Single Replicate Factorial Experiments in Generalized Cyclic Designs: II. Asymmetrical Arrangements

Dean, Angela; John, J. A.

doi:10.1111/j.2517-6161.1975.tb01031.x

Cited by 19 publications

(28 citation statements)

References 4 publications

(8 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…These designs exploit the theory of cyclic groups and are quite easy to construct. The construction and analysis of cyclic designs for symmetric factorials was described in John and Dean (1975); Dean and John (1975) extended the theory to asymmetrical factorials. The latter article also listed designs for various factor combinations and blocking patterns.…”

Section: Factorial Designsmentioning

confidence: 99%

Experimental Design: Review and Comment

Steinberg¹,

Hunter²

1984

Technometrics

234

View full text Add to dashboard Cite

We review major developments in the design of experiments, offer our thoughts on important directions for the future, and make specific recommendations for experimenters and statisticians who are students and teachers of experimental design, practitioners of experimental design, and researchers jointly exploring new frontiers. Specific topics covered are optimal design, computer-aided design, robust design, response surface design, mixture design, factorial design, block design, and designs for nonlinear models.

show abstract

Section: Factorial Designsmentioning

confidence: 99%

Experimental Design: Review and Comment

Steinberg¹,

Hunter²

1984

Technometrics

234

View full text Add to dashboard Cite

show abstract

“…Worthley and Banerjee (1974) have further extended the ring theory methods to any asymmetrical factorial. John and Dean (1975) and Dean and John (1975) have given confounding methods, for single replicate factorial designs, based on generalised cyclic designs. Other confounding schemes have been given by Das (1964), Cotter (1974), Bailey (1977), Giovagnoli (1977), and Collings (1984).…”

Section: Factorial Experimentsmentioning

confidence: 99%

Fisher's Contributions to Agricultural Statistics

Street¹

1990

Biometrics

View full text Add to dashboard Cite

“…Various methods exist in the literature for the construction of orthogonal single replicate factorial designs in blocks (see, e.g., Bailey 1977;Bose 1947;Dean and John 1975;John and Dean 1975;Kempthorne 1952;Mukerjee 1981;Raktoe 1969Raktoe , 1970Sihota and Banerjee 1981;White and Hultquist 1965;Worthley and Banerjee 1974). If effects below a given order are to be estimable, however, the condition that a design have orthogonal factorial structure imposes a bound on the minimum possible block size (see Kempthorne 1952, p. 347).…”

Section: Introductionmentioning

confidence: 99%

First-Order Deletion Designs and the Construction of Efficient Nearly Orthogonal Factorial Designs in Small Blocks

Voss

1986

Journal of the American Statistical Association

View full text Add to dashboard Cite

Single replicate factorial designs for incomplete block experiments are obtained by first constructing a single replicate preliminary design in incomplete blocks for the same number of factors but an excessive number of levels of the first factor, then deleting the excess treatment combinations to obtain a deletion design. Any single replicate preliminary design yields a single replicate deletion design. Furthermore, if the preliminary design is orthogonal, then the resulting deletion design is shown to be nearly orthogonal and, under certain reduced models, to provide efficient estimation of lower-order effects and in some cases an orthogonal analysis. For example, a 2 x 32 deletion design is constructed in three blocks of size 6, the 2 df confounded being the sum of interaction effects of Fz and F3 and second-order interaction effects. If second-order interactions are assumed negligible, then the deletion design provides efficient estimation of interactions between F2 and F3 and an orthogonal analysis. In another example, a 2 x 3, deletion design is constructed in nine blocks of size 2 with main effects of Fl unconfounded. In a maineffects model, main effects of F2 and F3 are estimable with optimal average efficiency. Experimental settings involving more factor levels are also considered, tables are given showing the efficiency of the resulting deletion designs to compare favorably with optimal upper bounds, and the deletion designs are shown by comparison to be more efficient on lower-order effects than competing orthogonal designs.

show abstract

Single Replicate Factorial Experiments in Generalized Cyclic Designs: II. Asymmetrical Arrangements

Abstract: Summary This paper extends the results of John and Dean (1975) to asymmetrical factorial experiments, and lists a number of designs.

Cited by 19 publications

References 4 publications

Experimental Design: Review and Comment

Experimental Design: Review and Comment

Fisher's Contributions to Agricultural Statistics

First-Order Deletion Designs and the Construction of Efficient Nearly Orthogonal Factorial Designs in Small Blocks

Contact Info

Product

Resources

About