Basic Descriptive Statistics

Table 1 presents basic descriptive statistics of obtained data. Finally, the stochastic sample was consisting of 2838 cases and the total number of obtained cases of all considered variables was equal to 23,967. However, there are many missing data, so in further study the set of 333 cases was considered. This set consists of these sample points for which the chloroform concentration at network point and at water treatment plant were given (laboratory analyzes are made according to the monitoring plan which takes into account high costs of gas chromatography). 

Table 1. Basic descriptive statistics of obtained data. 

Table 2 shows the basic descriptive statistics for PbB levels over time for both cohorts, classified by method of collection. 

London [11] was the first to describe dispersion forces, which were originally termed London s dispersion forces. Subsequently, London s name has been eschewed and replaced by the simpler term dispersion forces. Dispersion forces ensue from charge fluctuations that occur throughout a molecule that arise from electron/nuclei vibrations. They are random in nature and are basically a statistical effect and, because of this, a little difficult to understand. Some years ago Glasstone [12] proffered a simple description of dispersion forces that is as informative now as it was then. He proposed that,... 

Application of statistics in expert systems is a topic that fills more than a single book. However, some of the investigations presented in the next chapters are based on methods of descriptive statistics. The terms and basic concepts of importance for the interpretation of these methods should be introduced first. Algorithms and detailed descriptions can be found in several textbooks [43-47]. 

AiVhen doing measurements, statistics are needed if we want to describe the data (descriptive statistics) or if we want to draw conclusions based on the data (inferential statistics). There is a vast amount of statistical methods in the literature, and the choice of method depends on what we want to know and what type of data we have. In this chapter, we will give an overview of the most basic and the most relevant methods for... 

The most basic step in statistical analysis of a data set is to describe it descriptively, that is, to compute properties associated with the data set and to display the data set in an informative manner. A data set consists of a finite number of samples or data points. In this book, a data set will be denoted using either set notation, that is, jti, X2,..., x or vector notation, that is, as if = (x],jC2,..., x ). Set notation is useful for describing and listing the elements of a data set, while vector notation is useful for mathematical manipulation. The size of the data set is equal to n. The most common descriptive statistics include measures of central tendency and dispersion. 

The results from different studies carried out independently, or in collaboration, can be combined statistically by meta-analysis. Meta-analysis is the quantitative cumulation and analysis of descriptive statistics across studies (Hunter et al, 1982). Although methods for combining probabilities across studies have been available for some years, the methods and techniques of meta-analysis are recent, and have been developed within the last decade, mostly for experimental or quasi-experimental studies. The basic statistic of meta-analysis is d, which is computed as the difference between group means, divided by the pooled within-group standard deviation. 

A microscopic description characterizes the structure of the pores. The objective of a pore-structure analysis is to provide a description that relates to the macroscopic or bulk flow properties. The major bulk properties that need to be correlated with pore description or characterization are the four basic parameters porosity, permeability, tortuosity and connectivity. In studying different samples of the same medium, it becomes apparent that the number of pore sizes, shapes, orientations and interconnections are enormous. Due to this complexity, pore-structure description is most often a statistical distribution of apparent pore sizes. This distribution is apparent because to convert measurements to pore sizes one must resort to models that provide average or model pore sizes. A common approach to defining a characteristic pore size distribution is to model the porous medium as a bundle of straight cylindrical or rectangular capillaries (refer to Figure 2). The diameters of the model capillaries are defined on the basis of a convenient distribution function. 

This expression has a formal character and has to be complemented with a prescription for its evaluation. A priori, we can vary the values of the fields independently at each point in space and then we deal with uncountably many degrees of freedom in the system, in contrast with the usual statistical thermodynamics as seen above. Another difference with the standard statistical mechanics is that the effective Hamiltonian has to be created from the basic phenomena that we want to investigate. However, a description in terms of fields seems quite natural since the average of fields gives us the actual distributions of particles at the interface, which are precisely the quantities that we want to calculate. In a field-theoretical approach we are closer to the problem under consideration than in the standard approach and then we may expect that a simple Hamiltonian is sufficient to retain the main features of the charged interface. A priori, we have no insurance that it... 

This chapter contains the algorithms necessary for approximating statistical tables, some program kernels in BASIC, instructions on how to install the VisualBasic programs, and finally, a description of each of the VB programs and the Excel files. 

At a later stage, the basic model was extended to comprise several organic substrates. An example of the data fitting is provided by Figure 8.11, which shows a very good description of the data. The parameter estimation statistics (errors of the parameters and correlations of the parameters) were on an acceptable level. The model gave a logical description of aU the experimentally recorded phenomena. 

In physical chemistry the most important application of the probability arguments developed above is in the area of statistical mechanics, and in particular, in statistical thermodynamics. This subject supplies the basic connection between a microscopic model of a system and its macroscopic description. The latter point of view is of course based on the results of experimental measurements (necessarily carried out in each experiment on a very large number of particle ) which provide the basis of classical thermodynamics. With the aid of a simple example, an effort now be made to establish a connection between the microscopic and macroscopic points of view. 

This chapter will describe how we can apply an understanding of thermodynamic behavior to the processes associated with polymers. We will begin with a general description of the field, the laws of thermodynamics, the role of intermolecular forces, and the thermodynamics of polymerization reactions. We will then explore how statistical thermodynamics can be used to describe the molecules that make up polymers. Finally, we will learn the basics of heat transfer phenomena, which will allow us to understand the rate of heat movement during processing. 

The main concept addressed in this new multi-part series is the idea of correlation. Correlation may be referred to as the apparent degree of relationship between variables. The term apparent is used because there is no true inference of cause-and-effect when two variables are highly correlated. One may assume that cause-and-effect exists, but this assumption cannot be validated using correlation alone as the test criteria. Correlation has often been referred to as a statistical parameter seeking to define how well a linear or other fitting function describes the relationship between variables however, two variables may be highly correlated under a specific set of test conditions, and not correlated under a different set of experimental conditions. In this case the correlation is conditional and so also is the cause-and-effect phenomenon. If two variables are always perfectly correlated under a variety of conditions, one may have a basis for cause-and-effect, and such a basic relationship permits a well-defined mathematical description. 

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