Electronic Journal of Statistics

Construction of minimal balanced cross over designs having good efficiency of separability

Jyoti Divecha and Jignesh Gondaliya

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Minimal balanced cross over designs having lesser, equal and more periods than the number of treatments are constructed using directed m-terraces and their modified forms. A complementary pair and trio of the terraces constructs a cross over design with lesser periods while a uniform terrace yields a uniform cross over design. Two new series of cross over designs in even number of treatments have been obtained. All the designs possess good efficiency of separability and therefore they are suitable for the estimation of direct and first order carry over effects of treatments. A list of terraces for the construction of minimal balanced cross over designs having three to nine treatments is given.

Article information

Electron. J. Statist., Volume 8, Number 2 (2014), 2923-2936.

First available in Project Euclid: 9 January 2015

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K05: Optimal designs 62K25: Robust parameter designs
Secondary: 62K10: Block designs

Cross over direct effect minimal directed m-terrace carry over effect


Divecha, Jyoti; Gondaliya, Jignesh. Construction of minimal balanced cross over designs having good efficiency of separability. Electron. J. Statist. 8 (2014), no. 2, 2923--2936. doi:10.1214/14-EJS979. https://projecteuclid.org/euclid.ejs/1420815882

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  • [1] Afsarinejad, K. and Hedayat, A.S., Repeated measurements designs for a model with self and mixed carryover effects, Journal of Statistical Planning and Inference 106 (2002), pp. 449–459.
  • [2] Bailey, R.A., Quasi-complete Latin squares: Construction and randomization, Journal of the Royal Statistical Society B 46 (1984), pp. 323–334.
  • [3] Blaisdell, E.A. and Raghavaravo, D., Partially balanced change-over designs based on m-associate class PBIB designs, Journal of the Royal Statistical Society B 42 (1980), pp. 334–338.
  • [4] Carriere, K.C., Optimal two-period repeated measurement designs with two or more treatments, Biometrika 80 (1993), pp. 924–929.
  • [5] Cheng, C.S. and Wu, C.F., Balanced repeated measurements designs, Annals of Statistics 8 (1980), pp. 1272–1283.
  • [6] Collombier, D. and Merchermek, I., Optimal cross-over experimental designs, Sankhya: The Indian Journal of Statistics B 55 (1993), pp. 249–261.
  • [7] Dey, A., Gupta, V.K. and Singh, M., Optimal change over designs, Sankhya: The Indian Journal of Statistics B 45 (1983), pp. 233–239.
  • [8] Fletcher, D.J., A new class of change-over designs for factorial experiments, Biometrika 74 (1987), pp. 649–654.
  • [9] Gill, J.L., Design and Analysis of Experiments in the Animal and Medical Sciences, Vol II, Iowa State Univ. Press, Ames, 1978.
  • [10] Grizzle, J.E., The two-period change-over design and its use in clinical trials, Biometrics 21 (1965), pp. 467–480.
  • [11] Hanford, K., Lecture Notes on Mixed Models, Spring, United States, 2005.
  • [12] Hedayat, A.S. and Afsarinejad, K., Repeated measurements designs, I., In, A Survey of Statistical Design and Linear Models (J.N. Srivastava, Ed.), pp. 229–242, North-Holland, Amsterdam, 1975.
  • [13] Jones, B. and Kenward, M.G., Design and Analysis of Crossover Trials, Chapman and Hall/CRC, Boca Raton, 2003.
  • [14] Jones, B. and Donev, A.N., Modelling and design of cross-over trials, Statistics in Medicine 15 (1996), pp. 1435–1446.
  • [15] Kiefer, J. and Wynn, H.P., Optimal balanced block and Latin squares designs for correlated observations, The Annals of Statistics 9 (1981), pp. 737–757.
  • [16] Kunert, J., Optimality of balanced uniform repeated measurement designs, The Annals of Statistics 12 (1984), pp. 1006–1017.
  • [17] Kunert, J., Crossover designs for two treatments and correlated errors, Biometrika 78 (1991), pp. 315–324.
  • [18] Kushner, H.B., Optimal repeated measurements designs: The linear optimality equations, The Annals of Statistics 25 (1997), pp. 2328–2344.
  • [19] Martin, R.J. and Eccleston, J.A., Variance-balanced change-over designs for dependent observations, Biometrika 85 (1998), pp. 883–892.
  • [20] Matthews, J.N.S., Estimating dispersion parameters in the analysis of data from crossover trials, Biometrika 76 (1989), pp. 239–244.
  • [21] Morgan, J.P., Balanced polycross designs, Journal of the Royal Statistical Society B 50 (1988), pp. 93–104.
  • [22] Nason, M. and Follmann, D., Design and analysis of crossover trials for absorbing binary endpoints, Biometrics 66 (2010), pp. 958–965.
  • [23] Senn, S., Cross-Over Trials in Clinical Research, John Wiley and Sons, New York, 1993.
  • [24] Taka, M.T. and Armitage, P., Autoregressive models in clinical trials, Communications in Statistics: Theory and Methods 12 (1983), pp. 865–867.
  • [25] Vonesh, E.F. and Chinchilli, V.M., Linear and Nonlinear Models for the Analysis of Repeated Measurements, Marcel Dekker/CRC, New York, 1996.
  • [26] Williams, E.J., Experimental designs balanced for the estimation of residual effects of treatments, Australian Journal of Scientific Research 2 (1949), pp. 149–168.