Chapter 1 Introduction to Ranking Methods

Abstract

Publisher Summary The statistical analysis based on the distribution of the ranks (order of the experimental values) has had an increasing development. Outcomes associated with an experiment may be numerical in nature, such as quantity in an analytical sample. The types of measurements are usually called “measurement scales” and are, from the weakest to the strongest, nominal, ordinal, interval and ratio scale. This chapter describes procedures that can be used with data in nominal scale. It presents statistical methods, which is the most powerful for data in ordinal scale—they are the test of ranks. The tests of ranks are valid for data with continuous, discrete or both continuous and discrete distributions. The chapter discusses order in graphs and optimization problems. Graphs are highly versatile models for analyzing many practical problems in which points and connections between them have some physical or conceptual meaning. Optimization refers to finding one or more feasible solutions that correspond to extreme values of one or more objectives or criteria. When an optimization problem involves only one objective, the task of finding the optimal solution is called “single-objective optimization,” whereas if the problem involves more than one objective, it is known as “multi-objective optimization.”