Simple Pilot Procedures for the Avoidance of Disconnected Experimental Designs

Abstract

Two simple pilot procedures are proposed for avoiding the problem of dealing with a disconnected experimental design. Both procedures should be carried out on the selected design before any experimentation is considered. The first procedure is a check that the suggested design is connected with respect to treatments. This makes use of the information matrix for the model and provides feed-back on a disconnected design. The second procedure specifies which observations are influential in causing a connected design to become disconnected, with respect to any set of parameter effects, if these observations are lost during the experimental period. This specification is found by examining the projection matrix for the model. These pilot procedures are illustrated by several examples. Copyright 2004 Royal Statistical Society.

Improved conditions for the robustness of binary block designs against the loss of whole blocks

“…Moreover, the maximum concurrence λ * = 7 and the bounds given by inequalities (4.6) and (4.7) are 7 and 9 respectively, so Theorem 6 applies. The bounds for conditions (4.8) (i) and (ii) of 6 25 and 24 25 are surpassed by concurrencies κ * and λ * respectively, implying that design D b is maximally robust.…”

“…In this case the terms x # = x 2 = r [6] − r Sathe and Satam (1992, Corollary 1) point out that inequalities (2.4) can be improved if λ * , the maximum concurrence between any pair of treatments, is suitably small, i.e.…”

“…It follows from the P -process of Godolphin (2004) that the blocks of D # can be arranged in two nonempty sets S 1 and S 2 such that no treatment allocated to blocks in S 1 occurs in any of the blocks in S 2 .…”

“…Researchers have investigated methods for guarding against a disconnected design because of observation loss during the experiment; see the survey of methods given by Godolphin (2004Godolphin ( , 2006 which considers cases where it is not possible to anticipate beforehand which observations may be missing. However, there are several experiments where the loss of a whole block is more likely than the loss of an individual observation; for example if the experimental units are the leaves on a plant then any damage to the plant will invalidate the block.…”

On the Connectivity Problem form-Way Designs

“…It is straightforward to detect this property of the design since the levels of factor i can be partitioned into sets in such a way that the levels of factor j in one set are distinct from the levels of factor j in the other sets, and simple checking procedures, such as the P-process of Godolphin (2004), can be used.…”