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ON TWO METHODS OF ANALYSING BALANCED INCOMPLETE BLOCK DESIGNS  [cached]
Chigozie Kelechi Acha
Pakistan Journal of Statistics and Operation Research , 2012, DOI: 10.1234/pjsor.v8i4.404
Abstract: The paper briefly discusses the balanced incomplete–block design (BIBD’s) and further compares two methods of analyzing them-the classical and vector space analysis of variance (ANOVA) methods. These methods are applied differently to the data arising from the balanced incomplete block designs (BIBD’s). The basic interest is to compare the performance of the two methods of analysis on the available data from National Root Crop Research Institute (N.R.C.R.I) Umudike, Abia State. To achieve this, we shall consider treatment (adjusted), block (adjusted) treatment (not adjusted) in the classical ANOVA method and the vector space ANOVA method. Block is adjusted to know if the experiment is symmetric balanced incomplete block design (SBIBD). The classical ANOVA method was easier to compute and more convenient to handle than the vector ANOVA method. The classical ANOVA method is found to be preferable to the vector space ANOVA method.
Characterization Tensors of Balanced Incomplete Block Designs  [PDF]
Liqun Qi,Ziyan Luo
Mathematics , 2015,
Abstract: Balanced incomplete block designs (BIBDs) have wide applications in engineering, business and sciences. In this paper, for each (v, k, \lambda)-BIBD, we construct a strongly symmetric k-th order v-dimensional tensor. We call such a strongly symmetric tensor the characterization tensor of that BIBD, and the absolute value tensor of the characterization tensor the signless characterization tensor of that BIBD. We study some spectral properties of such characterization tensors and signless characterization tensors. In this way, we provide a new tool to study BIBDs.
On the Construction of Balanced Incomplete Block Designs Using Lotto Designs
O.A. Alawode,G.N. Amahia,A.A. Eludire
Journal of Modern Mathematics and Statistics , 2012, DOI: 10.3923/jmmstat.2010.50.52
Abstract: Researchers present two algorithms for constructing Balanced Incomplete Block Designs (BIBD); the first, for determining the BIBDs that qualify to be Lotto Designs (LD) and the second for generating BIBDs from the LD parameters (n, k, p, t). The algorithms are tested using (υ = 6, b = 20, r = 10, k = 3, λ = 4) and (υ = 13, b = 130, r = 30, k = 3, λ = 4) BIBDs. One of the results, the (υ = 4, b = 4, r = 3, k = 3, λ = 2) BIBD which is pair wise balanced is shown to be D-optimal. Also, the (13, 130, 30, 3, 5) BIBD yielded (13, 56, 21, 3, 6), (13, 84, 28, 3, 7), (13, 120, 36, 3, 8) and (13, 165, 45, 3, 9) BIBDs; the first three being less cumbersome and more economical for experimental purposes. In general, a BIBD that qualifies as a LD can be used to generate other BIBDs.
Symmetric and Unsymmetric Balanced Incomplete Block Designs: A Comparative Analysis
International Journal of Statistics and Applications , 2012, DOI: 10.5923/j.statistics.20120204.02
Abstract: This paperdiscusses a comparative analysis on balanced incomplete block designs by using the classical analysis of variance (ANOVA) method. Fortunately, the data collected for the analysis were in two groups of the balanced incomplete-block designs (BIBD’s), that is, symmetric, and unsymmetric (BIBD’s). In this paper, the basic interest is to apply classical ANOVA on the two types of BIBD’s and check whether they are significant and also minimizes error. A secondary data from N.R.C.R.I, Umudike, Abia State was used. To achieve this, we shall consider treatment (adjusted), block (adjusted) treatment (not adjusted) in the classical ANOVA method on the available data. Though, symmetric balanced incomplete block design (SBIBD) and unsymmetric balanced incomplete block design (USBIBD) are significant, it is pertinent to note that the SBIBD classical ANOVA method is found to be preferable to the USBIBD with reference to their variances at different level of significance.
New lower bounds for the number of blocks in balanced incomplete block designs  [PDF]
Muhammad Ali Khan
Mathematics , 2008,
Abstract: Bose proved the inequality $b\geq v+r-1$ for resolvable balanced incomplete block designs (RBIBDs) and Kageyama improved it for RBIBDs which are not affine resolvable. In this note we prove a new lower bound on the number of blocks $b$ that holds for all BIBDs. We further prove that for a significantly large number of BIBDs our bound is tighter than the bounds given by the inequalities of Bose and Kageyama.
