Decision makers have long relied on experts to inform their decision making. Expert judgment analysis is a way to elicit and combine the opinions of a group of experts to facilitate decision making. The use of expert judgment is most appropriate when there is a lack of data for obtaining reasonable statistical results. The experts are asked for advice by one or more decision makers who face a specific real decision problem. The decision makers are outside the group of experts and are jointly responsible and accountable for the decision and committed to finding solutions that everyone can live with. The emphasis is on the decision makers learning from the experts. The focus of this thesis is an overview and comparison of the various elicitation and combination methods available. These include the traditional committee method, the Delphi method, the paired comparisons method, the negative exponential model, Cooke’s classical model, the histogram technique, using the Dirichlet distribution in the case of a set of uncertain proportions which must sum to one, and the employment of overfitting. The supra Bayes approach, the determination of weights for the experts, and combining the opinions of experts where each opinion is associated with a confidence level that represents the expert’s conviction of his own judgment are also considered.

A method is presented for analysing a 2 x 2 factorial experiment in which the data consist cf relative rankings in pairwise comparisons. Maximum likelihood estimates are developed for the ratings of the various levels of each factor und for the treatment combinations. Likelihood ratio tests of the most important hypotheses likely to arise are derived in detail. The large sample approximations are used. In addition, the method is presented in a manner such that tests of other hypotheses in which the experimenter might be interested can easily be derived. The equations for the analysis of a factorial design of arbitrary size are presented, It can be seen, however, that the complexity of these equations render an attempt at their solution impractical in most cases and more work must be done if a useful method of analysing experiments of this, type is to be found. / Master of Science