A Link Between the<i>E</i>-Value and the Robustness of Block Designs

Godolphin, J. D.

doi:10.1080/01621459.2015.1114949

Cited by 1 publication

(3 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A design in

D_{υ, b, k}

with largest E ‐value is E‐optimal in the class. Godolphin () derived a lower bound for t * in terms of μ :

min false{⌈ T ⌉, r false} \leq t_{*},

where ⌈ x ⌉ denotes the ceiling of x and

T = \frac{8 μ k^{2} false(υ - k false)}{υ (2 k^{2} - 1 + {(- 1)}^{k})} .

…”

Section: Preliminariesmentioning

confidence: 99%

“…Ghosh () established that all BIBDs have t * = r . For binary incomplete block designs, not necessarily with equal treatment replication, robustness against the loss of whole blocks was investigated by Baksalary & Tabis (), Sathe & Satam (), Godolphin & Warren () and Godolphin (). Bailey, Schiffl & Hilgers () and Tsai & Liao () focussed attention on robustness of designs with blocks of size two.…”

Section: Introductionmentioning

confidence: 99%

“…Thus D has tÅ = 2 < r. This demonstrates that having optimal block breakdown number is a stronger robustness property than the property of being robust against the loss of r − 1 observations. Ghosh (1982) established that all BIBDs have t Å = r. For binary incomplete block designs, not necessarily with equal treatment replication, robustness against the loss of whole blocks was investigated by Baksalary & Tabis (1987), Sathe & Satam (1992), Godolphin & Warren (2011) and Godolphin (2016). Bailey, Schiffl & Hilgers (2013) and Tsai & Liao (2013) focussed attention on robustness of designs with blocks of size two.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A note on the robustness of PBIBD(2)s against breakdown in the event of observation loss

Godolphin

2018

Aus NZ J of Statistics

View full text Add to dashboard Cite

Summary Robustness against design breakdown following observation loss is investigated for Partially Balanced Incomplete Block Designs with two associate classes (PBIBD(2)s). New results are obtained which add to the body of knowledge on PBIBD(2)s. In particular, using an approach based on the E‐value of a design, all PBIBD(2)s with triangular and Latin square association schemes are established as having optimal block breakdown number. Furthermore, for group divisible designs not covered by existing results in the literature, a sufficient condition for optimal block breakdown number establishes that all members of some design sub‐classes have this property.

show abstract

“…A design in