Journal of Statistical Theory and Practice

, Volume 11, Issue 1, pp 63–75 | Cite as

Nonbinary variance-balanced designs-part I, optimality

  • Nutan MishraEmail author


Let D(v,b,k) be a class of designs with ν treatments and b blocks, each of size k. We show that (i) if a variance-balanced design exists in D(v, b, k), then it is Ε-optimal. Let Δ(ν, b, k)D(v, b, k) containing all the variance-balanced designs. Then we prove that (ii) a design d ∈′ Δ(ν, b,k) is ER-optimal in Δ(ν, b,k) if its replication numbers are as uniform as possible, (iii) a design d in Δ(ν, b,k) is AR-optimal and DR-optimal in Δ(ν, b, k) if its replication numbers are all equal except one, and (iv) a design d in Δ(ν, b, k) has maximum average efficiency in Δ(ν, b,k) if its replications numbers are all equal but one. Average efficiencies of designs in three classes are computed and tabulated at the end.


Proper block design connected design variance balance completely symmetric matrix C-matrix efficiency factors nonbinary designs 

AMS Subject Classification

Primary 62K05 62K10 


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Copyright information

© Grace Scientific Publishing 2017

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsUniversity of South AlabamaMobileUSA

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