The Efficiency Factor of a Class of Incomplete Block Designs

Conniffe, D.; Stone, Joan

doi:10.2307/2334752

Cited by 7 publications

(11 citation statements)

References 5 publications

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“…All 2concurrence designs will have n 1 = 14, Al = 0, n z = 12, ).z = 1. Then we have e = 0·6923 and the bound of Conniffe and Stone (1974) is 0·6773. Table 1 shows the bounds (5.2) and (5.3), together with the results for the cyclic incomplete block (CIB) design with the highest value for p1z.…”

Section: A New Bound For the Efficiency Factormentioning

confidence: 97%

“…The efficiency factor iff1 has been used as a criterion for optimality for some years and a number of papers giving upper bounds for it have appeared (Conniffe and Stone, 1974;Jarrett, 1977;Williams and Patterson, 1977). The importance of these bounds is that, when searching for optimal designs, we may curtail the search if we feel that the designs found are close enough for practical purposes.…”

Section: A New Bound For the Efficiency Factormentioning

confidence: 99%

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Definitions and Properties for M-Concurrence Designs

Jarrett

1983

Journal of the Royal Statistical Society Series B: Statistical Methodology

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Summary Incomplete block designs can be regarded as being in some sense approximately partially balanced. In this paper, we show that parameters pjki corresponding to those used for partially balanced designs can be defined for certain designs with m distinct concurrences. These parameters have properties analogous to those for m associate‐class partially balanced incomplete block (PBIB(m)) designs and have proved useful in searching for optimal designs. This leads to a new upper bound for the efficiency factor which, for given pjki values, is attained if a PBIB(2) design exists. Some results on complement and dual designs are also given.

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Section: A New Bound For the Efficiency Factormentioning

confidence: 97%

Section: A New Bound For the Efficiency Factormentioning

confidence: 99%

Definitions and Properties for M-Concurrence Designs

Jarrett

1983

Journal of the Royal Statistical Society Series B: Statistical Methodology

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“…Such bounds can be found in Pearce (1968), Conniffe and Stone (1974), Jarrett (1977) and Williams and Patterson (1977). Clearly, these bounds can be used as lower bounds for maxNj var(al-cxj)' However, the bound given for var(a;-&j) in Lemma 2.2 seems to be in general tighter for at least some values of i and j than the other bounds referred to above.…”

Section: =1 J*1 ;=1mentioning

confidence: 97%

Some Minimum Variance Block Designs for Estimating Treatment Differences

Jacroux

1983

Journal of the Royal Statistical Society Series B: Statistical Methodology

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SUMMARY In this paper we consider experimental settings requiring usage of a block design in which v treatments are to be tested in b blocks of size k. A block design is called MV‐optimal in such a setting if the maximal variance with which it estimates elementary treatment differences is minimal among all available designs. MV‐optimal designs are particularly useful in exploratory experiments where as much information as possible is desired on the effects of all treatments being studied. Some sufficient conditions are derived which can be used to establish the MV‐optimality of certain types of generalized group divisible designs as defined in Jacroux (1982) and some easy methods for constructing such MV‐optimal designs are given.

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“…Table 3 contains the average efficiency under the main effects model for estimating simple main effects of Fz in an (m -i) x m main effects deletion design in blocks of size(m -i ) , f o r 3 I m 5 6 , 2 I m -i S r n -l . U p p e r bounds on average efficiency are also given-namely , the lower upper-bound of those given by Conniffe and Stone (1974) and Williams and Patterson (1977). [See Dean (1983) for a comparison of average efficiency upper bounds.]…”

Section: Efficient Main Effect Deletion Designsmentioning

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

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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.

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The Efficiency Factor of a Class of Incomplete Block Designs

Cited by 7 publications

References 5 publications

Definitions and Properties for M-Concurrence Designs

Definitions and Properties for M-Concurrence Designs

Some Minimum Variance Block Designs for Estimating Treatment Differences

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

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