Robustness of block designs on the basis of pairwise treatment comparisons against missing data

Article type: Research Article

Authors: Lal, Krishan^{; *} | Parsad, Rajender | Gupta, V. K.

Affiliations: I. A. S. R. I., New Delhi, India

Correspondence: [*] Corresponding author: IASRI, Library Avenue, New Delhi – 110 012, India. Fax: +91 11 25841564; E-mail: [email protected].

Abstract: Robustness of incomplete block designs against the unavailability of data has been investigated in the literature in terms of average variance of all possible pairwise treatment comparisons in the design. But if we examine the robustness of a design for the loss of observation(s) on the basis of pairwise treatment comparisons, loss of information of some of treatment comparisons may be more than that the loss of information on the basis of average variance of the residual design. A design that is robust on the basis of overall efficiency may not be robust when the efficiency is worked out on the basis of paired treatment comparisons. We, therefore, investigate all the estimates of individual pairwise treatment contrasts for the loss of any number of observation(s) in a block for balanced incomplete block design and variance balanced block designs. Designs that are robust on the basis of average variance but not on the basis of pairwise treatment contrasts have been identified.

Keywords: BIB designs, efficiency criterion, pairwise treatment comparisons, robustness, variance balanced block designs

DOI: 10.3233/MAS-2011-0213

Journal: Model Assisted Statistics and Applications, vol. 7, no. 1, pp. 75-80, 2012