Circular neighbour-balanced designs and one-sided circular neighbour-balanced designs

Abstract

In most block designs for agricultural experiments, the nature of the yield underlying treatments may reach such a stage that the treatment received by a plot may influence the response on the neighbouring plots of the same block or sometimes it may influence the response only on the following plot. As an example of the second type, the tall varieties may affect the crops grown on the neighbouring plots by their shades. Bailey (J Indian Soc Agric Stat 56 (3): [302][303][304][305][306][307][308][309][310][311][312][313][314] 2003) has developed a type of design concerned with the study of one sided neighbour effects for application under such conditions. This paper gives, introducing a lemma, constructions of new series of (i) Circular Neighbour-Balanced designs and (ii) One-sided Circular Neighbour-Balanced designs.

Universally Optimal One-sided Circular Neighbour-balanced Designs with k = 5

“…Further, in each of the six initial sets, there exist three distinct elements, two appearing twice and another once. By Lemma 2.1, proposed by Meitei [8] , the proof of the one-sided CNBD is completed.…”

“…For the construction of one-sided CNBD, Lemma 2.1, by Meitei [8] , is called for in this section. The terms and the notations to be used in the lemma are as follows.…”

“…The Theorem 10, page no. 1658, Bailey and Druilhet [7] states that one-sided CNBD, so-called by Meitei [8] , is universally optimal for estimation of the total effects among all possible designs with same size, if the design has sequences in an optimal equivalence class of sequences equally often.…”

Study of Covariates’ Effects in the Presence of Neighbor Effects : An Informative Review

“…Azais et al (1993) constructed a series of neighbor-balanced designs incomplete blocks and also mentioned about the analysis of different models with one-sided, two-sided neighbor effects. Meitei (1996) gives a method of construction of incomplete block neighbor design in which number of blocks is not a multiple of number of treatments. Jaggi et al (2018) described some construction methods of circular neighbor balanced and also circular partially neighbor balanced block designs for estimation of direct and neighbor effects of the treatments.…”

Some New Generators to Produce Minimal Circular Strongly Balanced Generalized Neighbor Designs of Class-I

“…Hwang (1973) [9] presented some infinite classes of neighbor designs for v odd. Mettei (1996) [14] presented balanced NDs for v = 2m and k = m. Ahmed and Akhtar (2008) [1] also developed some series of NDs. Ahmed and Akhtar (2011) [2] presented these design for k = 6.…”