• International Journal of Reliability and Applications
• /
• v.2 no.2
• /
• pp.131-135
• /
• 2001

Two general methods of construction leading to several series of universally optimal block designs for complete diallel crosses are provided in this paper. A method of constructing variance balance designs is also given.

• Journal of the Korean Data and Information Science Society
• /
• v.26 no.2
• /
• pp.347-354
• /
• 2015

This paper deals with a method for intrablock anlaysis of balanced incomplete block designs on the basis of projections under the assumption of mixed effects model. It shows how to construct a model at each step by the stepwise procedure and discusses how to use projection for the analysis of intrablock. Projections are obtained in vector subspaces orthogonal to each other. So the estimates of the treatment effects are not affected by the block effects. The estimability of a parameter or a function of parameters is discussed and eigenvectors are dealt for the construction of estimable functions.

• Journal of the Korean Statistical Society
• /
• v.8 no.2
• /
• pp.125-130
• /
• 1979

It is well known that $L_2(m)$ type PBIB designs have the Property A, so they are BNAS PBIB designs. However, $L_3(m)$ type PBIB designs are not of type of Property A but do have the factorial structure (Cotter, John, and Smith(1973)). In this paper, the properties of the $L_3(m)$ type PBIB designs are investigated. Extended Property A and fractional BNAS are defined and a solution formula for the treatment effects in the $L_32(m)$ type designs is obtained.

• Journal of the Korean Data and Information Science Society
• /
• v.1
• /
• pp.7-33
• /
• 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 Integrative Natural Science
• /
• v.5 no.2
• /
• pp.135-138
• /
• 2012

The reduction of efficiency of missing observations on complete diallel cross designs are examined. we studies robustness of optimal block designs for estimating general combining ability against loss of missing observations in diallel cross. A-efficiencies suggest that these designs are fairly robust. Simple g-inverses may be found for the information matrices of the line effects which allow evaluation of expressions for the variances of the differences between the pairs of line effects with missing observations. we numerically calculate the reduction of efficiency for estimating general combining ability against loss of missing observations in diallel cross.

• The Korean Journal of Applied Statistics
• /
• v.28 no.2
• /
• pp.151-158
• /
• 2015

This paper discusses how to use projections for the analysis of data from balanced incomplete block designs. A model is suggested as a matrix form for the interblock analysis. A second set of treatment effects can be found by projections from the suggested interblock model. The variance and covariance matrix of two estimated vectors of treatment effects is derived. The uncorrelation of two estimated vectors can be verified from their covaraince structure. The fitting constants method is employed for the calculation of block sum of squares adjusted for treatment effects.

• Journal of the Korean Statistical Society
• /
• v.35 no.2
• /
• pp.179-192
• /
• 2006

In this paper, a new method of modified second order slope rotatable designs (SOSRD) using balanced incomplete block designs (BIBD) for $4{\le}v{\le}16$ is presented. In this method the number of design points required is in some cases less than the number required in Victorbabu (2305) modified slope rotatable central composite designs. Further, a new method of construction of three level modified SOSRD using BIBD is presented. The modified SOSRD can be viewed as SOSRD constructed with the technique of augmentation of second order rotatable design (SORD) using BIBD to SOSRD. These designs are useful in parts to estimate responses and slopes with spherical variance functions.

• The Korean Journal of Applied Statistics
• /
• v.12 no.1
• /
• pp.253-260
• /
• 1999

이어진 블록계획 중에서 대칭 균형된 불완비 블록계획(Symmetrical Balanced Incomplete Block Design : SBIBD)을 이용하여 n-ary를 블록 완전이면교배(Complete Diallel Cross : CDC)계획을 설계하였다. 처리 수와 반복 수가 고정된 경우, 이렇게 설계된 계획이 균형된 불완비 블록계획을 이용해서 설계한 계획들 중에서 가장 효율이 높은 계획임을 보인다.

• Journal of the Korean Data and Information Science Society
• /
• v.3 no.1
• /
• pp.47-63
• /
• 1992

Bechhofer and Tamhane(1981) proposed Balanced Treatment Incomplete Block (BTIB) desings for comparing p test treatments with a control treatment in blocks of size ${\kappa}$. Notz and Tamhane(1983) solved the problem about determination of the minimal complete class for ${\kappa}=3$. However there are a number of design parameters for which BTIB designs do not exist. We suggest a new class of designs called Group Divisible Treatment Desings(GDTD's) that is a larger class including BTIB designs as a subclass. In this paper we give the minimal complete classes of generator designs for GDTD's with ${\kappa}=2,\;p{\geq}4(except\;prime\;number)\;and\;{\kappa}=3,\;p=4(2)6$.

• 한국데이터정보과학회:학술대회논문집
• /
• 2006.04a
• /
• pp.121-129
• /
• 2006

Two color or cDNA microarrays are extensively used to study relative expression levels of thousands of genes simultaneously. 0かy two tissue samples can be hybridized on a single microarray slide. Thus, a microarray slide necessarily forms an incomplete block design with block size two when more than two tissue samples are under study. We also need to control for variability in gene expression values due to the two dyes. Thus, red and green dyes form the second blocking factor in addition to slides. General design problem for these microarray experiments is discussed in this paper. Designs for factorial cDNA microarrays are also discussed.