Statistical methods terminology

Table 5.1 Definition of Some Basic Terminology Relating to the Statistical Method...

As in all analytical determinations, the potential for uncertainties affecting results of a testing laboratory from sources outside the laboratory and outside the applied method must be understood and may not be underestimated (Iyengar 1981 Zeisler 1986). According to the ISO terminology, the uncertainties can be divided into Type A (uncertainties evaluated by statistical methods) and Type B (all other). The Type A terms are dependent mostly on the amount and the reaction cross section of the analyte. In the context of this chapter, only the method-specific sources of uncertainty will be treated, with the main emphasis on NAA. 

Probability distribution was introduced in the section in this chapter on Terminology, and the components of a normal distribution and how to work with them were discussed. Some distributions are not normal because they are skewed to one side of the mode. Unless the values can be treated by some mathematical function to yield a new set of values that approximates a normal distribution, the use of normal statistical techniques could lead to erroneous conclusions. Sometimes the distribution is skewed in such a way that the logarithms of the values have a normal distribution. Fortunately, although the values are not amenable to standard statistical methods, their logarithms are. In contrast, maximum pit depths have an extreme value distribution and should be treated with extreme value statistics. We wUl discuss these three distributions. 

You may be surprised that for our example data from Miller and Miller ([2], p. 106), the correlation coefficient calculated using any of these methods of computation for the r-value is 0.99887956534852. When we evaluate the correlation computation we see that given a relatively equivalent prediction error represented as (X - X), J2 (X - X), or SEP, the standard deviation of the data set (X) determines the magnitude of the correlation coefficient. This is illustrated using Graphics 59-la and 59-lb. These graphics allow the correlation coefficient to be displayed for any specified Standard error of prediction, also occasionally denoted as the standard error of estimate (SEE). It should be obvious that for any statistical study one must compare the actual computational recipes used to make a calculation, rather than to rely on the more or less non-standard terminology and assume that the computations are what one expected. 

For the statistical copolymer the distribution may follow different statistical laws, for example, Bemoullian (zero-order Markov), first- or second-order Markov, depending on the specific reactants and the method of synthesis. This is discussed further in Secs. 6-2 and 6-5. Many statistical copolymers are produced via Bemoullian processes wherein the various groups are randomly distributed along the copolymer chain such copolymers are random copolymers. The terminology used in this book is that recommended by IUPAC [Ring et al., 1985]. However, most literature references use the term random copolymer independent of the type of statistical distribution (which seldom is known). 

As with many terms used in the section, the term robust is often used differently by statisticians, relative to use by other scientists. In statistical terminology, the term robust denotes that a procedure will perform well under different situations (not only if a single particular model is assumed to be true). Often the term refers to outlier resistance, particularly relative to methods that are optimal under normality assumptions. 

Statistical data analysis methods have made it possible to identify and address HTS measurement errors (Zhang, Chung, and Oldenburg, 1999 Malo et al., 2006). Within-plate and assay-wide controls are required to monitor quality by plate and stability over an entire screening run. Terminology... 

Before investigating these methods briefly, it will be necessary to become familiar with the terminology which is used in this particular application of statistical analysis. (The terminology is not always very meaningful in industrial problems since the early work in this area was originally developed in agricultural experimentation.)... 

It is impossible to conduct an infinite number of extractions of a speciman to determine the accuracy of a method. As a result, we estimate the accuracy of an assay by performing a finite number of extractions (n) on the specimen. We report the accuracy as the mean (x- = Hxifn, i = 1,2,. ..,n) of the multiple determinations, expressed as a percent of the known concentration. The finite group of determinations is a sample from the population, and its mean is referred to as the sample mean. The sample mean is a statistic that estimates the population parameter p. If we could obtain the means from an infinite number of same-size samples, regardless of their size, then the mean of these infinite sample means would equal p. In statistical terminology, we say that the sample mean is an unbiased estimator of the population mean. Unbiasedness is a... 

Nonlinear dynamics of complex processes is an active research field with large numbers of publications in basic research and broad applications from diverse fields of science. Nonlinear dynamics as manifested by deterministic and stochastic evolution models of complex behaviour has entered statistical physics, physical chemistry, biophysics, geophysics, astrophysics, theoretical ecology, semiconductor physics and -optics etc. This research has induced a new terminology in science connected with new questions, problems, solutions and methods. New scenarios have emerged for spatio-temporal structures in dynamical systems far from equilibrium. Their analysis and possible control are intriguing and challenging aspects of the current research. 

In order to evaluate the delay-time data of a production lot, it is necessary to delve into the methods and the terminology of statistics, of which a few highlights will be given here. 

Many objections against the usefulness of pattern recognition methods for chemical problems are legitimated because the statistical evaluation was performed unsatisfactorily in many papers. Further confusions result from a non-uniform terminology (Chapter 11.5). An objective mathematical evaluation of classifiers is an absolute necessary prerequisite to a further application to actual classification problems. 

It might be pointed out here that secular equations are important in many other fields, such as quantum mechanics, electrical and mechanical engineering, astronomy, and statistics. The methods described below are applicable no matter what the source of the equation. For this reason, it will prove desirable in Sec. 9-1 to introduce some terminology and principles common to all secular equations. Section 9-2 gives a method for reducing the secular determinant to a symmetrical form which is frequently desirable, while Secs. 9-3 and 9-4 deal with methods of solution appropriate in case only the frequencies, and not the transformations to normal coordinates, are required. Following this. Secs. 9-5 to 9-7 deal with methods appropriate when both the frequencies and forms of the normal modes are desired. The remaining sections include discussions of machines which can be used to solve the problem. 

Although calibrating or classifying spectra are merely two different applications of the mathemati-cal/statistical technique of regression, historically they have evolved independently, with different goals and requirements. Whenever possible attempts will be made to connect the two by drawing attention to common concepts and methods that only differ in their terminology and emphasis. Occasionally, for the sake of simplicity in presentation, discussion will cover certain aspects and peculiarities of the two disciplines separately. 

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