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Construction of circular partially balanced-repeated measurement designs using cyclic shifts.(English)Zbl 07551448

Summary: Repeated measurement designs are widely used in medicine, pharmacology, animal sciences and psychology. These designs balance out the residual effects. The situations where balanced repeated measurements designs require a large number of the subjects, partially-balanced repeated measurements designs should be used. In this paper some infinite series are developed which provide circular partially-balanced repeated measurement designs for \(p\) (periods) even. Catalogues of circular partially-balanced repeated measurement designs are also presented for \(v\) (treatments) \( \leq 100\) with \(p\) = 5, 7 & 9.

MSC:

05B05 Combinatorial aspects of block designs
62K10 Statistical block designs
62K05 Optimal statistical designs

Cite

References:

[1]Afsarinejed, K., Repeated measurements designs-a review, 1990. Communication in Statistics—Theory and Methods, 19, 3985-4028 ·Zbl 0728.62071 ·doi:10.1080/03610929008830426
[2]Bailey, R. A.; Cemeron, P. J.; Fillipiak, K.; Kunert, J.; Markiewicz, A., On optimality and construction of circular repeated measurements designs, 2017. Statistica Sinica, 27, 1-22 ·Zbl 1468.62325
[3]Cheng, C. S.; Wu, C. F., Balanced repeated measurements designs, 1980. Annals of Statistics, 8, 1272-83 ·Zbl 0461.62064 ·doi:10.1214/aos/1176345200
[4]Hedayat, A. S.; Yang, M., Universal optimality of balanced uniform crossover designs, 2003. Annals of Statistics, 31, 978-83 ·Zbl 1028.62060 ·doi:10.1214/aos/1056562469
[5]Iqbal, I.; Jones, B., Efficient repeated measurements designs with equal and unequal period sizes, 1994. Journal of Statistical Planning and Inference, 42, 79-88 ·Zbl 0803.62072 ·doi:10.1016/0378-3758(94)90190-2
[6]Iqbal, I.; Tahir, M. H., Circular strongly balanced repeated measurements designs, 2009. Communications in Statistics—Theory and Methods, 38, 3686-96 ·Zbl 1285.05019 ·doi:10.1080/03610920802642566
[7]Iqbal, I.; Tahir, M. H.; Ghazali, S. S. A., Circular first-and second-order balanced repeated measurements designs, 2010. Communications in Statistics-Theory and Methods, 39, 228-40 ·Zbl 1227.05076 ·doi:10.1080/03610920902941728
[8]Jones, B.; Kenward, M. G., 1989. Design and analysis of cross over trials, London: Chapman and Hall, London ·Zbl 0729.62068
[9]Magda, C. G., Circular balanced repeated measurements designs, 1980. Communications in Statistics-Theory and Methods, 9, 1901-18 ·Zbl 0457.62061 ·doi:10.1080/03610928008828004
[10]Roy, B. K., Construction of strongly balanced uniform repeated measurements designs, 1988. Journal of Statistical Planning and Inference, 19, 341-8 ·Zbl 0642.62043 ·doi:10.1016/0378-3758(88)90041-9
[11]Sharma, V. K.; Jaggi, S.; Varghese, C., Minimal balanced repeated measurements designs, 2003. Journal of Applied Statistics, 30, 867-72 ·Zbl 1121.62485 ·doi:10.1080/0266476032000075958
[12]Williams, E. R., Experimental designs balanced for the estimation of residual effects of treatments, 1949. Australian Journal of Science Research, A2, 149-68
[13]Williams, E. R., Experimental designs balanced for pairs of residual effects, 1950. 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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