Statistical methods data analysis

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. 

Polynomial regression with indicator variables is another recommended statistical method for analysis of fish-mercury data. This procedure, described by Tremblay et al. (1998), allows rigorous statistical comparison of mercury-to-length relations among years and is considered superior to simple hnear regression and analysis of covariance for analysis of data on mercury-length relations in fish. 

A general comment that affects all statistical multivariate data analysis techniques, namely that each of the variables should be given equal chance to influence the outcome of the analysis. This can be achieved by scaling the variables in appropriative way. One popular method for scaling variables is autoscaling, whereby the variance of each variable is adjusted to 1. 

Keil, D. et al., Evaluation of multivariate statistical methods for analysis and modeling of immunotoxicology data, Toxicol. Sci. 51, 245, 1999. 

The most commonly employed univariate statistical methods are analysis of variance (ANOVA) and Student s r-test [8]. These methods are parametric, that is, they require that the populations studied be approximately normally distributed. Some non-parametric methods are also popular, as, f r example, Kruskal-Wallis ANOVA and Mann-Whitney s U-test [9]. A key feature of univariate statistical methods is that data are analysed one variable at a rime (OVAT). This means that any information contained in the relation between the variables is not included in the OVAT analysis. Univariate methods are the most commonly used methods, irrespective of the nature of the data. Thus, in a recent issue of the European Journal of Pharmacology (Vol. 137), 20 out of 23 research reports used multivariate measurement. However, all of them were analysed by univariate methods. 

Caulcutt, R., Boddy, R. Statistics for Analytical Chemists, Chapman and Hall, London, 1983 Chatfield, C., Collins, A.J. Introduction to Multivariate Analysis, Chapman and Hall, London, 1989 Davis, J. C. Statistics and Data Analysis in Geology, 2nd Ed., Wiley, New York, 1986 Dillon, W.R., Goldstein, M. Multivariate Analysis Methods and Applications, Wiley, New York, Chichester, Brisbane, Toronto, Singapore, 1984... 

Another type of classification is outlier selection or contamination identification. As an example, in Fig. 4.23(b), the butter is the desired material and bacteria the contamination. An arbitrary threshold for this image would be 0.02, in which all pixels >0.02 are considered suspect, and hopefully, because this is a food product, decontamination procedures are pursued. In these two examples of classification, only arbitrary thresholds have been defined and, as such, confidence in these classifications is lacking. This confidence can be achieved through statistical methods. Although this chapter is not the appropriate place for an involved discussion of application of statistics toward data analysis, we will give one example often used in chemometric classification. 

There is an analysis of the results of the study adequate to assess the effects of the drug. The report of the study should describe the results and the analytic methods used to evaluate them, including any appropriate statistical methods. The analysis should assess, among other things, the comparability of test and control groups with respect to pertinent variables, and the effects of any interim data analyses performed. 

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... 

A different approach to mathematical analysis of the solid-state C NMR spectra of celluloses was introduced by the group at the Swedish Forest Products Laboratory (STFI). They took advantage of statistical multivariate data analysis techniques that had been adapted for use with spectroscopic methods. Principal component analyses (PCA) were used to derive a suitable set of subspectra from the CP/MAS spectra of a set of well-characterized cellulosic samples. The relative amounts of the I and I/3 forms and the crystallinity index for these well-characterized samples were defined in terms of the integrals of specific features in the spectra. These were then used to derive the subspectra of the principal components, which in turn were used as the basis for a partial least squares analysis of the experimental spectra. Once the subspectra of the principal components are validated by relating their features to the known measures of variability, they become the basis for analysis of the spectra of other cellulosic samples that were not included in the initial analysis. Here again the interested reader can refer to the original publications or the overview presented earlier. ... 

Clinical Simulation Studies. These protocols allow assessment of each of the characteristics of the proposed indications described in Table 4 [27] and include the basic principles articulated by the Antimicrobial I Panel (Table 2). The design is also based on reviewer experiences gained from the development of topical antibiotic and antimicrobial drug products through the NDA process. Examples of changes or recommendations include the incorporation of a positive control to validate the performance of the study, a test product vehicle arm, and proposed statistical methods of analysis to evaluate the data. Studies must be... 

Accurate measurement of monomer reactivity ratios requires a large amount of experimental work and the use of statistically valid data analysis methods. This subject is beyond the scope of this chapter and the reader is referred to recent reviews for details of the different procedures available and their relative merits [3,5,6]. 

The four Py-MS spectra — for pollen, bee feces, and two of the unknowns — presented as a figure in this report (but not shown in this chapter) clearly showed distinct differences, but the authors found that the complexity present in the 93 spectra made visual classification of the samples impossible. A discussion of the data analysis techniques used for the classification of these samples is beyond the scope of this chapter, but a brief summary of the results can be made. (Those readers with interest in statistical methods for analysis of data generated by analytical pyrolysis-mass spectrometry should find this paper interesting and may also want to read more recent work in this area. - )... 

Comparisons between means (and standard deviations) can be extended to the study of three or more sets of data. Such comparisons require the very important statistical method called analysis of variance (ANOVA). 

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. 

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. 

The previously mentioned data set with a total of 115 compounds has already been studied by other statistical methods such as Principal Component Analysis (PCA), Linear Discriminant Analysis, and the Partial Least Squares (PLS) method [39]. Thus, the choice and selection of descriptors has already been accomplished. 

A statistical analysis allows us to determine whether our results are significantly different from known values, or from values obtained by other analysts, by other methods of analysis, or for other samples. A f-test is used to compare mean values, and an F-test to compare precisions. Comparisons between two sets of data require an initial evaluation of whether the data... 

A variety of statistical methods may be used to compare three or more sets of data. The most commonly used method is an analysis of variance (ANOVA). In its simplest form, a one-way ANOVA allows the importance of a single variable, such as the identity of the analyst, to be determined. The importance of this variable is evaluated by comparing its variance with the variance explained by indeterminate sources of error inherent to the analytical method. 

To gain the most predictive utility as well as conceptual understanding from the sequence and structure data available, careful statistical analysis will be required. The statistical methods needed must be robust to the variation in amounts and quality of data in different protein families and for structural features. They must be updatable as new data become available. And they should help us generate as much understanding of the determinants of protein sequence, structure, dynamics, and functional relationships as possible. 

The role of quality in reliability would seem obvious, and yet at times has been rather elusive. While it seems intuitively correct, it is difficult to measure. Since much of the equipment discussed in this book is built as a custom engineered product, the classic statistical methods do not readily apply. Even for the smaller, more standardized rotary units discussed in Chapter 4, the production runs are not high, keeping the sample size too small for a classical statistical analysis. Run adjustments are difficult if the run is complete before the data can be analyzed. However, modified methods have been developed that do provide useful statistical information. These data can be used to determine a machine tool s capability, which must be known for proper machine selection to match the required precision of a part. The information can also be used to test for continuous improvement in the work process. 

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