• Communications for Statistical Applications and Methods
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• v.8 no.1
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• pp.65-71
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• 2001

In this paper, optimal block designs for complete diallel crosses are proposed. These optimal block designs are constructed by using triangular partially balanced incomplete designs derived from symmetric balanced incomplete block designs. Also, it is shown that block designs for complete dialle crosses derived from complementary designs of triangular designs are optimal block designs.

• Proceedings of the Korean Statistical Society Conference
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• 2001.11a
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• pp.121-124
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• 2001

In this paper, partial diallel crosses designs are proposed. These designs for estimating general combining abilities are constructed by using m-associate class partially balanced incomplete block designs. Also, the efficiency of the partially diallel crosses designs obtained through this method is reported in table.

• The Korean Journal of Applied Statistics
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• v.15 no.2
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• pp.367-379
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• 2002

In this paper, the method of constructing incomplete block designs for comparing general combining abilities of p inbred lines for partial diallel crosses is proposed. These partial diallel crosses block designs are constructed by using m-associate class partially balanced incomplete block designs with block size 2 and balanced incomplete block designs. Also, the efficiencies of block designs obtained through this method are tabulated for number of lines 24 or less.

• Communications for Statistical Applications and Methods
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• v.9 no.2
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• pp.435-441
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• 2002

In this paper, orthogonal block designs for partial diallel crosses are proposed. These partial diallel crosses block designs for estimating general combining abilities are constructed by using $\alpha$-resolvable partially balanced incomplete block designs. Also, the efficiencies of the partial diallel crosses block designs obtained through this method are reported in table.

• Journal of the Korean Statistical Society
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• v.14 no.1
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• pp.29-38
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• 1985

Cyclic Factorial Association Scheme (CFAS) for incomplete block designs in a factorial experiment is defined. It is a generalization of EGD/($2^n-1$)-PBIB designs defined by Hinkelmann (1964) or Binary Number Association Scheme (BNAS) named by Paik and Federer (1973). A property of PBIB designs having CFAS is investigated and it is shown that the structural matrix NN' of such designs has a pattern of multi-nested block circulant matrix. The generalized inverse of (rI-NN'/k) is obtained. Generalized Cyclic incomplete block designs for factorial experiments introduced by John (1973) are presented as the examples of CFAS-PBIB designs. Finally, the relationship between CFAS and BNAS in block designs is briefly discussed.

• Proceedings of the Korean Statistical Society Conference
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• 2002.05a
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• pp.171-174
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• 2002

In this paper, diallel crosses block designs for control versus test comparisons among the lines are proposed. These designs are constructed by using partially balanced incomplete block designs with C-properties. Also, the efficiencies of the diallel crosses block designs obtained through this method are tabulated for number of lines 24 or less.

• Journal of the Korean Statistical Society
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• v.36 no.3
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• pp.373-386
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• 2007

In this paper, a review on second order slope rotatable designs (SOSRD) is studied. Further, different methods of constructions of SOSRD like slope rotatable central composite designs (SRCCD), SOSRD using balanced incomplete block designs (BIBD), SOSRD using pairwise balanced designs (PBD), SOSRD using partially balanced incomplete block type designs (PBIBD) and SOSRD using symmetrical unequal block arrangements (SUBA) with two unequal block sizes are examined in detail. A table is provided where for a range of different values of v (v stands for number of factors) the design points needed by different methods are compared. The optimum SOSRD with minimum number of design points for each factor is suggested for $2{\leq}v{\leq}16$.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.175-184
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• 2002

In this paper, diallel crosses block designs for control versus test comparisons among the lines are proposed. These block designs are constructed by using partially balanced incomplete block designs with C-properties. Also, the efficiencies of the diallel crosses block designs obtained through this method are tabulated for number of lines 22 or less.

• Journal of the Korean Data and Information Science Society
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• v.1
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• pp.7-33
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• 1990

Bechhofer and Tamhane(1981) developed a theory of optimal incomplete block designs for comparing several treatments with a control. This class of designs is appropriate for comparing simultaneously $p{\geq}2$ test treatments with a control treatment (the so-called multiple comparisons with a control (MCC) problem) when the observations are taken in incomplete blocks of common size $K{\<}p+1$. In this paper we want to extend to partially BTIB designs with two associate classes for the MCC problem. We propose a new class of incomplete block designs that are partially balanced with respect to test treatments. Because the class of designs that we consider is larger than the class of designs in Bechhofer and Tamhane and provides us with designs that improve on the optimal designs in their class. We shall use the abbreviation PBTIB to refer to such designs. We study their structure and give some methods of construction. Also we describe a procedure for making exact joint confidence statements for the MCC problem in PBTIB Designs with two associate classes. We study Optimality, Admissibility considerations in PBTIB designs with two associate classes.

• Journal of the Korean Statistical Society
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• v.3 no.2
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• pp.85-101
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• 1974

In a Balanced Factorial Experiments (BFE) with n factors $F_1, F_2,\cdots,F_n$ at $m_1, m_2,\cdots,m_n$ levels respectively, Shah [15] has considered the following association scheme: the two treatments are the $(P_1, P_2,\cdot,P_n)$th associates, where $p_i=1$ if the ith factor occurs at the same level in both treatments and $p_i=0$ otherwise; $\lambda_{(p_1,p_2,\cdots,p_n)}$ will denote the number of times these treatments occur together in a block. He has showed that a BFE is partially Blanced Incomplete Block(PBIB) design with repsect to the above association scheme. Kurjian and Zelan [6] have proved that factorial designs possessing a Property A (a particular structure for their matrix NN') are factorially balanced.