Robustness of neighbour balanced complete block designs against missing observation(s)

Article type: Research Article

Authors: Abeynayake, N.R.^a | Jaggi, Seema^{b; *} | Varghese, Cini^b

Affiliations: [a] Department of Agribusiness Managemant, Wayamba University, Gonawila (NWP), Sri Lanka | [b] Indian Agricultural Statistics Research Institute, Library Avenue, New Delhi, India

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: A block design with neighbour effect(s) is said to be neighbour balanced if every treatment has every other treatment appearing constant number of times as neighbour(s). These designs are used when the treatment applied to one experimental plot may affect the response on neighbouring plot(s) besides the response to which it is applied. Neighbour-balanced designs ensure that no treatment is unduly disadvantaged by its neighbour(s). However, there is a possibility that some of the observations could become unavailable for analysis. In this paper, we examine the robustness of neighbour balanced complete block designs when specific observations are missing. The information matrix for direct treatment effects of the resultant design (one-sided neighbour effects) after missing of an observation from a block is derived and the efficiency of resulting design is investigated. Robustness of neighbour balanced complete block design has also been investigated against missing of more than one observation. The efficiencies are found to be quite high indicating the designs to be fairly robust against missing observations.

Keywords: Neighbour balanced block design, missing observations, information matrix, eigenvalues, direct and neighbour effects

DOI: 10.3233/MAS-2011-0176

Journal: Model Assisted Statistics and Applications, vol. 6, no. 2, pp. 81-87, 2011