Applied statistics correlation

Table 5.9 summarises the main features of FTIR spectroscopy as applied to extracts (separated or not). Since many additives have quite different absorbance profiles FTIR is an excellent tool for recognition. Qualitative identification is relatively straightforward for the different classes of additives. Library searching entails a sequential, point-by-point, statistical correlation analysis of the unknown spectrum with each of the spectra in the library. Fully automated analysis of... 

A final comment addresses the use of statistics. If judiciously applied, statistics is an invaluable tool for finding values of coefficients that best fit experimental data. However, caution is called for in two respects A good statistical correlation provides no guarantee that the equation or model used is indeed correct. In complex systems, the evaluation may converge on a false optimum. Also, primitive statistics programs do not distinguish between random scatter and systematic deviations. As an illustration, Figure 3.11 shows a comparison of two first-order concentration plots of data with approximately the same statistical deviation from... 

S.G. Shi, W. Taam, Non-linear canonical correlation analysis with a simulated annealing solution. Journal of Applied Statistics, 19 (1992) 155. 

Good results are obtained with the Kawabata approach, which measures several different mechanical properties of the fabric at the same time. The Kawabata evaluation system for fabrics uses four devices measuring the tensile and shearing, pure bending, and compressional properties, and surface characteristics of fabrics. Key parameters are the applied force, the rate of deformation, and the tension on the sample. By comparison with subjectively evaluated standards, statistical correlations can be drawn, leading to the objective quantification of fabric softness. The method, however, is too complex for routine work [26], Some other methods are reviewed by Mooney [52] ... 

The digital patient record will be the heart of future medicine, and such a record needs to be a little more conceptually structured. It should be a structure to which we can apply statistical methods because, if we can find correlations between things in many patient records, we can use them for diagnosis and prognosis for a specific patient and also for medical research. 

The ultimate development in the field of sample preparation is to eliminate it completely, that is, to make a chemical measurement directly without any sample pretreatment. This has been achieved with the application of chemometric near-infrared methods to direct analysis of pharmaceutical tablets and other pharmaceutical solids (74-77). Chemometrics is the use of mathematical and statistical correlation techniques to process instrumental data. Using these techniques, relatively raw analytical data can be converted to specific quantitative information. These methods have been most often used to treat near-infrared (NIR) data, but they can be applied to any instrumental measurement. Multiple linear regression or principal-component analysis is applied to direct absorbance spectra or to the mathematical derivatives of the spectra to define a calibration curve. These methods are considered secondary methods and must be calibrated using data from a primary method such as HPLC, and the calibration material must be manufactured using an equivalent process to the subject test material. However, once the calibration is done, it does not need to be repeated before each analysis. 

Application of statistical design techniques to develop correlations over a range of specific systems, equipment characteristics, and operating conditions. A computer is essential to apply the correlation equations to practical design cases. 

The book presents a well-defined procedure for adding or subtracting independent variables to the model variable and covers how to apply statistical forecasting methods to the serially correlated data characteristically found in clinical and pharmaceutical settings. The standalone chapters allow you to pick and choose which chapter to read first and hone in on the information that fits your immediate needs. Each example is presented in computer software format. The author uses MiniTab in the book but supplies instructions that are easily adapted for SAS and SPSSX, making the book applicable to individual situations. 

The apparent bulk that hair assumes after grooming is an important aesthetic characteristic often referred to as body, which can be considered a property associated with Robbins term style retention. Tolgyesi and co-workers (67) proposed the following definition of this hair assembly property Body is a measure of a hair mass s resistance to and recovery from externally induced deformation. This definition correlates well with the descriptive components springiness, volume, and stiffness that Wedderbum and Prall have obtained by applying statistical techniques to word association (58). The structural strength and resiliency of the hair mass are influenced by a number of independent parameters. Tolgyesi has identified the five most important parameters as fiber density... 

Another main parameter, which needs to be determined in equation (1), is the local axial velocity. Applying cross-correlation techniques to determine the speed of moving profiles had been widely demonstrated (Beck Plaskowski [5]) and the mathematical principle behind this technique is also documented in statistical literature such as Bendat Piersol [10]. The basic function of the cross-correlation technique is to find the time offset between two signals where the similarities are most obvious. These signals can be of any value and is not limited to quantitative conductivity data. A back-projection-type qualitafive reconstruction algorithm requires less computational resources and will suffice Kotre [11]. 

TABLE 3.38 The Parameters and Statistical Correlation Coefficients for the Residual-QSAR Algorithm of Eqs. (3.139) and (3.140), As Applied To the Molecules of Table 3.36 in All Possible Combinations of Variables (Putz, 2011a)... 

After an alignment of a set of molecules known to bind to the same receptor a comparative molecular field analysis CoMFA) makes it possible to determine and visuahze molecular interaction regions involved in hgand-receptor binding [51]. Further on, statistical methods such as partial least squares regression PLS) are applied to search for a correlation between CoMFA descriptors and biological activity. The CoMFA descriptors have been one of the most widely used set of descriptors. However, their apex has been reached. 

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