Data analysis 2-statistics

Sigmund Brandt, Glen Gowan. Data Analysis Statistical and Computational Methods for Scientists and Engineers (3rd edition). Springer 1998... 

FIGURE 14.2 (See color insert following page 114.) Components of transactional and data analysis (statistical and cheminformatics) environment in the context of HTS campaign. 

Whereas the results in this section could probably be obtained fairly easily by inspecting the original data, numerical values of class membership have been obtained which can be converted into probabilities, assuming that the measurement error is normally distributed. In most real situations, there will be a much larger number of measurements, and discrimination (e.g. by spectroscopy) is not easy to visualise without further data analysis. Statistics such as %CC can readily be obtained from the data, and it is also possible to classify unknowns or validation samples as discussed in Section 4.5.1 by this means. Many chemometricians use the Mahalanobis distance as defined above, but the normal Euclidean distance or a wide range of other measures can also be employed, if justified by the data, just as in cluster analysis. 

The reports often include extensive data analysis, statistical summaries, and plots. The mean of all results or the mean of results from peer laboratories (those performing the test with similar methods) is taken as the target value and is used for comparison with the individual laboratory s result. Different programs do this in different ways. For example, the statistical significance of any difference between an individual laboratory s observed result and the group mean can be tested by use of the t-test. When the difference is significant, the laboratory is alerted that its results are biased compared with the results of most of the other laboratories. Another approach is to divide the difference by the overall standard deviation of the group, and then to express the difference in terms of the number of standard deviations... 

Adverse event reporting Trial medication Premature withdrawal Subject replacement policy Criteria for excluding data Data analysis/statistical methods Quality control/assurance Data handling and record keeping Ethics (e.g. IRB/IEC approval)... 

Haseman, J. K. (1995). Data analysis Statistical analysis and use of historical control data. Regul Toxicol Pharmacol 21, 52-59 discussion 81-86. 

Helsel - Nondetects and Data Analysis Statistics for Censored Environmental Data... 

Some bioinformatics software tools for proteomics combine data analysis, statistics and artificial intelligence methods to manage MS data, to identify proteins and to update databases. In this section, specific tools used to identify proteins are reviewed. They use lists of peptide mass values from MS or MS/MS as input, and they may also combine this information with amino acid sequence tag information or amino acid composition to enhance the identification of proteins. Figure 6 shows a simplified flow chart of sample preparation and MS data collection. It also shows the techniques and tools for protein identification described in this section. 

Helsel D. Nondetects and data analysis. Statistics for censored environmental data. New York John WUey 2005. 

Carlin, B.P. and T.A. Louis 1997. Bayes and Empirical Bayes Methods for Data Analysis. Statistics Computing Series, Springer, New York. 

For example, the objects may be chemical compounds. The individual components of a data vector are called features and may, for example, be molecular descriptors (see Chapter 8) specifying the chemical structure of an object. For statistical data analysis, these objects and features are represented by a matrix X which has a row for each object and a column for each feature. In addition, each object win have one or more properties that are to be investigated, e.g., a biological activity of the structure or a class membership. This property or properties are merged into a matrix Y Thus, the data matrix X contains the independent variables whereas the matrix Ycontains the dependent ones. Figure 9-3 shows a typical multivariate data matrix. 

The data analysis module of ELECTRAS is twofold. One part was designed for general statistical data analysis of numerical data. The second part offers a module For analyzing chemical data. The difference between the two modules is that the module for mere statistics applies the stati.stical methods or rieural networks directly to the input data while the module for chemical data analysis also contains methods for the calculation ol descriptors for chemical structures (cl. Chapter 8) Descriptors, and thus structure codes, are calculated for the input structures and then the statistical methods and neural networks can be applied to the codes. 

Data input for both modules can be done via file upload, whereby the module for mere statistics reads in plain ASCI I files and the module For chemical data analysis takes the chemical structures in the Form of SD-files (cf. Chapter 2) as an input. In... 

Easy and intuitive data analysis The data analysis process is easy and intuitive, because the pattern recognition only requires the knowledge and intuition of the scientists. DifEcult statistical and mathematical methods are not necessary. 

In general, the first step in virtual screening is the filtering by the application of Lipinski s Rule of Five [20]. Lipinski s work was based on the results of profiling the calculated physical property data in a set of 2245 compounds chosen from the World Drug Index. Polymers, peptides, quaternary ammonium, and phosphates were removed from this data set. Statistical analysis of this data set showed that approximately 90% of the remaining compounds had ... 

