Catalogue of Efficient Repeated Measurements Designs for p3 = 5, 6, 7
Keywords:
Carry over effects, Residual effects, Strongly balanced RMDs, Weakly balanced RMDs, Minimal designsAbstract
Minimal strongly balanced repeated measurements designs are economical to (i) balance the residual effects, and (ii) estimate the treatment effects and residual effects independently. The situations where these minimal designs cannot be constructed, minimal nearly strongly balanced repeated measurements designs are used. In this article, some efficient minimal circular nearly strongly balanced repeated measurements designs are constructed in periods of three different sizes with the smallest of sizes 5, 6, and 7.
References
E. R. Williams. Experimental designs balanced for the estimation of residual effects of treatments, Australian Journal of Science Research, A2, pp. 149-168, 1949.
E. R. Williams. Experimental designs balanced for pairs of residual effects, Australian Journal of Science Research, A3, pp. 351-363, 1950.
C. G. Magda. Circular balanced repeated measurements designs. Communications in Statistics-Theory and Methods, Vol. 9, pp. 1901-1918, 1980.
K. Afsarinejad. Repeated measurements designs with unequal periods sizes, Journal of the Italian Statistical Society, Vol. 2, pp. 161-168, 1994.
I. Iqbal, and B. Jones. Efficient repeated measurements designs with equal and unequal period sizes, Journal of Statistical Planning and Inference, Vol. 42, pp. 79-88, 1994.
R. A. Bailey, P. J. Cemron, K. Fillipiak, J. Kunert and A. Markiewicz. On optimality and construction of circular repeated measurements designs, Statistica Sinica, Vol. 27, pp. 1-22, 2017.
Z. Bashir, R. Ahmed, M. H. Tahir, S. S. A. Ghazali, and F. Shehzad. Some extensions of circular balanced and circular strongly balanced repeated measurements designs, Communications in Statistics - Theory and Methods, Vol. 47(9), pp. 2183-2194, 2018.
A. Khan, R. Ahmed, F. Shehzad, M. H. Tahir and S. S. A. Ghazali. Construction of circular partially-balanced repeated measurement designs using cyclic shifts, Communications in Statistics-Simulation and Computation, Vol. 48(2), pp. 506-515, 2019.
R. Jabeen, H. M. K. Rasheed, R. Ahmed and F. Shehzad. Construction of circular strongly partially-balanced repeated measurements designs, Journal of King Saud University- Science, Vol. 31, pp. 345-351, 2019.
U. Rasheed, H. M. K. Rasheed, M. Rasheed and R. Ahmed. Minimal circular strongly balanced repeated measurements designs in periods of three different sizes, Communications in Statistics - Theory and Methods, Vol. 47(16), pp. 4088-4094, 2018.
M. Daniyal, R. Ahmed, F. Shehzad, M. H. Tahir, and Z. Iqbal. Construction of repeated measurements designs strongly balanced for residual effects, Communications in Statistics-Theory and Methods, Vol. 49(17), pp. 4288-4297, 2019.
H. M. K. Rasheed, H. Khan, R. Ahmed and F. Jamal. Minimal circular nearly strongly balanced repeated measurements designs in unequal period sizes, Proceedings of Pakistan Academy of Sciences, Vol. 58(4), pp. 59-65, 2022.
A. T. James and G. N. Wilkinson. Factorization of the residual operator and canonical decomposition of non-orthogonal factors in the analysis of variance, Biometrika, Vol. 58, pp. 258-294, 1971.
S. C. Pearce, T. Calinski and T. F. de C. Marshall. The basic contrasts of an experimental design with special reference to the analysis of data, Biometrika, Vol. 61, pp. 449-460, 1974.
J. Divecha, and J. Gondaliya. Construction of minimal balanced crossover designs having good efficiency of separability, Electronic Journal of Statistics, Vol. 8, pp. 2923-2936, 2014.
I. Iqbal. Construction of experimental designs using cyclic shifts, Unpublished Ph.d Thesis, U.K: University of Kent at Canterbury, 1991.
