between different lambda values in both lean gas mixtures (excess air) and rich gas mixtures (excess fuel). The MISiC-FET sensor is seen to behave as a linear lambda sensor [133]. It... 

Each of these methods has both merits and demerits. For example, the integration method can easily be used to test several well-known specific mechanisms. In more complicated cases the differential method may be useful, but this requires more data points. Analysis by the integration method can generally be summarized as follows. 

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