An Efficient Class of Repeated Measurements Designs to Control the Residual Effects Using Periods of Three Different Sizes
DOI:
https://doi.org/10.53560/PPASA(60-1)665Keywords:
Repeated Measurement Design, Carry Over Effects, Residual Effects, Strongly Balanced RMDs, Minimal DesignsAbstract
Repeated measurements designs (RMDs) are always economical but with the use of these designs, there may arise residual effects. Minimal strongly balanced RMDs are well known to estimate the treatment effects and residual effects independently. In the situation, where these designs cannot be constructed, minimal nearly strongly balanced RMDs are used which is an efficient class of RMDs to control the residual effects. In this article, efficient minimal circular nearly strongly balanced RMDs are constructed in periods of three different sizes.
References
E.R. Williams. Experimental designs balanced for the estimation of residual effects of treatments. Australian Journal of Science Research A 2: 149-168 (1949).
E.R. Williams. Experimental designs balanced for pairs of residual effects. Australian Journal of Science Research, A 3: 351-363 (1950).
S.C. Pearce. Experimenting with blocks of natural size. Biometrics 18: 699-706 (1964).
S. Kageyman. Construction of balanced block designs. Utilitas Mathematica 9: 209-229 (1976).
C.G. Magda. Circular balanced repeated measurements designs. Communications in Statistics-Theory and Methods 9: 1901-1918 (1980).
G. Constantine, and A. Hedayat. A construction of repeated measurements designs balance for residual effects. Journal of Statistical Planning and Inference 6: 153-164 (1982).
K. Afsarinejad. Circular balanced uniform repeated measurements designs. Statistics and Probability Letters 7: 187-189 (1989).
K. Afsarinejad. Circular balanced uniform repeated measurements designs, II. Statistics and Probability Letters 9: 141-143 (1990).
K. Afsarinejad. Repeated measurements designs with unequal periods sizes. Journal of the Italian Statistical Society 2: 161-168 (1994).
I. Iqbal, and B. Jones. Efficient repeated measurements designs with equal and unequal period sizes. Journal of Statistical Planning and Inference 42: 79-88 (1994).
V.K. Sharma, S. Jaggi, and C. Varghese. Minimal balanced repeated measurements designs. Journal of Applied Statistics 30: 867–872 (2003).
I. Iqbal, and M.H. Tahir. Circular strongly balanced repeated measurements designs. Communications in Statistics-Theory and Methods 38: 3686-3696 (2009).
V.K. Sharma, Y. Gharde, and C. Varghese. Minimal strongly balanced changeover designs with first residuals. African Journal of Mathematics and Computer Science Research 3(9): 195-198 (2010).
I. Iqbal, M.H. Tahir, and S.S. A. Ghazali. Circular first-and second-order balanced repeated measurements designs. Communications in Statistics-Theory and Methods 39: 228-240 (2010).
R.A. Bailey, P.J. Cemron, K. Fillipiak, J. Kunert, and A. Markiewicz. On optimality and construction of circular repeated measurements designs. Statistica Sinica 27: 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 47(9): 2183-2194 (2018).
M. Rajab, R. Ahmed, F. Shehzad, and M.H. Tahir. Some new constructions of circular balanced repeated measurements designs. Communications in Statistics -Theory and Methods 47(17): 4142-4152 (2018).
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 47(16): 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 49(17): 4288-4297 (2020).
R. Ahmed, F. Shehzad, M. Rajab, M. Daniyal, and M.H. Tahir. Minimal circular balanced repeated measurements designs in periods of unequal sizes. Communications in Statistics-Theory and Methods 48(21): 5223-5232 (2019).
H.M.K. Rasheed, M. Rasul, R. Ahmed, M. Batool, M.H. Tahir, and F. Shehzad. Circular balanced repeated measurement designs in periods of three different sizes. Communications in StatisticsSimulation and Computation 48(10): 3022-3030 (2019).
A. Khan, R. Ahmed, F. Shehzad, M.H. Tahir, and S.S.A. Ghazali. Construction of circular partiallybalanced repeated measurement designs using cyclic shifts. Communications in Statistics-Simulation and Computation 48(2): 506-515 (2019).
R. Jabeen, H.M.K. Rasheed, R. Ahmed, and F. Shehzad. Construction of circular strongly partiallybalanced repeated measurements designs. Journal of King Saud University- Science 31: 345-351 (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 58(4): 49-59 (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 58: 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 61: 449-460 (1974).
J. Divecha, and J. Gondaliya. Construction of minimal balanced crossover designs having good efficiency of separability. Electronic Journal of Statistics 8: 2923-2936 (2014).
I. Iqbal. Construction of experimental designs using cyclic shifts. Unpublished Ph.D Thesis. U.K: University of Kent at Canterbury (1991).