A Tool for Constructing Pair-Wise Balanced Incomplete Block Designs
E.O. Effanga,J.A. Ugboh,E.I. Enang,B.E.A. Eno
Journal of Modern Mathematics and Statistics , 2012,
Abstract: This study deals with the construction of Pair-wise Balanced Incomplete Block Designs (PBIBD). We developed a non-linear non-preemptive binary integer goal programming model for the construction of PBIBD for any set of parameters (b, k, t, r, λ). The model so developed is tested using two set of parameters (b = 4, k = 4, t = 3, r = 3, λ = 2) and (b = 7, k = 7, t = 3, r = 3, λ = 1). It is shown that the PBIBD is not unique for any given set of parameters and that the design obtained by our model is D-optimal.
Robustness of Doubly Balanced Incomplete Block Mating Designs against Unavailability of Two Blocks  [PDF]
a R. Shunmugathi*,,a Dr. M. R. Srinivasan.
Biomirror , 2011,
Abstract: Mating designs are the study of progenies developed through various methods like Diallel Cross plans which are subjected to Incomplete Block Designs. The concept of robustness in designs has been studied and available in the literature. The effects of missing blocks on Complete Diallel Cross designs are examined in this study. A-efficiencies based on non -zero eigenvalues suggest that these designs are fairly robust. The investigation shows that Doubly Balanced Incomplete Block Mating Designs are fairly robust in terms of efficiency. In this paper, the robustness of Doubly Balanced Incomplete Block Design when two blocks are lost has been discussed.
Expurgated PPM Using Symmetric Balanced Incomplete Block Designs  [PDF]
Mohammad Noshad,Maite Brandt-Pearce
Mathematics , 2012,
Abstract: In this letter, we propose a new pulse position modulation (PPM) scheme, called expurgated PPM (EPPM), for application in peak power limited communication systems, such as impulse radio (IR) ultra wide band (UWB) systems and free space optical (FSO) communications. Using the proposed scheme, the constellation size and the bit-rate can be increased significantly in these systems. The symbols are obtained using symmetric balanced incomplete block designs (BIBD), forming a set of pair-wise equidistance symbols. The performance of Q-ary EPPM is better than any Q-ary pulse position-based modulation scheme with the same symbol length. Since the code is cyclic, the receiver for EPPM is simpler compared to multipulse PPM (MPPM).
Robustness of Nested Balanced Incomplete Block Designs against Unavailability of One or More Observations  [PDF]
R. Shunmugathi,Dr. M. R. Srinivasan
Biomirror , 2011,
Abstract: Mating designs are the study of progenies developed through variousmethods like Diallel Cross plans which are subjected to IncompleteBlock Designs. The concept of robustness in designs has been studiedand available in the literature. The paper dealt with a class of Nested Balanced Incomplete Block Designs for varying parametric valueswith unavailability of one or more observations and efficiencies arecalculated. The effects of missing blocks on Complete Diallel Crossdesigns are examined in this study. A-efficiencies based on non -zeroeigenvalues suggest that these designs are fairly robust. The investigation shows that Nested Balanced Incomplete Block Designsare fairly robust in terms of efficiency. In this paper, the robustness of Nested Balanced Incomplete Block Design when one or moreobservations are lost has been discussed.
A New Method of Construction of Robust Second Order Rotatable Designs Using Balanced Incomplete Block Designs  [PDF]
B. Re. Victorbabu, K. Rajyalakshmi
Open Journal of Statistics (OJS) , 2012, DOI: 10.4236/ojs.2012.21005
Abstract: The following article has been retracted due to the investigation of complaints received against it. Title: A New Method of Construction of Robust Second Order Rotatable Designs Using Balanced Incomplete Block Designs Authors: Bejjam Re. Victorbabu, Kottapalli Rajyalakshmi. The above paper is a copy of Dr. Rabindra Nath Das’s former article, entitled \"“Robust second order rotatable designs (Part I)”. The scientific community takes a very strong view on this matter and we solemnly withdrawn?the paper from the journal OJS. This paper published in OJS Vol.2 No.1, 39-47, 2012, has been retracted.?
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