Advanced nonparametric tests for multiple comparisons in the design of experiments in computational intelligence and data mining: Experimental analysis of power

Experimental analysis of the performance of a proposed method is a crucial and necessary task in an investigation. In this paper, we focus on the use of nonparametric statistical inference for analyzing the results obtained in an experiment design in the field of computational intelligence. We present a case study which involves a set of techniques in classification tasks and we study a set of nonparametric procedures useful to analyze the behavior of a method with respect to a set of algorithms, such as the framework in which a new proposal is developed. Particularly, we discuss some basic and advanced nonparametric approaches which improve the results offered by the Friedman test in some circumstances. A set of post hoc procedures for multiple comparisons is presented together with the computation of adjusted p-values. We also perform an experimental analysis for comparing their power, with the objective of detecting the advantages and disadvantages of the statistical tests described. We found that some aspects such as the number of algorithms, number of data sets and differences in performance offered by the control method are very influential in the statistical tests studied. Our final goal is to offer a complete guideline for the use of nonparametric statistical procedures for performing multiple comparisons in experimental studies.