Statistical Correlation Analysis

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... 

Conduct statistical correlation analysis of these two sets of data. 

The calculation of characteristic values causes a high amount of values which contain redundant informations. Due to this the forth partial step will be to reduce this amount of values using extraction methods. This can be realized with statistical methods like cross correlation analysis. 

Correlation analysis reveals the interdependence between variables. The statistical measure for the interdependence is the correlation coefficient. 

Moin, R. and J. Kim, The structure of the vorticity field in turbulent channel flow. Rart 1. Analysis of instantaneous fields and statistical correlations. /. Fluid Mech., 1985.155 441 4. 

In most studies, phytoestrogen intake has been estimated by direct methods that evaluate food intake either by recall (food-frequency questionnaires -FFQs) or by record (food diary), and subsequently by composition databases based on information of this kind. Food-frequency questionnaires are widely administered to subjects involved in epidemiological studies. Their validity and reproducibility is considered sufficient when statistically correlated to data obtained from dietary records (a properly-completed and comprehensive food diary) and from analysis of blood and urine samples (Kirk et ah, 1999 Huang et al, 2000 Yamamoto et al, 2001 Verkasalo et al, 2001). FFQs can be repeated several times a year and may be administered to large populations. Such an approach provides an easy and low-cost method of assessing the... 

Simple correlational analysis of the NHANES II data by Harlan (1988) and Harlan et al. (1985) revealed statistically significant associations between PbB levels and systolic and diastolic blood pressure for both men and women, aged 12-74 years. Statistical analyses controlling for a number of other potentially confounding factors (e.g., age, race, and body mass index), however, indicated significant associations between PbB level and blood pressure only for the men. Based on these analyses, the effect of PbB concentration on blood pressure was estimated to be an increase in blood pressure of 7 mm Hg at PbB levels between 14 and 30 pg/dL. 

The results have been statistically processed by means of Spearman s non-parametrical correlation analysis and by multiple regression analysis to assess the complex effects induced by toxic and essential elements (Evstafyeva, Slusarenko, 2003 Evstafyeva et al., 2004). 

Another way for BOD estimation is the use of sensor arrays [37]. An electronic nose incorporating a non-specific sensor array of 12 conducting polymers was evaluated for its ability to monitor wastewater samples. A statistical approach (canonical correlation analysis) showed a linear relationship between the sensor responses and BOD over 5 months for some subsets of samples, leading to the prediction of BOD values from electronic nose analysis using neural network analysis. 

It should be emphasized that the deviations from the logarithmic correlation obey the normal distribution statistics, allowing one to apply convenient statistical procedures to analytical measurement results. As will be shown below, the logarithmic linear correlation rule was observed for all types of geo-chemical samples, i. e., snow, air, water, and soil. The correlation analysis of the elemental composition of melted-snow fractions showed with confidence level 95% that no significant discrepancy exists between the element composition within the correlation curves (see Table 1) and the corresponding variances are thus homogeneous for any two randomly chosen samples (i. e., points of the territory). 

Level B utilizes the principles of statistical moment analysis. The mean in vitro dissolution time is compared to either the mean residence time or the mean in vivo dissolution time. Like correlation Level A, Level B utilizes all of the in vitro and in vivo data, but unlike Level A it is not a point-to-point correlation because it does not reflect the actual in vivo plasma level curve. It should also be kept in mind that there are a number of different in vivo curves that will produce similar mean residence time values, so a unique correlation is not guaranteed. 

The first stage includes the selection of a dataset for QSAR studies and the calculation of molecular descriptors. The second stage deals with the selection of a statistical data analysis and correlation technique, either linear or nonlinear such as PLS or ANN. Many different algorithms and computer software are available for this purpose in all approaches, descriptors serve as independent variables and biological activities serve as dependent variables. 

Correlation functions are powerful tools in statistical physics, and in the above example they permit one to examine the behavior of a fluctuating system from a reference time back to previous times. Such fluctuations can occur in the concentration of two (or more) interconverting chemical species in dynamic equilibrium, and the technique of concentration correlation analysis permits one to determine the forward and reverse rate constants for their interconversion. See Concentration Correlation Analysis... 

A correlation analysis is a powerful tool used widely in various fields of theoretical and experimental chemistry. Generally, such an analysis, based on a statistically representative mass of data, can lead to reliable relationships that allow us to predict or to estimate important characteristics of still unknown molecular systems or systems unstable for direct experimental measurements. First, this statement concerns structural, thermodynamic, kinetic, and spectroscopic properties. For example, despite the very complex nature of chemical screening in NMR, particularly for heavy nuclei, various incremental schemes accurately predict their chemical shifts, thus providing a structural analysis of new molecular systems. Relationships for the prediction of physical or chemical properties of compounds or even their physiological activity are also well known. 

A more common use of informatics for data analysis is the development of (quantitative) structure-property relationships (QSPR) for the prediction of materials properties and thus ultimately the design of polymers. Quantitative structure-property relationships are multivariate statistical correlations between the property of a polymer and a number of variables, which are either physical properties themselves or descriptors, which hold information about a polymer in a more abstract way. The simplest QSPR models are usually linear regression-type models but complex neural networks and numerous other machine-learning techniques have also been used. 

Analysis of trends in transition metal chemical shifts was in most cases attempted by exploring statistical correlations with other observable spectroscopic quantities such as ligand atom chemical shifts or metal-ligand coupling constants... 

In a review article entitled How to get wrong results from good experimental data a survey of incorrect applications of regression , Exner offered some trenchant warnings which should be heeded by all those who engage in correlation analysis.133 Numerous examples are given from the literature, in which experimental data were processed in an incorrect way from the point of view of statistics. The results were more or less biased and sometimes completely wrong. 

Laurence51 has derived cr/ values (he uses the symbol correlation analysis of the carbonyl stretching frequencies of 4-substituted camphors in carbon tetrachloride. The value of 0.11 is given for the vinyl group, in good agreement with the reactivity-based values discussed above, in spite of the use of a non-polar medium. Laurence compares this with a statistical value of 0.06 from Taft and Topsom57, said to refer to effects on physical properties in either the gas phase or in hydrocarbon or similar solvents. 

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