Graham R C 1993. Data Analysis for the Chemical Sciences. A Guide to Statistical Techniques. New York, VCH Publishers. 

Moore, D. S., Statistics Concepts and Controversies, W. H. Freeman, New York, 1985. MuUiolland, H., and C. R. Jones, Fundamentals of Statistics, Plenum Press, New York, 1968. Taylor, J. K., Statistical Techniques for Data Analysis, Lewis, Boca Raton, FL, 1990. 

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. 

A more comprehensive discussion of the analysis of data, covering all topics considered in this chapter as well as additional material, can be found in any textbook on statistics or data analysis following are several such texts. 

J. Davis, Statistics and Data Analysis in Geology, 2nd ed., John Wiley Sons, Inc., New York, 1986. 

Evidence of the appHcation of computers and expert systems to instmmental data interpretation is found in the new discipline of chemometrics (qv) where the relationship between data and information sought is explored as a problem of mathematics and statistics (7—10). One of the most useful insights provided by chemometrics is the realization that a cluster of measurements of quantities only remotely related to the actual information sought can be used in combination to determine the information desired by inference. Thus, for example, a combination of viscosity, boiling point, and specific gravity data can be used to a characterize the chemical composition of a mixture of solvents (11). The complexity of such a procedure is accommodated by performing a multivariate data analysis. 

Chapter 7 (by H. Ishida and A Ishitani) review microscopic and surface analytical techniques. Chapter 8 (by D. M. Haaland) reviews developments in statistical chemometrics for data analysis. 

In this review we put less emphasis on the physics and chemistry of surface processes, for which we refer the reader to recent reviews of adsorption-desorption kinetics which are contained in two books [2,3] with chapters by the present authors where further references to earher work can be found. These articles also discuss relevant experimental techniques employed in the study of surface kinetics and appropriate methods of data analysis. Here we give details of how to set up models under basically two different kinetic conditions, namely (/) when the adsorbate remains in quasi-equihbrium during the relevant processes, in which case nonequilibrium thermodynamics provides the needed framework, and (n) when surface nonequilibrium effects become important and nonequilibrium statistical mechanics becomes the appropriate vehicle. For both approaches we will restrict ourselves to systems for which appropriate lattice gas models can be set up. Further associated theoretical reviews are by Lombardo and Bell [4] with emphasis on Monte Carlo simulations, by Brivio and Grimley [5] on dynamics, and by Persson [6] on the lattice gas model. 

This expression constitutes an improvement. There are two advantages. First, the statistical reliability of the data analysis improves, because the variance in [A] is about constant during the experiment, whereas that of the quantity on the left side of Eq. (3-27) is not. Proper least-squares analysis requires nearly constant variance of the dependent variable. Second, one cannot as readily appreciate what the quantity on the left of Eq. (3-27) represents, as one can do with [A]t. Any discrepancy can more easily be spotted and interpreted in a display of (A] itself. 

Sec. 820.50 Statistical techniques - Use appropriate statistical methods for data analysis and... 

A good model is consistent with physical phenomena (i.e., 01 has a physically plausible form) and reduces crresidual to experimental error using as few adjustable parameters as possible. There is a philosophical principle known as Occam s razor that is particularly appropriate to statistical data analysis when two theories can explain the data, the simpler theory is preferred. In complex reactions, particularly heterogeneous reactions, several models may fit the data equally well. As seen in Section 5.1 on the various forms of Arrhenius temperature dependence, it is usually impossible to distinguish between mechanisms based on goodness of fit. The choice of the simplest form of Arrhenius behavior (m = 0) is based on Occam s razor. 

Prediction of the useful life, or the remaining life, of coatings from physical or analytical measurements presents many problems in data analysis and interpretation. Two important considerations are that data must be taken over a long period of time, and the scatter from typical paint tests is large. These considerations require innovative application of statistical techniques to provide adequate prediction of the response variables of interest. 

Figure 21.3 Modeling and simulation in the general context of the study of xenobiot-ics. The network of signals and regulatory pathways, sources of variability, and multistep regulation that are involved in this problem is shown together with its main components. It is important to realize how between-subject and between-event variation must be addressed in a model of the system that is not purely structural, but also statistical. The power of model-based data analysis is to elucidate the (main) subsystems and their putative role in overall regulation, at a variety of life stages, species, and functional (cell to organismal) levels. Images have been selected for illustrative purposes only. See color plate.

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