Overview
- Introduces closed testing procedures for all-pairwise comparisons
- Discusses multiple comparison procedures under simple ordered restrictions of location parameters in multi-sample models
- Explains the sinc method, which is optimal for computing the upper 100a percentiles of complicated distributions
Part of the book series: SpringerBriefs in Statistics (BRIEFSSTATIST)
Part of the book sub series: JSS Research Series in Statistics (JSSRES)
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Table of contents (8 chapters)
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Front Matter
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Back Matter
Keywords
About this book
This book focuses on all-pairwise multiple comparisons of means in multi-sample models, introducing closed testing procedures based on maximum absolute values of some two-sample t-test statistics and on F-test statistics in homoscedastic multi-sample models. It shows that (1) the multi-step procedures are more powerful than single-step procedures and the Ryan/Einot–Gabriel/Welsh tests, and (2) the confidence regions induced by the multi-step procedures are equivalent to simultaneous confidence intervals. Next, it describes the multi-step test procedure in heteroscedastic multi-sample models, which is superior to the single-step Games–Howell procedure. In the context of simple ordered restrictions of means, the authors also discuss closed testing procedures based on maximum values of two-sample one-sided t-test statistics and based on Bartholomew's statistics. Furthermore, the book presents distribution-free procedures and describes simulation studies performed under the null hypothesis and some alternative hypotheses. Although single-step multiple comparison procedures are generally used, the closed testing procedures described are more powerful than the single-step procedures. In order to execute the multiple comparison procedures, the upper 100α percentiles of the complicated distributions are required. Classical integral formulas such as Simpson's rule and the Gaussian rule have been used for the calculation of the integral transform that appears in statistical calculations. However, these formulas are not effective for the complicated distribution. As such, the authors introduce the sinc method, which is optimal in terms of accuracy and computational cost.
Authors and Affiliations
About the authors
Hiroshi Sugiura, Nanzan University
Shin-ichi Matsuda, Nanzan University
Bibliographic Information
Book Title: Pairwise Multiple Comparisons
Book Subtitle: Theory and Computation
Authors: Taka-aki Shiraishi, Hiroshi Sugiura, Shin-ichi Matsuda
Series Title: SpringerBriefs in Statistics
DOI: https://doi.org/10.1007/978-981-15-0066-4
Publisher: Springer Singapore
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2019
Softcover ISBN: 978-981-15-0065-7Published: 14 October 2019
eBook ISBN: 978-981-15-0066-4Published: 30 September 2019
Series ISSN: 2191-544X
Series E-ISSN: 2191-5458
Edition Number: 1
Number of Pages: VIII, 102
Number of Illustrations: 11 b/w illustrations
Topics: Statistical Theory and Methods, Applied Statistics, Computational Mathematics and Numerical Analysis, Biomedical Engineering/Biotechnology