Data analysis and normalization

Data analysis would normally commence with the calculation of means and standard deviations for each column of numbers where this was appropriate. Next, tests would be performed to establish whether or not the data were normally distributed. The data could then be grouped according to a particular variable (e.g., year of manufacture, oscillator screen size, or assay method) and compared statistically for differences between the mean and standard deviations. For ease of review by the validation team, a table should be printed summarizing the statistics calculated and the conclusions reached as a result of these data manipulations. 

Like many classical methods of data analysis, the normal probability plot has limitations. It is only useful if there are several factors, and clearly will not be much use in the case of two or three factors. It also assumes that a large number of the factors are not significant, and will not give good results if there are too many significant effects. However, in certain cases it can provide useful preliminary graphical information, although probably not much used in modern computer based chemometrics. 

PCA techniques can be used either as a detrending (filtering) tool for efficient data analysis and visualization or as a model-building structure to describe the expected variation under normal operation (NO). For a particular process, NO data set covers targeted operating conditions during satisfactory performance. PCA model is based on this representative... 

Figure 19.1 is a block diagram of a typical process analyzer system, consisting of a sample collection and conditioning system, sample manifold, sample inlet, ion source, mass analyzer, detector, and a data analysis and output system that interfaces with the process control system. The dashed line indicates the parts of the overall system that are considered to comprise the analyzer itself (i.e., what is normally included when one purchases a process MS). Figure 19.2 is a photograph of a commercial process MS that incorporates these components. Aspects of these various components are described below, with emphasis on how they are applied in a process mass spectrometer. 

Polarization infrared spectral data. X-ray analysis and normal coordinate treatment revealed the stable molecular conformation of poly(methylene disulfide) to be the GG G form [88] which was also confirmed from the results of semi-empirical CNDO/2SCF MO calculations [89]. Poly(ethylene disulfide) was also found to exist in a similar conformation as that of poly(methylene disulfide) [90]. Under vacuum at 50 °C, polysulfide polymers of methylene and ethylene with sulfur rank of two and four were exposed to UV radiation [91]. While poly(methylene disulfide) and poly(methylene tetrasulfide) yielded polymeric carbon monosulfide, hydrogen sulfide and carbon disulfide as the major degradation products, the ethylene counterparts produced the same compounds except carbon disulfide. The tetrasulfide polymers also formed volatile products which on condensation gave the original polymer. 

Bounaceur, R., Warth, V., Glaude, P.A., Battin-Leclerc, F., Scacchi, G., Come, G.M., Faravelli, T., Ranzi, E. Chemical lumping of mechanisms generated by computer—Application to the modeling of normal-butane oxidation. J. Chim. Phys. Phys. Chim. Biol. 93, 1472-1491 (1996) Box, G.E.P., Hunter, W.G., Hunter, J.S. Statistics for Experiments. An Introduction to Design, Data Analysis, and Model Building. Wiley, New York (1978)... 

The comparison with experiment can be made at several levels. The first, and most common, is in the comparison of derived quantities that are not directly measurable, for example, a set of average crystal coordinates or a diffusion constant. A comparison at this level is convenient in that the quantities involved describe directly the structure and dynamics of the system. However, the obtainment of these quantities, from experiment and/or simulation, may require approximation and model-dependent data analysis. For example, to obtain experimentally a set of average crystallographic coordinates, a physical model to interpret an electron density map must be imposed. To avoid these problems the comparison can be made at the level of the measured quantities themselves, such as diffraction intensities or dynamic structure factors. A comparison at this level still involves some approximation. For example, background corrections have to made in the experimental data reduction. However, fewer approximations are necessary for the structure and dynamics of the sample itself, and comparison with experiment is normally more direct. This approach requires a little more work on the part of the computer simulation team, because methods for calculating experimental intensities from simulation configurations must be developed. The comparisons made here are of experimentally measurable quantities. 

Larsen (18-21) has developed averaging time models for use in analysis and interpretation of air quality data. For urban areas where concentrations for a given averaging time tend to be lognormally distributed, that is, where a plot of the log of concentration versus the cumulative frequency of occurrence on a normal frequency distribution scale is nearly linear,... 

Beware that this type of coupling often may go undetected in a normal vibration analysis. Since the ghost frequencies are relatively high compared to the expected real frequencies, they are often outside the monitored frequency range used for data acquisition and analysis. 

The effects of solvent on reactivity ratios and polymerization kinetics have been analyzed for many copolymerizations in terms of this theory.98 These include copolymerizations of S with MAH,"7 118 S with MAA,112 S with MMA,116 117 "9 121 S with HEMA,122 S with BA,123,124 S with AN,103415 125 S with MAN,112 S with AM,11" BA with MM A126,127 and tBA with HEMA.128 It must, however, be pointed out that while the experimental data for many systems are consistent with a bootstrap effect, it is usually not always necessary to invoke the bootstrap effect for data interpretation. Many authors have questioned the bootstrap effect and much effort has been put into finding evidence both for or against the theory.69 70 98 129 "0 If a bootstrap effect applies, then reactivity ratios cannot be determined by analysis of composition or sequence data in the normal manner discussed in Section 7.3.3. 

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