This project deals with nonparametric statistical solutions for hypotheses testing problems and codes for the software environment R for the application of these solutions. In particular, the methods presented here consist of rank or permutation procedures which have been applied to real data related to the level of knowledge of students of the faculty of Mathematics in the University of Seville in some statistics subjects. Chapter 1 deals with one-sample and two-sample location problems, tests for symmetry and tests to compare two independent populations in terms of central tendency. According to the number of response variables and to the number of samples, we distinguish four kinds of methods: univariate one-sample tests, multivariate one-sample tests, univariate two-sample tests and multivariate two-sample tests. In this first category are the Kolmogorov goodness-of-fit test and the permutation test for symmetry; in the second group of procedures are the multivariate rank test for central tendency and the multivariate extension of the permutation test on symmetry; among the procedures included in the third family of solutions are the Wilcoxon test and the permutation test on central tendency; finally some other general procedures in the basis of rank and permutation approaches are discussed. Chapter 2 deals with two independent random samples, one sample drawn from each of two underlying populations. This chapter presents some tests for comparing variabilities and distributions. For problems of variability comparisons the Ansary-Bradley test, the permutation Pan test and the permutation O’Brien test are considered. For jointly comparing central tendency and variability the Lepage test and the Cucconi test are presented. While for problems of comparing the statistical distributions of both population the Kolmogorov-Smirnov and the Cramer-von Mises are analyzed.

Universidad de Sevilla. Grado en Matemáticas