Efficient repeated measurements designs with equal and unequal period sizes.

*(English)*Zbl 0803.62072Summary: We describe a general method of constructing repeated measurements designs using sets of cyclic shifts. Efficient designs for \(t\) treatments in \(p\) periods, where \(t\leq 10\) and \(p\leq 8\), are given. In addition, efficient strongly balanced designs and designs that are balanced for first- and second-order residual effects are given. Finally, some efficient designs with two different period sizes are given. The designs extend and fill in gaps in previously published tables.

##### MSC:

62K99 | Design of statistical experiments |

62K05 | Optimal statistical designs |

62P10 | Applications of statistics to biology and medical sciences; meta analysis |

##### Keywords:

cross-over design; combinatorial balance; direct treatment effect; first- order residual effect; repeated measurements designs; cyclic shifts; efficient strongly balanced designs; second-order residual effects; different period sizes
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\textit{I. Iqbal} and \textit{B. Jones}, J. Stat. Plann. Inference 42, No. 1--2, 79--88 (1994; Zbl 0803.62072)

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##### References:

[1] | Afsarinejad, K., Balanced repeated measurements designs, Biometrika, 70, 199-204, (1983) · Zbl 0502.62068 |

[2] | Constantine, G.; Hedayat, A., A construction of repeated measurements designs with balance for residual effects, J. statist. plann. inference, 6, 153-164, (1982) · Zbl 0486.62074 |

[3] | Davis, A.W.; Hall, W.B., Cyclic change-over designs, Biometrika, 56, 283-293, (1969) · Zbl 0179.23803 |

[4] | Hedayat, A.; Afsarinejad, K., Repeated measures designs, I, () · Zbl 0304.62009 |

[5] | Hedayat, A.; Afsarinejad, K., Repeated measures designs, II, Ann. statist., 6, 619-628, (1978) · Zbl 0395.62056 |

[6] | Iqbal, I., Construction of experimental designs using cyclic shifts, Unpublished ph.D. thesis, (1991), University of Kent at Canterbury UK |

[7] | Iqbal, I.; Jones, B., The construction of efficient repeated measurements designs with equal and unequal period sizes, Technical report UKC/IMS/S93/2, (1993), University of Kent at Canterbury · Zbl 0803.62072 |

[8] | Jones, B.; Kenward, M.G., The design and analysis of cross-over trials, (1989), Chapman and Hall London · Zbl 0729.62068 |

[9] | Patterson, H.D.; Lucas, H.L., Change-over designs, Tech bull. no. 147, (1962), North Carolina Agricultural Experiment Station · Zbl 0086.12601 |

[10] | Sharma, V.K., Change-over designs with complete balance for first and second residual effects, Canad. J. statist., 5, 121-132, (1977) · Zbl 0382.62067 |

[11] | Sheehe, P.R.; Bross, I.D.J., Latin squares to balance immediate residual and other effects, Biometrics, 17, 405-414, (1961) · Zbl 0101.36302 |

[12] | Williams, E.J., Experimental designs balanced for the estimation of residual effects of treatments, Austral. J. scientific res., 2, 149-168, (1949) |

[13] | Williams, E.J., Experimental designs balanced pairs of residual effects, Austral. J. scientific res., 3, 351-363, (1950) |

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