Statistical Method Selection Overview

The statistical method, to be appropriate, must measure and reflect the data accurately and precisely. The test hypothesis should be formulated clearly and concisely. If, for example, the study is designed to test whether products A and B are different, statistical analysis should provide an answer. 

Roger H. Green, in his book Sampling Designs and Statistical Methods for Environmental Biologists, describes 10 steps for effective statistical analysis (Green, 1979). These steps are applicable to any analysis  

State the test hypothesis concisely to be sure that what you are testing is what you want to test. 

Always replicate the treatments. Without replication, measurements of variability may not be reliable. 

As far as possible, keep the number of replicates equal throughout the study. This practice makes it much easier to analyze the data. 

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Before presenting oin discussion, we present a brief and select overview of some relevant literature. Peto (1987) discusses some foimdational issues in systematic reviews of randomized trials for rare outcomes, in particular the need for such reviews and considerations of heterogeneity of the treatment effect. Hammad et al. (2011) present a thorough overview of the issues associated with the secondary use of randomized trials to evaluate safety. Bradbum et al. (2007) evaluate statistical meta-analysis methods for rare events. Kaizer et al. (2006) present an interesting example of a hierarchical Bayesian method for meta-analysis of safety. Crowe et al. (2009) provide recommendation for a premarket safety program. 

PCM modeling aims to find an empirical relation (a PCM equation or model) that describes the interaction activities of the biopolymer-molecule pairs as accurate as possible. To this end, various linear and nonlinear correlation methods can be used. Nonlinear methods have hitherto been used to only a limited extent. The method of prime choice has been partial least-squares projection to latent structures (PLS), which has been found to work very satisfactorily in PCM. PCA is also an important data-preprocessing tool in PCM modeling. Modeling includes statistical model-validation techniques such as cross validation, external prediction, and variable-selection and signal-correction methods to obtain statistically valid models. (For general overviews of modeling methods see [10]). 

In a robustness test the following steps can be identified (a) identification of the variables to be tested, (b) definition of the different levels for the variables, (c) selection of the experimental design, (d) definition of the experimental protocol, (e) definition of the responses to be determined, (f) execution of the experiments and determination of the responses of the method, (g) calculation of effects, (h) statistical and/or graphical analysis of the effects, and (i) drawing chemically relevant conclusions from the statistical analysis and, if necessary, taking measures to improve the performance of the method. A general overview of robustness testing can be found in [35). 

Voigt K, Welzl G (2002a) Chemical Databases An Overview of Selected Databases and Evaluation Methods. Online Information Review 26 172-192 Voigt K, Welzl G (Ed.) (2002b) Order Theoretical Tools in Environmental Sciences, Order Theory (Hasse Diagram Technique) Meets Multivariate Statistics. Shaker-Verlag, Aachen... 

The number of papers published in the literature relating to supervised variable selection methods is vast. Its obvious association with the ubiquitous publication of regression modeling means that trying to provide an exhaustive overview of the literature is an impossible task. Although this chapter aims to review variable selection methods, all that we can hope to achieve realistically is a broad coverage of the more obvious source methods and report here techniques that are sound from a statistical point of view and for which the software is available... 

As mentioned earlier, the supplier selection activity plays a key role in cost reduction and is one of the most important functions of the purchasing department. Different mathematical, statistical, and game theoretical models have been proposed to solve the problem. References Weber et al. (1991), Aissaoui et al. (2007), De Boer et al. (2001), and Dickson (1966), provide an overview of supplier selection methods. De Boer et al. (2001) stated that that supplier selection is made up of several decision making steps as shown in Figure 6.3. 

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