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Journal articles on the topic 'Balanced Incomplete Block Design'

Author: Grafiati

Published: 4 June 2021

Last updated: 11 February 2022

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1

Ghosh, D. K., and K. S. Joshi. "Construction of Variance Balanced Designs through Triangular PBIB Designs." Calcutta Statistical Association Bulletin 45, no. 1-2 (March 1995): 111–18. http://dx.doi.org/10.1177/0008068319950107.

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Several authors have obtained variance balanced (VB) and ternary variance balanced ( V B) designs using balanced incomplete block (BIB) designs and group divisible (GD) designs. In the present investigation, another systematic methods have been developed for the construction of VB designs using A Triangular PBIB design and an incomplete block design where the blocks of the incomplete block design are formed by taking the second associate treatments of the given triangular PBIB design. Two Triangular PBIB designs. The methods of construction of VB designs are further illustrated by examples.

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2

Breach, D. R., and Anne Penfold Street. "Irreducible designs from supplementary difference sets." Bulletin of the Australian Mathematical Society 31, no. 1 (February 1985): 105–15. http://dx.doi.org/10.1017/s0004972700002318.

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A family of n k-subsets of the integers modulo ν are said to be supplementary difference sets if developing them by addition modulo ν leads to a balanced incomplete block design, and to be minimal if no proper subfamily leads to a balanced incomplete block design when developed modulo ν. In other words, the family of supplementary difference sets is minimal precisely when it leads to a balanced incomplete block design which cannot be partitioned into a union of proper subdesigns, each consisting of complete cyclic sets of ν blocks. We discuss the conditions under which such a balanced incomplete block design can be partitioned in some non-cyclic fashion into a union of proper subdesigns.

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3

Jhee, Yoon Kyoo. "Spectral Efficiency 0f Symmetric Balance Incomplete Block Design Codes." Journal of the Institute of Electronics and Information Engineers 50, no. 1 (January 25, 2013): 117–23. http://dx.doi.org/10.5573/ieek.2013.50.1.117.

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4

Lal, Kishan, Rajender Prasad, and V. K. Gupta. "Trend‐Free Nested Balanced Incomplete Block Designs and Designs for Diallel Cross Experiments." Calcutta Statistical Association Bulletin 59, no. 3-4 (September 2007): 203–21. http://dx.doi.org/10.1177/0008068320070306.

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Abstract: Nested balanced incomplete block (NBIB) designs are useful when the experiments are conducted to deal with experimental situations when one nuisance factor is nested within the blocking factor. Similar to block designs, trend may exist in experimental units within sub‐blocks or within blocks in NBIB designs over time or space. A necessary and sufficient condition, for a nested block design to be trend‐free at sub‐block level, is derived. Families and catalogues of NBIB designs that can be converted into trend‐free NBIB designs at sub‐block and block levels have been obtained. A NBIB design with sub‐block size 2 has a one to one correspondence with designs for diallel crosses experiments. Therefore, optimal block designs for dialled cross experiments have been identified to check if these can be converted in to trend‐free optimal block designs for diallel cross experiments. A catalogue of such designs is also obtained. Trend‐free design is illustrated with example for a NBIB design and a design for diallel crosses experiments. AMS (2000) Subject Classification: 62K05, 62K10.

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5

Goud, T. Shekar, and N. Ch Bhatra Charyulu. "Variance balanced incomplete block designs." Bulletin of Pure & Applied Sciences- Mathematics and Statistics 37e, no. 2 (2018): 286. http://dx.doi.org/10.5958/2320-3226.2018.00031.0.

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6

Morgan, J. P., D. A. Preece, and D. H. Rees. "Nested balanced incomplete block designs." Discrete Mathematics 231, no. 1-3 (March 2001): 351–89. http://dx.doi.org/10.1016/s0012-365x(00)00332-0.

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7

Whiteman, A. L. "Some balanced incomplete block designs." Computers & Mathematics with Applications 39, no. 11 (June 2000): 117–19. http://dx.doi.org/10.1016/s0898-1221(00)00116-4.

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8

Dauran, N. S., A. B. Odeyale, and A. Shehu. "CONSTRUCTION AND ANALYSIS OF BALANCED INCOMPLETE SUDOKU SQUARE DESIGN." FUDMA JOURNAL OF SCIENCES 4, no. 2 (July 2, 2020): 290–99. http://dx.doi.org/10.33003/fjs-2020-0402-219.

