Titlebook: Rank and Pseudo-Rank Procedures for Independent Observations in Factorial Designs; Using R and SAS Edgar Brunner,Arne C. Bathke,Frank Konie

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Derivation of Main Results,gns might skip this chapter. But those readers who are interested in the background of the results and procedures will find the respective proofs and derivations in the following pages. The presentation of these derivations assumes about a year of Master’s level coursework in statistics, with the respective mathematical understanding.

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Types of Data and Designs,tudy designs, illustrated with several examples. Good scientific practice requires research reproducibility. This includes sound statistical modeling and informed choice of appropriate statistical methods for inference. Choosing valid statistical methods requires a firm understanding of the basic te

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Distributions and Effects,nally been used for parametric and semiparametric inference. As a consequence, effect sizes have to be quantified differently. To this end, the nonparametric relative treatment effect is defined. It measures how strong the stochastic tendency of observations from a particular treatment group is to a

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Several Samples,rvations are taken at .. independent subjects (experimental units).Mathematically, we can describe this by random variables .. Observations taken at different subjects within the same factor level . are considered replications. Therefore, they are modeled using the same distribution function ... Tha

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Two-Factor Crossed Designs,n Sect. .. For simplicity, often two relevant factors are chosen, and their effect on the response is analyzed. In this section, methods for the analysis of such designs are presented. First, in Sect. 5.1, the basic ideas are illustrated using two examples. In Sect. 5.2, nonparametric effects and th

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Designs with Three and More Factors,ssessing the individual effects (main effects) of each of the factors, as well as their combination effects (interaction effects). In Sect. 6.1, some motivating examples are described. Section 6.2 introduces the nonparametric statistical model, along with the hypotheses to be tested, as well as appr

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Mathematical Techniques,hout the previous chapters. It is our aim to provide unique notations when referring to elementary results and using some well-known mathematical techniques. Regarding more detailed explanations and derivations, we refer to the literature listed in the subsequent sections.

CRAMP

mpressive advances in both the theoretical understanding of fracture mechanisms and practical developments that offer possibilities of control have re-shaped the subject over the past four decades. The contributors to this volume, including some of the most prominent researchers in the field, give t