Nonparametric Hypothesis Testing: Rank and Permutation Methods with Applications in R

The importance and usefulness of nonparametric methods for testing statistical hypotheses has been growing in recent years mainly due to their flexibility, their efficiency and their ease of application to several different types of problems, including most important and frequently encountered multivariate cases. By also taking account that with respect to parametric counterparts they are much less demanding in terms of required assumptions, these peculiarities of nonparametric methods are making them quite popular and widely used even by non-statisticians. The growing availability of adequate hardware and software tools for their practical application, and in particular of free access to software environments for statistical computing like R, represents one more reason for the great success of these methods. The recognized simplicity and good power behavior of rank and permutation tests often make them preferable to the classical parametric procedures based on the assumption of normality or other distribution laws. In particular, permutation tests are generally asymptotically as powerful as their parametric counterparts in the conditions for the latter. Moreover, when data exchangeability with respect to samples is satisfied in the null hypothesis, permutation tests are always exact in the sense that their null distributions are known for any given dataset of any sample size. On the other hand, those of parametric counterparts are often known only asymptotically. Thus for most sample sizes of practical interest, the related lack of efficiency of unidimensional permutation solutions may sometimes be compensated by the lack of approximation of parametric asymptotic competitors. For multivariate cases, especially when the number of processed variables is large in comparison with sample sizes, permutation solutions in most situations are more powerful than their parametric counterparts. For these reasons in the specialized literature a book dedicated to rank and permutation tests, problem oriented with exhaustive but simple and easy to understand theoretical explanations, a practical guide for the application of the methods to most frequently encountered scientific problems, including related R codes and with many clearly discussed examples from several different disciplines, was lacking.The present book fully satisfies these objectives and can be considered a practical and complete handbook for the application of the most important rank and permutation tests. The presentation style is simple and comprehensible also for nonstatisticians with elementary education in statistical inference, but at the same time precise and formally rigorous in the theoretical explanations of the methods.A novel presentation of rank and permutation tests, with accessible guidance to applications in R. Nonparametric testing problems are frequently encountered in many scientific disciplines, such as engineering, medicine and the social sciences. This book summarizes traditional rank techniques and more recent developments in permutation testing as robust tools for dealing with complex data with low sample size. Key Features: Examines the most widely used methodologies of nonparametric testing. Includes extensive software codes in R featuring worked examples, and uses real case studies from both experimental and observational studies. Presents and discusses solutions to the most important and frequently encountered real problems in different fields. Features a supporting website (www.wiley.com/go/hypothesis_testing) containing all of the data sets examined in the book along with ready to use R software codes. Nonparametric Hypothesis Testing combines an up to date overview with useful practical guidance to applications in R, and will be a valuable resource for practitioners and researchers working in a wide range of scientific fields including engineering, biostatistics, psychology and medicine