反復測度デザイン概説-2-球形検定とその周辺についての批判的レビュ-  [in Japanese] <Material>A critical review on and around sphericity tests  [in Japanese]

Search this Article

Author(s)

Abstract

A critical review on and around sphericity tests was made in the context of univariate and multivariate mixed models in order to clarify the present state of researches and problems which remained to be solved. We overviewed (1) mathematical statistical studies of Mauchly's LR criterion, (2) studies on the Mauchly's criterion in the context of repeated measures ANOVA as well as the Thomas' criterion in MMM (multivariate mixed model), (3) studies on the power of the Mauchly's criterion in the neighborhood of the null hypothesis, and the LBI test (locally best in variance test), and (4) robustness studies on the sphericity tests under non-normality conditions. It was concluded, from the overview, that there existed various problems yet to be solved concerning the sphericity tests. These are (1) the exact distribution of the LBI criterion when the number of variates is greater than three, and (2) exact distribution of the LR multivariate sphericity criterion proposed by Thomas (1983). Moreover, the necessity for robustness studies was suggested under the non-normal distributions with light tail such as multivariate beta distribution and so on.

Journal

  • Bulletin of the Faculty of Humanities of Aichigakuin University

    Bulletin of the Faculty of Humanities of Aichigakuin University (24), p103-119, 1994

    Aichi Gakuin University

Cited by:  2

Codes

  • NII Article ID (NAID)
    110000042554
  • NII NACSIS-CAT ID (NCID)
    AN0000649X
  • Text Lang
    JPN
  • Article Type
    Journal Article
  • Journal Type
    大学紀要
  • ISSN
    02858940
  • NDL Article ID
    3273434
  • NDL Source Classification
    H61;SB0
  • NDL Source Classification
    ZV1(一般学術誌--一般学術誌・大学紀要)
  • NDL Call No.
    Z22-789
  • Data Source
    CJPref  NDL  NII-ELS 
Page Top