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JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. American Statistical Association and American Society for Quality are collaborating with JSTOR to digitize, preserve and extend access to Technometrics.A new method for sensitivity analysis (SA) of model output is introduced. It is based on the Fourier amplitude sensitivity test (FAST) and allows the computation of the total contribution of each input factor to the output's variance. The term "total" here means that the factor's main effect, as well as all the interaction terms involving that factor, are included. Although computationally different, the very same measure of sensitivity is offered by the indices of Sobol'. The main advantages of the extended FAST are its robustness, especially at low sample size, and its computational efficiency. The computational aspects of the extended FAST are described. These include (1) the definition of new sets of parametric equations for the search-curve exploring the input space, (2) the selection of frequencies for the parametric equations, and (3) the procedure adopted to estimate the total contributions. We also address the limitations of other global SA methods and suggest that the total-effect indices are ideally suited to perform a global, quantitative, model-independent sensitivity analysis.

The formulae for calculating the sample size required to study the interaction between a continuous exposure and a genetic factor on a continuous outcome variable in the face of measurement error will be of considerable utility in designing studies with appropriate power. These calculations suggest that smaller studies with repeated and more precise measurement of the exposure and outcome will be as powerful as studies even 20 times bigger, which necessarily employ less precise measures because of their size. Even though the cost of genotyping is falling, the magnitude of the effect of measurement error on the power to detect interaction on continuous traits suggests that investment in studies with better measurement may be a more appropriate strategy than attempting to deal with error by increasing sample sizes.

The aim of sensitivity analysis (SA) is to ascertain how much the uncertainty in the output of a model is influenced by the uncertainty in its input factors. An SA can be performed using different methods, which are classified according to various criteria. One possible classification is that in which global and local approaches are identified. This paper strengthens the role of global SA methods and suggests their use in the context of MCDA. Useful applications of global SA already exist in a variety of fields where numerical models are considered, e.g. in economics, engineering and chemistry. Global SA is quite different in its formulation and application from local SA, which is seen more frequently in the literature. The global sensitivity indices adopted are derived from a variance decomposition scheme: they can be estimated by alternative computational strategies, such as the extended FAST or the method proposed by Sobol'. A truly global SA is capable of apportioning the output uncertainty according to any subgroup of input factors. Hence, the output uncertainty of an MCDA can, for instance, be decomposed into a part due to uncertain model inputs and a part due to poorly defined (or variable) weights attached to the criteria. This information could be useful to the decision maker (DM) since it explains synthetically how much the assessment of an MCDA study is biased by the assessor judgements. Alternative regrouping of the uncertain input elements might shed light on other features of the problem addressed by the DM.

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