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Sudoku squares have been widely used to design an experiment where each treatment occurs exactly once in each row, column or sub-block. For some experiments, the size of row (or column or sub-block) may be less than the number of treatments. Since not all the treatments can be compared within each block, a new class of designs called balanced incomplete Sudoku squares design (BISSD) is proposed. A general method for constructing BISSD is proposed by an intelligent selection of certain cells from a complete Latin square via orthogonal Sudoku designs. The relative efficiencies of a delete-one-transversal balance incomplete Latin Square (BILS) design with respect to Sudoku design are derived. In addition, linear model, numerical examples and procedure for the analysis of data for BISSD are proposed

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9

R. Rink, David. "Balanced incomplete block designs: selected business-related applications and usage caveats." Innovative Marketing 12, no. 1 (April 27, 2016): 15–28. http://dx.doi.org/10.21511/im.12(1).2016.02.

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Whenever respondents must rank-order a large number of items and/or the reliability of their rankings may be questionable, balanced incomplete block designs (BIBDs) represent a more effective means for doing so than either complete rankings or paired comparisons for business and marketing researchers. By providing a type of balancing and replication across items and respondents, BIBDs significantly reduce the number of subjective evaluations each individual must make. But, at the same time, BIBDs allow a limited number of respondents as a group to rank many items. This balancing and replication in BIBDs also reduces standard deviation, which increases the precision of a study. BIBDs, therefore, can improve response rates as well as increase the accuracy and reliability of the data collected. After discussing the general nature of BIBDs and statistical techniques for analyzing preference data collected by BIBDs, three business-related applications are presented to illustrate the benefits of BIBDs. Next, caveats concerning the use of BIBDs are presented. In the last section, advantages of BIBDs are discussed

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10

Colburn, Wayne A. "Balanced Incomplete-Block Design: Its Use and Misuse." Journal of Pharmaceutical Sciences 74, no. 7 (July 1985): 795. http://dx.doi.org/10.1002/jps.2600740725.

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11

Alvo, M., and P. Cabilio. "On the Balanced Incomplete Block Design for Rankings." Annals of Statistics 19, no. 3 (September 1991): 1597–613. http://dx.doi.org/10.1214/aos/1176348264.

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12

Dobcsányi, P., D. A. Preece, and L. H. Soicher. "On balanced incomplete-block designs with repeated blocks." European Journal of Combinatorics 28, no. 7 (October 2007): 1955–70. http://dx.doi.org/10.1016/j.ejc.2006.08.007.

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13

Cheng, Ching-Shui. "N-way balanced incomplete block designs." Journal of Statistical Planning and Inference 72, no. 1-2 (September 1998): 109–19. http://dx.doi.org/10.1016/s0378-3758(98)00026-3.

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14

Luther, Robert D., and David A. Pike. "Equitably Colored Balanced Incomplete Block Designs." Journal of Combinatorial Designs 24, no. 7 (April 17, 2015): 299–307. http://dx.doi.org/10.1002/jcd.21427.

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15

Bailey, R. A., and Peter J. Cameron. "Multi-part balanced incomplete-block designs." Statistical Papers 60, no. 2 (January 23, 2019): 405–26. http://dx.doi.org/10.1007/s00362-018-01071-x.

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16

Sinha, Kishore. "Generalized partially balanced incomplete block designs." Discrete Mathematics 67, no. 3 (December 1987): 315–18. http://dx.doi.org/10.1016/0012-365x(87)90182-8.

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17

Abel, R. J. R. "Forty-three balanced incomplete block designs." Journal of Combinatorial Theory, Series A 65, no. 2 (February 1994): 252–67. http://dx.doi.org/10.1016/0097-3165(94)90023-x.

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18

Abel, R. Julian R., Iliya Bluskov, and Malcolm Greig. "Balanced incomplete block designs with block size 8." Journal of Combinatorial Designs 9, no. 4 (2001): 233–68. http://dx.doi.org/10.1002/jcd.1010.

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19

Graczyk, Małgorzata, and Malwina Janiszewska. "Remarks about a construction method for D-optimal chemical balance weighing designs." Biometrical Letters 56, no. 2 (December 1, 2019): 215–38. http://dx.doi.org/10.2478/bile-2019-0012.

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SummaryThis paper presents some constructions of regular D-optimal weighing designs based on the incidence matrices of a balanced incomplete block design, balanced bipartite weighing design and ternary balanced block design. We determine optimality conditions and relations between the parameters of the design, and give an example.

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20

Graczyk, Małgorzata, and Bronisław Ceranka. "A Regular D‑optimal Weighing Design with Negative Correlations of Errors." Acta Universitatis Lodziensis. Folia Oeconomica 5, no. 344 (September 30, 2019): 7–16. http://dx.doi.org/10.18778/0208-6018.344.01.

