An efficient procedure for the avoidance of disconnected incomplete block designs. (English) Zbl 1471.62075

Summary: Knowledge of the cardinality and the number of minimal rank reducing observation sets in experimental design is important information which makes a useful contribution to the statistician’s tool-kit to assist in the selection of incomplete block designs. Its prime function is to guard against choosing a design that is likely to be altered to a disconnected eventual design if observations are lost during the course of the experiment. A method is given for identifying these observation sets based on the concept of treatment separation, which is a natural approach to the problem and provides a vastly more efficient computational procedure than a standard search routine for rank reducing observation sets. The properties of the method are derived and the procedure is illustrated by four applications which have been discussed previously in the literature.


62-08 Computational methods for problems pertaining to statistics
62K10 Statistical block designs


Full Text: DOI Link


[1] Angelis, L., An evolutionary algorithm for A-optimal incomplete block designs, J. Stat. Comput. Simul., 73, 753-771, (2003) · Zbl 1042.62070
[2] Bailey, R. A., Designs for two-colour microarray experiments, Appl. Statist., 56, 365-394, (2007)
[3] Bate, S. T.; Godolphin, E. J.; Godolphin, J. D., Choosing cross-over designs when few subjects are available, Comput. Statist. Data Anal., 52, 1572-1586, (2008) · Zbl 1452.62575
[4] Bose, R. C., Combinatorial properties of partially balanced designs and association schemes, Sankya Ser. A, 25, 109-136, (1963) · Zbl 0122.14606
[5] Cheng, C-S.; Wu, C-F., Nearly balanced incomplete block designs, Biometrika, 68, 493-500, (1981) · Zbl 0471.62079
[6] Clatworthy, W. H., Tables of two-associate-class partially balanced designs, Nat. Bureau Stand. Appl. Math. Ser., 63, (1973) · Zbl 0289.05017
[7] Cochran, W. G.; Cox, G. M., Experimental designs, (1957), Wiley New York · Zbl 0077.13205
[8] Dey, A.; Srivastava, R.; Parsad, R., Robustness of block designs for diallel crosses against missing observations, J. Indian Soc. Agricultural Statist., 54, 376-384, (2001) · Zbl 1188.62236
[9] Godolphin, J. D., Simple pilot procedures for the avoidance of disconnected experimental designs, Appl. Stat., 53, 133-147, (2004) · Zbl 1111.62318
[10] Godolphin, J. D., The specification of rank reducing observation sets in experimental design, Comput. Statist. Data Anal., 51, 1862-1874, (2006) · Zbl 1157.62475
[11] Godolphin, J. D., On the connectivity problem for \(m\)-way designs, J. Stat. Theory Pract., 7, 732-744, (2013)
[12] Godolphin, J. D.; Warren, H. R., Improved conditions for the robustness of binary block designs against the loss of whole blocks, J. Statist. Plann. Inference, 141, 3498-3505, (2011) · Zbl 1219.62122
[13] John, J. A.; Whitaker, D.; Triggs, C. M., Construction of cyclic designs using integer programming, J. Statist. Plann. Inference, 36, 357-366, (1993) · Zbl 0778.62064
[14] Jones, B.; Eccleston, J. A., Exchange and interchange procedures to search for optimal designs, J. R. Stat. Soc. Ser B, 42, 238-243, (1980) · Zbl 0443.62064
[15] Mitchell, T. J., Computer construction of D-optimal first-order designs, Technometrics, 16, 211-220, (1974) · Zbl 0299.62040
[16] Nguyen, N-K., Construction of optimal block designs by computer, Technometrics, 36, 300-307, (1994) · Zbl 0798.62079
[17] Nguyen, N-K.; Miller, A. J., A review of some exchange algorithms for constructing discrete D-optimal designs, Comput. Statist. Data Anal., 14, 489-498, (1992) · Zbl 0937.62628
[18] Soicher, L.H., 2011. The DESIGN package for GAP, Version 1.6, 2011. http://designtheory.org/software/gap_design/.
[19] The GAP Group, 2013. GAP-Groups, Algorithms and Programming, version 4.6.4; 2013. (http://www.gap-system.org).
[20] Theil, H., The analysis of disturbances in regression analysis, J. Amer. Statist. Assoc., 60, 1067-1079, (1965)
[21] Whitaker, D.; Triggs, C. M.; John, J. A., Construction of block designs using mathematical programming, J. R. Stat. Soc. Ser B, 52, 497-503, (1990)
[22] Yates, F., The analysis of replicated experiments when the field results are incomplete, Empire J. Experimental Agriculture, 1, 129-142, (1933)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.