Traditional Data Analysis

MD/CD decomposition separates the two-dimensional means one at a time from the data matrix Y n, k) that has N rows and K columns. First, the averages of all spatial locations for each scan are computed to get the MD trend as Then, the CD profile is computed by subtract- 

MD/CD decomposition is a sequence of two practically independent averaging or zero-order filtering operations with resulting variances that are 

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If poor initial parameter estimates are used, it becomes likely that the nonlinear regression will not be able to find an acceptable fit, or it may stride off on a mathematical tangent and arrive at a nonsensical fit to the data. It turns out that the values determined by traditional methods of residual analyses typically offer excellent starting estimates for the model parameters. Hence the traditional data analysis methods described in this chapter remain highly useful, even when nonlinear regression curve fitting is employed as the final step of parameter evaluation. 

In the new field of genetic engineering, scientific data management software is used to manage the long alphabetic codes that represent genetic sequences, as well as more traditional numeric and text applications. At Genentech, scientists use the software for these tasks as well as for laboratory data analysis. 

A comparison of Figures 9.18 and 9.19 shows that the acoustic chemometric approach is much more sensitive to changes in the process state(s) of the fluidized bed than the traditional process data alone. Of course an industrial implementation of this process monitoring facility would include both acoustic data and process data, together with relevant chemometric data analysis (PCA, PLS) and the resulting appropriate plots. 

In addition to the physical data analysis methods, traditional engineering analysis tools and methods are also useful during incident investigations. Traditional analysis tools can he used to determine the following. 

Prior Applications. The first application of this traditional factor analysis method was an attempt by Blifford and Meeker (6) to interpret the elemental composition data obtained by the National Air Sampling Network(NASN) during 1957-61 in 30 U.S. cities. They employed a principal components analysis and Varimax rotation as well as a non-orthogonal rotation. In both cases, they were not able to extract much interpretable information from the data. Since there is a very wide variety of sources of particles in 30 cities and only 13 elements measured, it is not surprising that they were unable to provide much specificity to their factors. One interesting factor that they did identify was a copper factor. They were unable to provide a convincing interpretation. It is likely that this factor represents the copper contamination from the brushes of the high volume air samples that was subsequently found to be a common problem ( 2). 

Traditionally, data was a single numerical result from a procedure or assay for example, the concentration of the active component in a tablet. However, with modem analytical equipment, these results are more often a spectrum, such as a mid-infrared spectrum for example, and so the use of multivariate calibration models has flourished. This has led to more complex statistical treatments because the result from a calibration needs to be validated rather than just a single value recorded. The quality of calibration models needs to be tested, as does the robustness, all adding to the complexity of the data analysis. In the same way that the spectroscopist relies on the spectra obtained from an instrument, the analyst must rely on the results obtained from the calibration model (which may be based on spectral data) therefore, the rigor of testing must be at the same high standard as that of the instrument... 

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