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The issues concerning optimal estimation of unknown parameters in the model of chemical balance weighing designs with negative correlated errors are considered. The necessary and sufficient conditions determining the regular D‑optimal design and some new construction methods are presented. They are based on the incidence matrices of balanced incomplete block designs and balanced bipartite weighing designs.

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21

Singh, Manjit, and Jagroop Kaur. "A New Solution of a Balanced Incomplete Block Design." Calcutta Statistical Association Bulletin 36, no. 3-4 (September 1987): 189–92. http://dx.doi.org/10.1177/0008068319870309.

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22

Singh, Manjit, and Jagroop Kaur. "‘A New Solution of a Balanced Incomplete Block Design’." Calcutta Statistical Association Bulletin 37, no. 1-2 (March 1988): 128. http://dx.doi.org/10.1177/0008068319880116.

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23

Ceranka, Bronisław, and Małgorzata Graczyk. "New Results Regarding the Construction Method for D‑optimal Chemical Balance Weighing Designs." Acta Universitatis Lodziensis. Folia Oeconomica 4, no. 349 (November 23, 2020): 129–41. http://dx.doi.org/10.18778/0208-6018.349.08.

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We study an experiment in which we determine unknown measurements of p objects in n weighing operations according to the model of the chemical balance weighing design. We determine a design which is D‑optimal. For the construction of the D‑optimal design, we use the incidence matrices of balance incomplete block designs, balanced bipartite weighing designs and ternary balanced block designs. We give some optimality conditions determining the relationships between the parameters of a D‑optimal design and we present a series of parameters of such designs. Based on these parameters, we will be able to set down D‑optimal designs in classes in which it was impossible so far.

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24

Saha, G. M., Aloke Dey, and Chand K. Midha. "Construction of Nested Incomplete Block Designs." Calcutta Statistical Association Bulletin 48, no. 3-4 (September 1998): 195–206. http://dx.doi.org/10.1177/0008068319980307.

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Nested balanced incomplete block designs were introduced by Preece (1967). Generalization of these designs were studied by Home! and Robinson (1975). In this communication, we present some systematic methods of construction of nested balanced and partially balanced incomplete block designs. These methods unify and generalize some of the existing ones.

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25

Jhee, Yoon Kyoo. "Two-Dimensional Symmetric Balance Incomplete Block Design Codes for Small Input Power." Journal of the Institute of Electronics Engineers of Korea 50, no. 5 (May 25, 2013): 121–27. http://dx.doi.org/10.5573/ieek.2013.50.5.121.

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26

Gujarathi, C. C., and Pravender. "On the Construction of VB Designs." Calcutta Statistical Association Bulletin 48, no. 1-2 (March 1998): 109–14. http://dx.doi.org/10.1177/0008068319980111.

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This paper gives complete analytical study of suitability and non-availability of I-associate and II-associate designs of a given 2-class partially balanced incomplete block (2-PBIB) design in the construction of a variance balance (VB) design using the given 2-PBIB design.

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27

Julian R. Abel, R., G. Ge, Malcolm Greig, and L. Zhu. "Resolvable balanced incomplete block designs with block size 5." Journal of Statistical Planning and Inference 95, no. 1-2 (May 2001): 49–65. http://dx.doi.org/10.1016/s0378-3758(00)00277-9.

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28

Choi, Jaesung. "Projection analysis for balanced incomplete block designs." Journal of the Korean Data and Information Science Society 26, no. 2 (March 31, 2015): 347–54. http://dx.doi.org/10.7465/jkdi.2015.26.2.347.

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29

Sinha, Kishore. "Construction of balanced treatment incomplete block designs." Communications in Statistics - Theory and Methods 21, no. 5 (January 1992): 1377–82. http://dx.doi.org/10.1080/03610929208830853.

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30

Dey, A., U. S. Das, and A. K. Banerjee. "Construction of Nested Balanced Incomplete Block Designs." Calcutta Statistical Association Bulletin 35, no. 3-4 (September 1986): 161–68. http://dx.doi.org/10.1177/0008068319860306.

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31

Marrero, Osvaldo, and Damaraju Raghavarao. "Overall A-optimal balanced incomplete block designs." Journal of Statistical Planning and Inference 21, no. 1 (January 1989): 125–27. http://dx.doi.org/10.1016/0378-3758(89)90025-6.

