Abstract
Partially balanced crossover designs (PBCODs) are needed in case a balanced design is not possible due to some reasons. Blaisdell and Raghavarao (1980) and Raghavarao and Blaisdell (1985) introduced the concept of PBCODs and gave certain classes of such designs, along with their efficiency factors. The work on the construction of PBCODs was further considered by Aggarwal and Jha (2006), wherein they gave a number of classes of such designs, based on certain partially balanced incomplete block (PBIB) (2) designs and rectangular association scheme. The present work provides some new classes of connected PBCODs based on 2-, 3-, 4-, and general m-associate class association schemes.
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Aggarwal, M. L., and M. K. Jha. 2006. Some new series of partially balanced residual treatment effects designs. Commun. Stat. Theory Methods, 35, 1477–1482.
Blaisdell, E. A., and D. Raghavarao. 1980. Partially balanced change-over designs based on m-associate class PBIB designs. J. R. Stat. Soc. B, 42, 334–338.
Bose, R. C., and K. R. Nair. 1939. Partially balanced incomplete block designs. Sankhya, 4, 337–372.
Bose, R. C., and T. Shimamoto. 1952. Classification and analysis of partially balanced incomplete block designs with two associate classes. J. Am. Stat. Assoc., 47, 151–184.
Hedayat, A., and K. Afsarinejad. 1975. Repeated measurement designs, I. In A survey of statistical designs and linear models, ed. J. N. Srivastava, 229–242. Amsterdam, The Netherlands: North-Holland Publishing Company.
Hedayat, A., and K. Afsarinejad. 1978. Repeated measurements designs, II. Ann. Stat., 6, 619–628.
Hinkelmann, K. 1964. Extended group divisible partially balanced incomplete block designs. Ann. Math. Stat., 35, 681–695.
John, P. W. M. 1966. An extension of the triangular association scheme to three associate classes. J. R. Stat. Soc. B, 28, 361–365.
Jones, B., and M. G. Kenward. 2003. Design and analysis of cross over trials, 2nd ed. New York, NY: Chapman and Hall/CRC.
Keifer, J. 1958. On the nonrandomized optimality and randomized non-optimality of symmetrical designs. Ann. Math. Stat., 29, 907–910.
Raghavarao, D., and E. A. Blaisdell., 1985. Efficiency bounds for partially balanced change-over designs based on m-associate class PBIB designs. J. R. Stat. Soc., B, 47, 132–135.
Raghavarao, D., and K. Chandrasekhararao. 1964. Cubic designs. Ann. Math. Stat., 35, 389–397.
Raghavarao, D., and L. Padgett. 2014. Repeated measurements and cross-over designs. Hoboken, NJ: John Wiley and Sons.
Satpati, S. K., V. K. Gupta, R. Parsad, and M. L. Aggarwal. 2012. Computer-generated change-over designs for correlated observations. Commun. Stat. Theory Methods, 41, 3786–3798.
Tharthare, S. K. 1963. Right angular designs. Ann. Math. Stat., 34, 1057–1067.
Tharthare, S. K. 1965. Generalised right angular designs. Ann. Math. Stat., 36, 1535–1553.
Williams, E. J. 1949. Experimental designs balanced for the estimation of residual effects of treatments. Austr. J. Sci. Res., 2A, 149–168.
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Singh, P., Jha, M.K. & Priyadarshini, G. Constructions of partially balanced crossover designs based on two and higher order association schemes. J Stat Theory Pract 9, 778–796 (2015). https://doi.org/10.1080/15598608.2015.1019165
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DOI: https://doi.org/10.1080/15598608.2015.1019165