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JSS Research Series in Statistics

Pairwise Multiple Comparisons

Theory and Computation

Authors: Shiraishi, Taka-Aki, Sugiura, Hiroshi, Matsuda, Shin-ichi

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  • 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 100α percentiles of complicated distributions
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eBook $44.99
price for USA in USD (gross)
  • ISBN 978-981-15-0066-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-981-15-0065-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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.


About the authors

Taka-aki Shiraishi, Nanzan University
Hiroshi Sugiura, Nanzan University
Shin-ichi Matsuda, Nanzan University

Table of contents (8 chapters)

Table of contents (8 chapters)
  • All-Pairwise Comparisons in Homoscedastic Multi-sample Models

    Pages 1-12

    Shiraishi, Taka-aki (et al.)

  • Multiple Comparisons in Heteroscedastic Multi-sample Models

    Pages 13-19

    Shiraishi, Taka-aki (et al.)

  • Multiple Comparison Procedures Under Simple Order Restrictions

    Pages 21-34

    Shiraishi, Taka-aki (et al.)

  • Nonparametric Procedures Based on Rank Statistics

    Pages 35-43

    Shiraishi, Taka-aki (et al.)

  • Comparison of Simulated Power Among Multiple Comparison Tests

    Pages 45-48

    Shiraishi, Taka-aki (et al.)

Buy this book

eBook $44.99
price for USA in USD (gross)
  • ISBN 978-981-15-0066-4
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.99
price for USA in USD
  • ISBN 978-981-15-0065-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Pairwise Multiple Comparisons
Book Subtitle
Theory and Computation
Authors
Series Title
JSS Research Series in Statistics
Copyright
2019
Publisher
Springer Singapore
Copyright Holder
The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
eBook ISBN
978-981-15-0066-4
DOI
10.1007/978-981-15-0066-4
Softcover ISBN
978-981-15-0065-7
Series ISSN
2364-0057
Edition Number
1
Number of Pages
VIII, 102
Number of Illustrations
11 b/w illustrations
Topics