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32

Kuriki, Shinji, Iwona Mejza, Masakazu Jimbo, Stanis?aw Mejza, and Kazuhiro Ozawa. "Resolvable semi-balanced incomplete split-block designs." Metrika 61, no. 1 (February 2005): 9–16. http://dx.doi.org/10.1007/s001840400320.

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33

Saka, A. Jamiu, B. Lateef Adeleke, and T. Gbolahan Jaiyeola. "Zig-Zag matrix for resolvable nested balanced incomplete block designs." International Journal of Algebra and Statistics 6, no. 1-2 (May 13, 2017): 81. http://dx.doi.org/10.20454/ijas.2017.1233.

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This paper presents a method of construction of designs which utilizes special matrix structures referred to as Zig-zag. The Zig-zag matrix structures give rise to initial blocks for resolvable nested balanced incomplete block designs (RNBIBDs). The construction of the designs for \((v)\) treatment number being a perfect square with specific interest on \((k)\) block size as a prime number are presented. The designs constructed are of high efficiency with minimum blocks. A generalized information matrix is also obtained.

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34

Dutta, Ganesh, Premadhis Das, and Nripes K. Mandal. "Optimum covariate designs in partially balanced incomplete block (PBIB) design set-ups." Journal of Statistical Planning and Inference 139, no. 8 (August 2009): 2823–35. http://dx.doi.org/10.1016/j.jspi.2009.01.009.

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35

Rotich, Jeremy, Mathew Kosgei, and Gregory Kerich. "Optimal Third Order Rotatable Designs Constructed from Balanced Incomplete Block Design (BIBD)." Current Journal of Applied Science and Technology 22, no. 3 (July 14, 2017): 1–5. http://dx.doi.org/10.9734/cjast/2017/34937.

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36

Sharma, M. K., and Sileshi Fanta. "Application of partially balanced incomplete block design in pps sampling." Model Assisted Statistics and Applications 6, no. 1 (March 14, 2011): 63–69. http://dx.doi.org/10.3233/mas-2011-0174.

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37

Abdy, Muhammad, and Wahida Sanusi. "The Application of Algebraic Methods in Balanced Incomplete Block Design." Journal of Physics: Conference Series 1028 (June 2018): 012123. http://dx.doi.org/10.1088/1742-6596/1028/1/012123.

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38

Bilous, R. T., and G. H. J. van Rees. "Self-dual codes and the (22,8,4) balanced incomplete block design." Journal of Combinatorial Designs 13, no. 5 (2005): 363–76. http://dx.doi.org/10.1002/jcd.20052.

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39

Mason, William D. "Response to “Balanced Incomplete-Block Design: Its Use and Misuse”." Journal of Pharmaceutical Sciences 74, no. 7 (July 1985): 795–96. http://dx.doi.org/10.1002/jps.2600740726.

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40

Dukes, Peter, Esther R. Lamken, and Alan C. H. Ling. "An Existence Theory for Incomplete Designs." Canadian Mathematical Bulletin 59, no. 2 (June 1, 2016): 287–302. http://dx.doi.org/10.4153/cmb-2015-073-7.

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AbstractAn incomplete pairwise balanced design is equivalent to a pairwise balanced design with a distinguished block, viewed as a ‘hole’. If there are v points, a hole of size w, and all (other) block sizes equal k, this is denoted IPBD((v;w), k). In addition to congruence restrictions on v and w, there is also a necessary inequality: v > (k − 1)w. This article establishes two main existence results for IPBD((v;w), k): one in which w is fixed and v is large, and the other in the case v > (k −1+∊)w when w is large (depending on ∊). Several possible generalizations of the problemare also discussed.

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41

Shu, Xiaohua, and Damaraju Raghavarao. "Balanced and partially balanced incomplete block designs with autocorrelation errors." Journal of Statistical Planning and Inference 140, no. 11 (November 2010): 3230–35. http://dx.doi.org/10.1016/j.jspi.2010.04.021.

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42

Baksalary, Jerzy K., and P. D. Puri. "Pairwise-balanced, variance-balanced and resistant incomplete block designs revisited." Annals of the Institute of Statistical Mathematics 42, no. 1 (1990): 163–71. http://dx.doi.org/10.1007/bf00050787.

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43

SOLÓRZANO, V., S. G. GILMOUR, K. PHELPS, and R. KENNEDY. "Assessment of suitable designs for field experiments involving airborne diseases." Journal of Agricultural Science 129, no. 3 (November 1997): 249–56. http://dx.doi.org/10.1017/s0021859697004826.

