Some extensions of circular balanced and circular strongly balanced repeated measurements designs.

*(English)*Zbl 1388.05023Summary: Repeated measurement designs are widely used in medicine, pharmacology, animal sciences, and psychology. In this paper the works of I. Iqbal and M. H. Tahir [ibid. 38, No. 20, 3686–3696 (2009; Zbl 1285.05019)] and I. Iqbal et al. [ibid. 39, No. 2, 228–240 (2010; Zbl 1227.05076)] are generalized for the construction of circular-balanced and circular strongly balanced repeated measurements designs through the method of cyclic shifts for three periods.

##### MSC:

05B05 | Combinatorial aspects of block designs |

62K10 | Statistical block designs |

62K05 | Optimal statistical designs |

##### Keywords:

circular-balanced repeated measurements designs; circular strongly balanced repeated measurements designs; method of cyclic shifts; repeated measurement designs
PDF
BibTeX
XML
Cite

\textit{Z. Bashir} et al., Commun. Stat., Theory Methods 47, No. 9, 2183--2194 (2018; Zbl 1388.05023)

Full Text:
DOI

##### References:

[1] | Afsarinejed, K.1990. Repeated measurements designs: A review. Communication in Statistics—Theory and Methods 19:3985-4028. · Zbl 0728.62071 |

[2] | Cheng, C. S., and C. F. Wu. 1980. Balanced repeated measurements designs. Annals of Statistics 8:1272-83. · Zbl 0461.62064 |

[3] | Hedayat, A. S., and M. Yang. 2003. Universal optimality of balanced uniform crossover designs. Annals of Statistics 31:978-83. · Zbl 1028.62060 |

[4] | Iqbal, I., and B. Jones. 1994. Efficient repeated measurements designs with equal and unequal period sizes. Journal of Statistical Planning and Inference 42:79-88. · Zbl 0803.62072 |

[5] | Iqbal, I., and M. H. Tahir. 2009. Circular strongly balanced repeated measurements designs. Communications in Statistics—Theory and Methods 38:3686-96. · Zbl 1285.05019 |

[6] | Iqbal, I., M. H. Tahir, and S. S. A. Ghazali. 2010. Circular first- and second-order balanced repeated measurements designs. Communications in Statistics—Theory and Methods 39:228-40. · Zbl 1227.05076 |

[7] | Jones, B., and M. G. Kenward. 1989. Design and analysis of cross over trials. London: Chapman and Hall. · Zbl 0729.62068 |

[8] | Magda, C. G.1980. Circular balanced repeated measurements designs. Communications in Statistics—Theory and Methods 9:1901-18. · Zbl 0457.62061 |

[9] | Roy, B. K.1988. Construction of strongly balanced uniform repeated measurements designs. Journal of Statistical Planning and Inference 19:341-8. · Zbl 0642.62043 |

[10] | Sharma, V. K., S. Jaggi, and C. Varghese. 2003. Minimal balanced repeated measurements designs. Journal of Applied Statistics 30:867-72. · Zbl 1121.62485 |

[11] | Williams, E. R.1949. Experimental designs balanced for the estimation of residual effects of treatments. Australian Journal of Science Research A2:149-68. |

[12] | Williams, E. R.1950. Experimental designs balanced for pairs of residual effects. Australian Journal of Science Research A3:351-63. |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.