THE UPPER BOUND FOR THE DISTRIBUTION OF TUKEY-KRAMER'S STATISTIC

• Shiraishi Taka-aki

  Department of Mathematical Sciences, International College of Arts and Sciences, Yokohama-City University

Bibliographic Information

Other Title

• Tukey-Kramer法に関連した分布の上界
• Tukey Kramerホウ ニ カンレンシタ ブンプ ノ ジョウカイ

Abstract

In the one-way layout assuming that the underlying distribution is normal, we may execute Tukey-Kramer multiple comparisons procedure for searching all pairwise differences of locations. For the unequal sample sizes, the Tukey-Kramer (T-K) method is conservative. The T-K method is given by using the upper α point of the studentized range distribution A(t). A(t) is a lower bound for the distribution of the statistic max_<1&le;i<i'&le;k>|T_<ii'>|. We derive the distribution B(t) which gives an upper bound for the distribution of max_<1&le;i<i'&le;k>|T_<ii'>|. By using numerical double integration, we show that the value of B(t) is a little larger than that of A(t). As the result, we may verify that the conservativeness of the T-K method is small.

Journal

• Bulletin of the Computational Statistics of Japan

  Bulletin of the Computational Statistics of Japan 19 (2), 77-87, 2008

  Japanese Society of Computational Statistics

Keywords

• Multiple comparisons
• Tukey's method
• Studentized range distribution
• One-way layout
• Underlying normal distribution

Details

• CRID: 1390282679357511552
• NII Article ID: 110006623882
• NII Book ID: AN10195854
• DOI: 10.20551/jscswabun.19.2_77
• ISSN: 21899789
• ISSN: 09148930
• NDL BIB ID: 9391060
• Web Site: http://id.ndl.go.jp/bib/9391060
• Web Site: https://ndlsearch.ndl.go.jp/books/R000000004-I9391060
• Text Lang: ja
• Data Source:
  • JaLC
  • NDL
  • CiNii Articles
• Abstract License Flag: Disallowed