Several fields, such as biological, medical, public health, agricultural sciences, etc., require circular balanced repeated measurement designs with fewer unequal number of repeated measurements than the number of treatments. Also, the availability and high cost of experimental subjects in these fields prefer the design in fewer experimental units. However, balancing the carryover effects of the treatments in minimal experimental subjects is one of the problems in this case. In this paper, several new series of minimal circular nearly strongly balanced RMDs in periods of two and three different sizes are constructed. The proposed construction of designs has high efficiency and, therefore, can save the cost of experimentations due to a fewer experimental subjects. Most of the designs are very useful because of the unavailability of strongly balanced RMDs for these combinations of parameters. A list of sets of shifts for the construction of minimal circular nearly SBRMDs has also been mentioned in the Appendix.

• Afsarinejad, K. (1994). Repeated measurements designs with unequal periods sizes. Journal of the Italian Statistical Society, 3(2), 161–168. https://doi.org/10.1007/BF02589224 
• Bashir, Z., Ahmed, R., Tahir, M. H., Ghazali, S. S. A., & Shehzad, F. (2018). Some extensions of circular balanced and circular strongly balanced repeated measurements designs. Cozzunications in Statistics – Theory and Zethods, 47(9), 2183–2194. https://doi.org/10.1080/03610926.2017.1337140
• Cheng, C. S., & Wu, C. F. (1980). Balanced repeated measurements designs. Annals of Statistics, 8(8), 1272–1283. https://doi.org/10.1214/aos/1176345200 
• Divecha, J., & Gondaliya, J. (2014). Construction of minimal balanced cross over designs having good efficiency of separability. Electronic Journal of Statistics, 8(2), 2923–2936. https://doi.org/10.1214/14-EJS979 
• Hanford, K. (2005). Lecture notes on mixed models. Spring. 
• Iqbal, I., & Jones, B. (1994). Efficient repeated measurements designs with equal and unequal period sizes. Journal of Statistical Planning and Inference, 42(1-2), 79–88. https://doi.org/10.1016/0378-3758(94)90190-2 
• Iqbal, I., & Tahir, M. H. (2009). Circular strongly balanced repeated measurements designs. Cozzunications in Statistics—Theory and Zethods, 38(20), 3686–3696. https://doi.org/10.1080/03610920802642566 
• Iqbal, I., Tahir, M. H., & Ghazali, S. S. A. (2010). Circular first-and second-order balanced repeated measurements designs. Cozzunications in Statistics-Theory and Zethods, 39(2), 228–240. https://doi.org/10.1080/03610920902941728 
• Magda, C. G. (1980). Circular balanced repeated measurements designs. Communications in Statistics – Theory and Methods, 9(18), 1901–1918. https://doi.org/10.1080/03610928008828004 
• Pearce, S. C. (1964). Experimenting with blocks of natural size. Biometrika, 20(4), 699–706. https://doi.org/10.2307/2528123 
• Rasheed, U., Rasheed, H. M. K., Rasheed, M., & Ahmed, R. (2018). Minimal circular strongly balanced repeated measurements designs in periods of three different sizes. Communications in Statistics – Theory and Methods, 47(16), 4088–4094. https://doi.org/10.1080/03610926.2017.1361995
• Schulz, K. F. (1995). Subverting randomization in controlled trials. JAMA: The Journal of the American Medical Association, 274(18), 1456–1458. https://doi.org/10.1001/jama.1995.03530180050029
• Schulz, K. F., & Grimes, D. A. (2002). Generation of allocation sequences in randomised trials: Chance, not choice. The Lancet, 359(9305), 515–519. https://doi.org/10.1016/S0140-6736(02)07683-3 

To cite this article: Muhammad Daniyal, Jigneshkumar Gondaliya & Rashid Ahmed (2023) On the construction of balanced repeated measurements designs with good circular properties, Statistical Theory and Related Fields, 7:2, 121-129, DOI: 10.1080/24754269.2023.2184607

To link to this article: https://doi.org/10.1080/24754269.2023.2184607