Statistics quantitative data

Statistics represents a body of knowledge which enables one to deal with quantitative data reflecting any degree of uncertainty. There are six basic aspects of apphed statistics. These are ... 

Random Variables Applied statistics deals with quantitative data. In tossing a fair coin the successive outcomes woula tend to be... 

Random Variables Applied statistics deals with quantitative data. In tossing a fair coin the successive outcomes would tend to be different, with heads and tails occurring randomly over a period of time. Given a long strand of synthetic fiber, the tensile strength of successive samples would tend to vary significantly from sample to sample. 

This chapter has outlined specifically how quantitative data on somewhat idealized reaction systems can be used as a basis for demonstrating the validity of our empirical electronic models in the field of reactivity. The multiparameter statistical models derived for the systems studied (PA, acidity, etc.) have limited direct application in EROS themselves. The next section develops the theme of applying the models in a much more general way, leading up to general reactivity prediction in EROS itself. 

Deaths from cancer of the stomach were statistically elevated in one study of six manufacturing plants in the United Kingdom involved in the polymerization of acrylonitrile and the spinning of acrylic fibers (Werner and Carter 1981). No quantitative data on the exposure levels to acrylonitrile were given and the numbers of expected deaths was too small to provide confidence in the results. 

The comparison of the safety of equipment is not straightforward. It depends on equipment themselves and process conditions. Equipment safety can be evaluated from quantitative accident and failure data and from engineering practice and recommendations. Experience-based information is found from layout recommendations and safety analysis methods such as the Dow E F Index (1987). Quantitative data can be found from accident and operational statistics. It should be remembered that all reliability or failure information does not express safety directly, since all failures are not dangerous and not all accidents are due to failures of equipment. 

Because these pyrograms are derived statistically from data on coals with a range of thermal properties and whose petrographic specifications are subject to considerable experimental uncertainty (29), they are quantitatively Imprecise and can be interpreted only in a broad qualitative manner. 

In this way, the fault tree can be quantified, which makes this technique very powerful for the reliability analysis of protection systems. The prerequisite is the availability of statistical reliability data of the different devices and instruments that is often difficult to obtain for multi-purpose plants, where devices can be exposed to very different conditions when changing from one process to another. Nevertheless, if the objective is to compare different designs, semi-quantitative data are sufficient. 

Response Surface Methodology (RSM) is a statistical method which uses quantitative data from appropriately designed experiments to determine and simultaneously solve multi-variate equations (3). In this technique regression analysis is performed on the data to provide an equation or mathematical model. Mathematical models are empirically derived equations which best express the changes in measured response to the planned systematic... 

Over the past 60 years a multitude of means have been used to capture SARs. We can broadly divide them into two groups those based on statistical or data mining methods (e.g., regression models) and those based on physical approaches (e.g., pharmacophore models). For a comprehensive review of quantitative structure-activity relationship (QSAR) methodologies the reader is referred... 

The Contract Laboratory Statistical Database reports that acrolein was detected in soil at 1 of 357 hazardous waste sites in the United States, at a mean concentration of 6.5 ppb (VIAR 1987). The National Priority List Technical Data Base (View 1989) indicates that acrolein was detected at 5 of 1177 National Priority List (NPL) sites however, the database does not contain media concentration data. Acrolein was identified in sediment/soil/water samples collected from Love Canal in Niagara Falls, NY (Hauser and Bromberg 1982) however, no quantitative data were available. 

Locomotor activity can be quantified in rodents by a variety of means. The method described below uses interruptions of photoelectric beams. The difference between Irwin estimations of drug effects on spontaneous activity and activity meter tests is mainly a question of quantification. Activity meter tests are generally carried out using automated apparatus with a larger number of animals, and are therefore less labor intensive but permit more precise statistical analyses. The quantitative data obtained enable the generation of dose-response curves and more precise estimations of the minimal effective dose (MED) or the dose which increases or decreases locomotion by 50 % (ED50). 

Histology may be reported in descriptive terms, evaluated by a semi-quantitative methods, or by computer-assisted histomorphometric methods. This information then can be used for quantitative statistical analysis. For the very specific add-on methods of in situ hybridization and gene expression, a description of the observed changes is generally appropriate together with quantitative data generated by computer-assisted analysis of gene expression profiles. 

For S3nnmetrical frequency distributions of quantitative data, an ideal measure of dispersion would take into account each value s deviation from the mean and provide a measure of the average deviation from the mean. Two such statistics are the sample variance, which is the sum of squared deviations from the mean (X (T— Yf) divided by — 1 (where n is the number of data values), and the sample standard deviation, which is the positive square root of the sample variance. 

Although considerable progress has been made in the metabolic profile approach, a number of problems remain to be overcome. Many of these centre around the fluctuations in component composition, not from metabolic disorders, but brought about by other influences. These are principally due to diet and the metabolic variations in individuals in relation to activity. Drugs can also affect the excretion levels of compounds, in addition to the production of their own metabolites. These factors all make quantitative data difficult to obtain and evaluate. Careful statistical analysis of the results are necessary and a population of 500 subjects, grouped in age and sex, has been studied with a view to obtaining a suitable data base for urinary organic acids [370]. 

Lowe et aL ) did not carry out a statistical analysis of the relative number of microcells and their size distribution in the bulk of the materiaL It should be mentioned, however, that they do not consider microcells as the most frequently occurring group of cells, i.e. as a morphological system, in contrast to our views. For a discussion of the difference in quantitative data see Chap. 5.3). 

Although extraction is one of the oldest procedures of organic chemistry, it is usually applied in such a manner that results only approximate in nature are obtained. Purity studies require quantitative data. Particularly in biological circles, it has been appreciated for some time that if enough cases are at hand, the results can be treated statistically and thereby greater precision achieved. Therefore, multiple extractions were performed in countercurrent manner so that the steps of the binomial expansion were exactly followed (see Fractionation Theory p. 292). Tliis permitted the mathematics of probability to be applied in the... 

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