Semi-aligned rank tests

  • Taka-Aki Shiraishi


The distribution-free test based on semi-aligned rankings for no treatment effects in a two-way layout, with unequal number of replications in each cell is considered. The asymptotic χ-square distribution of the test statistic under the null hypothesis is derived. The Pitman asymptotic relative efficiency of the test (i) based on semi-aligned rankings with respect to the test (ii) based on within-block rankings, is shown to be larger than one as the number of blocks tends to infinity. Also the asymptotic properties of linear rank statistics (i) and (ii) are investigated and the asymptotic relative efficiency of the test (i) with respect to the test (ii) is again shown to be larger than one.

AMS 1980 subject classification

Primary 62G10 secondary 62E20 

Key words and phrases

Distribution-free test two-way layout asymptotic distribution asymptotic relative efficiency 


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Copyright information

© The Institute of Statistical Mathematics, Tokyo 1984

Authors and Affiliations

  • Taka-Aki Shiraishi
    • 1
  1. 1.University of TsukubaTsukubaUSA

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