General Construction of Efficient Circular Weakly Balanced Repeated Measurements Designs

  • Qaisar Mehmood Government Post Graduate College Bahawalnagar.
  • Kashif Rasheed Department of statistics islamia university Bahawalpur
  • Khadija Noreen Department of statistics islamia university Bahawalpur
  • Rashid Ahmed Department of statistics islamia university Bahawalpur
  • Berihan R. Elemary Department of Applied, Mathematical and Actuarial Statistics, Damietta University and NUB-Nahda University, Beni Suef, Egypt
DOI: https://doi.org/10.32350/sir.61.05
Keywords: carry over effects, direct effects, efficiency of residual effects, repeated measurement designs (RMDs)

Abstract

Abstract Views: 139

Weakly balanced repeated measurements designs (RMDs) are used to balance out residual effects where minimal balanced RMDs cannot be obtained. RMDs are equally important in periods of both equal and unequal sizes. There should be a general procedure to construct these designs. In this article, some generators are developed for the general construction of efficient minimal circular weakly balanced RMDs.

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Author Biography

Berihan R. Elemary, Department of Applied, Mathematical and Actuarial Statistics, Damietta University and NUB-Nahda University, Beni Suef, Egypt

Department of Applied, Mathematical and Actuarial Statistics, Damietta University and NUB-Nahda University, Beni Suef, Egypt

References

Williams ER. Experimental designs balanced for the estimation of residual effects of treatments. Aus J Sci Res. 1949;2(2):149-168. https://doi.org/10.1071/CH9490149

Cheng CS, Wu CF. Balanced repeated measurements designs. Ann Stat. 1980;8(6):1272-1283. https://doi.org/10.1214/aos/1176345200

Magda CG. Circular balanced repeated measurements designs. Commun Stats Theory Methods. 1980;9(18):1901-1918. https://doi.org/10.1080/03610928008828004

Afsarinejad K. Repeated measurements designs with unequal periods sizes. J Italian Stat Soc. 1994;2:161-168. https://doi.org/10.1007/BF02589224

Iqbal I, Jones B. Efficient repeated measurements designs with equal and unequal period sizes. J Stat Plan Infer. 1994;42(1-2):79-88. https://doi.org/10.1016/0378-3758(94)90190-2

Sharma VK, Jaggi S, Varghese C. Minimal balanced repeated measurements designs. J Appl Stat. 2003;30(8):867-872. https://doi.org/10.1080/0266476032000075958

Iqbal I, Tahir MH. Circular strongly balanced repeated measurements designs. Commun Stats Theory Methods. 2009;38(20):3686-3696. https://doi.org/10.1080/03610920802642566

Iqbal I, Tahir MH, Ghazali SSA. Circular first-and second-order balanced repeated measurements designs. Commun Stats Theory Methods. 2010;39(2):228-240. https://doi.org/10.1080/03610920902941728

Bashir Z, Ahmed R, Tahir MH, Ghazali SSA, Shehzad F. Some extensions of circular balanced and circular strongly balanced repeated measurements designs. Commun Stats Theory Methods. 2018;47(9):2183-2194. https://doi.org/10.1080/03610926.2017.1337140

Rajab MR, Ahmed R, Shehzad F, Tahir MH. Some new constructions of circular balanced repeated measurements designs. Commun Stats Theory Methods. 2018;47(17):4142-4151. https://doi.org/10.1080/03610926.2017.1367817

Rasheed U, Rasheed HMK, Rasheed M, Ahmed R. Minimal circular strongly balanced repeated measurements designs in periods of three different sizes. Commun Stats Theory Methods. 2018;47(16):4088-4094. https://doi.org/10.1080/03610926.2017.1361995

Daniyal M, Ahmed R, Shehzad F, Tahir MH, Iqbal Z. Construction of repeated measurements designs strongly balanced for residual effects. Commun Stats Theory Methods. 2020;49(17):4288-4297. https://doi.org/10.1080/03610926.2019.1599019

Bailey RA, Cemeron PJ, Fillipiak K, Kunert J, Markiewicz A. On optimality and construction of circular repeated measurements designs. Stat Sinica. 2017;27(1):1-22. http://dx.doi.org/10.5705/ss.202015.0045

Khan A, Ahmed R, Shehzad F, Tahir MH, Ghazali SSA. Construction of circular partially balanced repeated measurement designs. Commun Stat Simul Computa. 2019;48(2):506-515. https://doi.org/10.1080/03610918.2017.1387661

Hussain S, Ahmed R, Aslam M, Shah A, Rasheed HMK. Some new construction of circular weakly balanced repeated measurements designs in periods of two different sizes. Commun Stats Theory Methods, 2020;49(9):2253-2263. https://doi.org/10.1080/03610926.2019.1570263

Hussain S, Gondaliya J, Ahmed R., Jabeen R. Some new generators to obtain efficient circular weakly balanced repeated measurements designs. Commun Stats Theory Methods. 2021;50(15):3713-3730. https://doi.org/10.1080/03610926.2019.1570263

Pearce SC, Calinski T, Marshall TFdeC. The basic contrasts of an experimental design with special reference to the analysis of data. Biometrika. 1974;61(3):449-460. https://doi.org/10.1093/biomet/61.3.449

Divecha J, Gondaliya J. Construction of minimal balanced crossover designs having good efficiency of separability. Elec J Stat. 2014;8:2923-2936. https://doi.org/10.1214/14-EJS979

Iqbal I. Construction of experimental designs using cyclic shifts. Dessertation. University of Kent at Canterbury;1991. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.293152

Published
2022-03-30
How to Cite
1.
Mehmood Q, Rasheed K, Khadija Noreen, Rashid Ahmed, Berihan R. Elemary. General Construction of Efficient Circular Weakly Balanced Repeated Measurements Designs. Sci Inquiry Rev. [Internet]. 2022Mar.30 [cited 2024Sep.8];6(1). Available from: https://journals.umt.edu.pk/index.php/SIR/article/view/2254
Issue
Vol 6 No 1 (2022): March
Section
Orignal Article

Copyright (c) 2022 Qaisar Mehmood, Kashif Rasheed , Khadija Noreen, Rashid Ahmed, Berihan R. Elemary

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