Data and Statistical Methods

Statistical handling of data and statistical methods (3) cyber infrastructure (data preservation, processing, access) (9) theory and modeling of scaling (4)... 

The probabilistic nature of a confidence interval provides an opportunity to ask and answer questions comparing a sample s mean or variance to either the accepted values for its population or similar values obtained for other samples. For example, confidence intervals can be used to answer questions such as Does a newly developed method for the analysis of cholesterol in blood give results that are significantly different from those obtained when using a standard method or Is there a significant variation in the chemical composition of rainwater collected at different sites downwind from a coalburning utility plant In this section we introduce a general approach to the statistical analysis of data. Specific statistical methods of analysis are covered in Section 4F. 

Documentation of experimental method so that work can be reproduced at a later time Appropriate data handling statistical methods conclusions based on fact, supportable by data Define and execute critical experiments to prove or disprove hypothesis Mechanistic or fundamental interpretation of data preferred Communication of Conclusions to Incorporate Technical Learning in Organization Experimental W rk Done in Support of New or Existing Processes Should be Captured in Process Models... 

Unknown Statistical Distributions Sixth, despite these problems, it is necessaiy that these data be used to control the plant and develop models to improve the operation. Sophisticated numerical and statistical methods have been developed to account for random... 

Population pharmacokinetics is the application of pharmacokinetic and statistical methods to sparse data to derive a pharmacokinetic profile of central tendency. 

Obtaining a good quality QSAR model depends on many factors, such as the quality of biological data and the choice of descriptors and statistical methods. As a consequence, the uncertainty of the QSAR predictions is a combination of experimental uncertainties and model uncertainties. QSAR methods have to be applied to individual chemicals, not on mixtures. If the QSAR demands it, the components of the mixture have to be addressed separately and individually - in case of unknown compounds, QSAR cannot identify the toxicity risk and is therefore not useful. 

Chemometrics is the chemical discipline that uses mathematical and statistical methods select optimal measurement procedures and experiments, and (b) to provide maximum chemical information by analyzing chemical data."(I)... 

A probabilistic risk assessment (PRA) deals with many types of uncertainties. In addition to the uncertainties associated with the model itself and model input, there is also the meta-uncertainty about whether the entire PRA process has been performed properly. Employment of sophisticated mathematical and statistical methods may easily convey the false impression of accuracy, especially when numerical results are presented with a high number of significant figures. But those who produce PR As, and those who evaluate them, should exert caution there are many possible pitfalls, traps, and potential swindles that can arise. Because of the potential for generating seemingly correct results that are far from the intended model of reality, it is imperative that the PRA practitioner carefully evaluates not only model input data but also the assumptions used in the PRA, the model itself, and the calculations inherent within the model. This chapter presents information on performing PRA in a manner that will minimize the introduction of errors associated with the PRA process. 

Chemometrics has been defined as the application of mathematical and statistical methods to chemical measurements, in particular in providing maximum chemical information through the analysis of chemical data. Because of the enormous increase in generating analytical data, analytical chemists were among the first to use chemometrical methods extensively. 

Giodici, P. (2003), Applied Data Mining. Statistical Methods for Business and Industry, Wiley, Hoboken, NJ. 

Classes of Estimation Methods Table 1.1.1 summarizes the property estimation methods considered in this book. Quantitative property-property relationships (QPPRs) are defined as mathematical relationships that relate the query property to one or several properties. QPPRs are derived theoretically using physicochemical principles or empirically using experimental data and statistical techniques. By contrast, quantitative structure-property relationships (QSPRs) relate the molecular structure to numerical values indicating physicochemical properties. Since the molecular structure is an inherently qualitative attribute, structural information has first to be expressed as a numerical values, termed molecular descriptors or indicators before correlations can be evaluated. Molecular descriptors are derived from the compound structure (i.e., the molecular graph), using structural information, fundamental or empirical physicochemical constants and relationships, and stereochemcial principles. The molecular mass is an example of a molecular descriptor. It is derived from the molecular structure and the atomic masses of the atoms contained in the molecule. An important chemical principle involved in property estimation is structural similarity. The fundamental notion is that the property of a compound depends on its structure and that similar chemical stuctures (similarity appropriately defined) behave similarly in similar environments. 

To conclude, the stochastic and error-influenced character of environmental data requires the use of mathematical and statistical methods for further analysis. 

In order to correctly design analytical procedures used for the detection of food allergens, it is necessary to have basic knowledge of food product chemistry to know how to collect, prepare, and store food samples to be able to fragment, mix, disintegrate, and extract samples to know (or be able to find quickly) relevant food quality standards and admissible contents of particular food ingredients and finally to understand precision of determinations, their sensitivity, and detection threshold levels, reproducibility, and errors of determination methods. In addition, it is essential to be able to gather the results of assays, process them with the aid of a computer and statistical methods, and to present the analytically derived data. 

Obtaining a good quality QSAR model depends heavily on many factors in the approach, particularly on the quality of biological data, descriptor selection, and statistical methods (see Chapter 19 for more details). Given the fact that any QSAR approach has strengths and weaknesses, the careful selection of a specific model, or a combination of models, also needs to be emphasized, and is often specific to the particular application in question. 

The terms bioinformatics and cheminformatics refer to the use of computational methods in the study of biology and chemistry. Information from DNA or protein sequences, protein structure, and chemical structure is used to build models of biochemical systems or models of the interaction of a biochemical system with a small molecule (e.g., a drug). There are mathematical and statistical methods for analysis, public databases, and literature associated with each of these disciplines. However, there is substantial value in considering the interaction between these areas and in building computational models that integrate data from both sources. In the most... 

Duboudin C, Ciffroy P, Magaud H. 2004. Effects of data manipulation and statistical methods on species sensitivity distributions. Environ Toxicol Chem 23 489-499. 

William J. Welch is Professor in the Department of Statistics, University of British Columbia. His research interests include design and analysis of computer experiments, quality improvement, data mining, and statistical methods for drug discovery. 

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