INDEX statistical methods

The effects of competition can be estimated by extending the statistical method introduced above for handling kinetic shifts [46]. This is accomplished by introducing a branching ratio for multiple channels indexed using j (Eq. 7) ... 

An analysis of the t(30) values, using multivariate statistical methods, has been carried out by Chastrette et al. [193]. According to this analysis, the x(30) values of non-HBD solvents are measures of the dipolarity and polarizability as well as the cohesion of the solvents. Another analysis of x(30) values in terms of functions of the dielectric constant sf and refractive index ( d) of forty non-HBD solvents has been given by Bekarek et al he emphasizes the predominant influence of the f(fir) term on the iix(30) parameter of those solvents [194]. For further correlations of the x(30) values with other empirical parameters of solvent polarity, see Section 7.6. 

Means of refractive indexes of various glass samples differ only slightly. Therefore, various statistical methods are used for comparison of glass samples when differences in their refractive indexes are being evaluated. Such methods enable... 

In Excel 97 and later versions you would click on Help, then select Contents and Index. This will give you three tabbed options first select Index, and type Analysis ToolPak (without the quotes). A number of choices appear, from which you can select general information . You are now offered three options Install and use Analysis ToolPak, Supplemental information about statistical methods and algorithms, and Ways to analyze statistics. Click on the first choice, and find out how to install the Analysis ToolPak. The same information would be available from Ways to analyze statistics. 

As indicated in the introdnction to this chapter, the freely available NIST/SEMATECH e-Handbook of Statistical Methods (available online at http //www.itl.nist.gov/div898/handbook/index.htm) is recommended as a resonrce for readers. This large handbook provides valuable information to engineers and scientists on the application of statistics to real-world problems. The main headings of its Table of Contents are as follows ... 

National Institute of Standards and Testing, Gaithersburg, MD, NIST/SEMATECH e-Handbook of Statistical Methods available online at http //www.itl.nist.gov/div898/handbook/index.htm accessed 22 May 2007. 

Because linkage mapping is a based on statistical methods, linkage maps are not guaranteed to show the correct order of markers. Therefore, it is important to be critical of the various available maps and to be aware of the statistical criteria that were used in map construction. Typically, only a subset of markers (framework or index markers) is mapped with high statistical support. The remainder are either placed into well-supported intervals or bins or placed into unique map positions but with low statistical support for order (see additional discussion below). 

After a product or a process has been appropriately evaluated in terms of its usefulness and adequacy in the manufacturing operation the evaluation of the resulting product in terms of its acceptability to the consumer remains to be done. This also should be done with the aid of statistical methods, since there is at present in many cases no substitute for the subjective evaluation of a quality attribute of a food product. Where they exist, objective methods are usually used in conjunction with subjective methods in an effort to correlate them, with a view to the ultimate use of the objective method as a simple and inexpensive index of the quality of the product in question. In terms of research, however, in many cases this may not be done because no objective methods of evaluation exist. A good example concerns the evaluation of the flavor of a food product where, with practically no exceptions, subjective evaluation must be used. 

Correlation methods discussed include basic mathematical and numerical techniques, and approaches based on reference substances, empirical equations, nomographs, group contributions, linear solvation energy relationships, molecular connectivity indexes, and graph theory. Chemical data correlation foundations in classical, molecular, and statistical thermodynamics are introduced. 

The comparison of the safety of equipment is not straightforward. It depends on several features of both process and equipment themselves. It can be evaluated from quantitative accident and failure data and from engineering practice and recommendations. Experience has been used for layout recommendations and for the development of safety analysis methods such as the Dow E F Index (Dow, 1987). Statistics contain details, causes and rates of failures of equipment and data on equipment involved in large losses. 

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