Designs with No Full Efficiency

  • Tadeusz Caliński
  • Sanpei Kageyama
Part of the Lecture Notes in Statistics book series (LNS, volume 170)


This chapter is devoted to methods of constructing block designs that do not provide unit efficiency factors for any contrasts of treatment parameters. Taking into account the practical point of view, the cases of (0;p1,p2,…,pm_1;0)-EB designs, with m = 2, 3 and more, will be considered. At first, a general consideration on such designs is presented in Section 8.1, by recalling relevant results discussed in Volume I and by providing some corresponding optimality results. Next, a large number of methods of construction are given for designs separated into four classes, covering designs that are (i) proper and equireplicate, (ii) proper and nonequireplicate, (iii) nonproper and equireplicate and (iv) nonproper and nonequireplicate, first for m = 2 (Section 8.2), then for m = 3 (Section 8.3), for m = 4 (Section 8.4), and finally for m> 4 (Section 8.5).


Prime Power Incidence Matrix Proper Design Efficiency Factor Association Scheme 
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Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Tadeusz Caliński
    • 1
  • Sanpei Kageyama
    • 2
  1. 1.Department of Mathematical and Statistical MethodsAgricultural University of PoznańPoznańPoland
  2. 2.Department of MathematicsGraduate School of Education Hiroshima UniversityHigashi-HiroshimaJapan

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