Robustness Of Block Designs Research Articles

A Link Between the E-Value and the Robustness of Block Designs

ABSTRACTThis article investigates the robustness of binary incomplete block designs against giving rise to a disconnected design in the event of observation loss. A link is established between the E-value of a planned design and the extent of observation loss that can be experienced while still guaranteeing an eventual design from which all treatment contrasts can be estimated. Patterns of missing observations covered include loss of entire blocks and loss of individual observations. Simple bounds are provided enabling practitioners to easily assess the robustness of a planned design.

Robustness of Variance Balanced Block Designs

The robustness of block designs against missing observations is revisited. It has been shown that A-efficiency criterion is not an appropriate measure to judge the efficiency of the residual design. As an alternate to this, E-efficiency criterion is defined. A lower bound of this criterion for the loss of any t observations in binary variance balanced block design is obtained. Balanced incomplete block designs (BIBD) that are robust as per E-efficiency criterion are identified.

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

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.

Robustness of Block Designs for Diallel Crosses Against Missing Data

Robustness aspects of block designs for diallel crosses against missing data have been investigated using connectedness and efficiency criteria. Sufficient condition for robustness of a design has been obtained for the loss of any q observations, using connectedness criterion. Designs robust against the loss of any two observations, loss of any q observations in a block and loss of any two blocks have been identified. Efficiencies of the residual designs have been evaluated for certain designs for diallel crosses for several pattern of loss of two observations. The efficiencies of the residual designs have also been calculated when any q observations in a block and any two blocks (not necessarily disjoint) are lost.

Robustness of designed experiments against missing data

This paper investigates the robustness of designed experiments for estimating linear functions of a subset of parameters in a general linear model against the loss of any t( U 1) observations. Necessary and sufficient conditions for robustness of a design under a homoscedastic model are derived. It is shown that a design robust under a homoscedastic model is also robust under a general heteroscedastic model with correlated observations. As a particular case, necessary and sufficient conditions are obtained for the robustness of block designs against the loss of data. Simple sufficient conditions are also provided for the binary block designs to be robust against the loss of data. Some classes of designs, robust up to three missing observations, are identified. A-efficiency of the residual design is evaluated for certain block designs for several patterns of two missing observations. The efficiency of the residual design has also been worked out when all the observations in any two blocks, not necessarily disjoint, are lost. The lower bound to A-efficiency has also been obtained for the loss of t observations. Finally, a general expression is obtained for the efficiency of the residual design when all the observations of m ( U 1) disjoint blocks are lost.

Robustness of some balanced block designs

During the last three decades, the robustness of experimental designs has been investigated under several criteria. The present paper surveys various results on robustness of block designs in three different directions, when some observations are missing. The criteria on robustness discussed here are taken up from a combinatorial point of view.

Robustness of BIB and extended BIB designs against the unavailability of any number of observations in a block

Robustness of block designs is investigated, when any observations in a block are lost, in terms of efficiency of the residual design. The designs are balanced incomplete block (BIB) and extended BIB designs. The investigation shows that the covered designs are fairly robust against the unavailability of any number of observations in a block. Furthermore, the robustness of any Youden design and Latin square design against the loss of a whole column is shown.