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The suitability was assessed of various designs for field experiments investigating plant diseases caused by airborne pathogens that can be subject to interplot interference. Use of a model to describe such interference showed that the treatments with the most dissimilar effects on controlling the disease should be allocated to experimental plots furthest apart in each block, in order to minimize the interplot interference within a block. When using large square plots, rectangular blocks were more efficient than square blocks in minimizing treatment-comparison biases due to interference between neighbours. For rectangular blocks with the square plots side by side, less biased treatment comparisons were obtained from designs with complete blocks than from designs with incomplete blocks, especially when larger numbers of treatments were included in the experiment. However, when interplot variance is taken into account, incomplete blocks may give better treatment comparisons. Similarly, unbalanced designs composed only of incomplete blocks that yield less biased treatment comparisons may be better than balanced incomplete block designs when interplot variance is low. For high levels of variation, balanced incomplete block designs may be more appropriate, as increasing the precision of the treatment comparisons becomes more important than reducing the bias.

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44

Pearce, S. C. "Some Design Problems in Crop Experimentation. III. Non-Orthogonality." Experimental Agriculture 31, no. 4 (October 1995): 409–22. http://dx.doi.org/10.1017/s0014479700026405.

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SUMMARYIdeally each block of an experiment should be made up in the same way with respect to treatments, that is, the design should be ‘orthogonal’. In practice that can be difficult to achieve, especially if the blocks have been chosen to fit the fertility pattern of the field. Sometimes it is impossible, in which case each block will have to contain its own selection of treatments. A number of simple and useful possibilities exist.Whatever non-orthogonal design is chosen some of the contrasts of interest (perhaps all of them) will be evaluated less efficiently, but that can be compensated by the smaller error mean-square given by a better blocking system. Also, where blocks do differ in their content, comparing their means will provide additional information about treatment effects. Sometimes the information may be worth the trouble of recovery.Special attention is given in this paper to total balance (including balanced incomplete block designs), supplemented balance, square and rectangular lattices and alpha-designs. The reinforcement of a design is explained and the advantages considered.Problemas de diseño en la experimentación con cultivos. III

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45

Mejza, Iwona, and Stanislaw Mejza. "Incomplete Split-Plot Designs Generatd By GDPBIBD(2)." Calcutta Statistical Association Bulletin 46, no. 1-2 (March 1996): 117–28. http://dx.doi.org/10.1177/0008068319960110.

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The paper deals with split-plot types of experiment in which some kind of incompleteness can be accepted. In particular, the considered designs can be incomplete with regard to the wboleplot treatments or with regard to the subplot treatments. In such a case the incomplete treatments are arranged in a Gtoup Divisible Partially Balanced Incomplete Block Design with Two Associate Classes (GDPBIBD{2)). Hence, the resulting desian is called incomplete split-plot design generated by GDPBIBD(2). AMS Subject Classification: 62K10, 62K15.

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46

Abel, R. Julian R., Iliya Bluskov, and Malcolm Greig. "Balanced incomplete block designs with block size 9: part II." Discrete Mathematics 279, no. 1-3 (March 2004): 5–32. http://dx.doi.org/10.1016/s0012-365x(03)00260-7.

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47

Du, Beiliang. "Splitting balanced incomplete block designs with block size 3 × 2." Journal of Combinatorial Designs 12, no. 6 (2004): 404–20. http://dx.doi.org/10.1002/jcd.20025.

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48

Tyagi, B. N., and S. K. H. Rizwi. "Efficiency-⁄Partially-Efficiency-Balanced Block Designs through Difference Sets." Calcutta Statistical Association Bulletin 42, no. 1-2 (March 1992): 97–102. http://dx.doi.org/10.1177/0008068319920107.

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In this paper, some new efficiency⁄partially efficiency Balanced block designs have been constructed using the method of differences. These designs are binary with incomplete blocks and are of much practical utility.

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49

Chowdhury, Kanchan, and Rumana Rois. "An Incomplete Block Change-Over Design Balanced for First and Second-Order Residual Effect." Journal of Agricultural Studies 1, no. 1 (February 5, 2013): 59. http://dx.doi.org/10.5296/jas.v1i1.3028.

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Balanced designs are often needed in agriculture, economics and other context. A series of balanced designs called incomplete block change-over design (IBCOD) has been developed. The analysis and the problems of IBCOD which also provide estimates of first-order and second-order residual effects have also been presented.

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50

Kaur, Parneet, and Davinder Kumar Garg. "Construction of incomplete Sudoku square and partially balanced incomplete block designs." Communications in Statistics - Theory and Methods 49, no. 6 (January 24, 2019): 1462–74. http://dx.doi.org/10.1080/03610926.2018.1563177.

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