On properties of efficiency-balanced designs

We consider a class of efficiency-balanced block designs which are design patterns for the analytical simplification of statistical analysis. This paper consists of eight sections which investigate various problems (such as, bounds on parameters, characterizations, existence and nonexistence, and dual designs) for efficiency-balanced block designs.     

Constructions of partially efficiency-balanced designs and their analysis

Partially Efficiency-Balanced (PEB) designs were introduced by Puri and Nigam $year:1977. These designs may be particularly useful for bio-assays and factorial experiments and have a very simple analysis. In the present paper, we give several new systematic procedures of constructing PEB designs with varying replications. A number of practical series of PEB designs are presented. We shall also pre- sent the methods of analysing these designs produced here.     

The efficiency and optimality characterization of certain six-Treatment incomplete-Block designs emanating from some quasi-Semi-Latin squares

Incomplete-block designs were constructed from three types of three-factor block-structured combinatorial designs which are not necessarily semi-Latin squares but whose treatments are ab initio arranged as in the semi-Latin square. The basic consideration for the construction involves the exploitation of the different block structures of the experimental units of the Quasi-semi-Latin Squares (QSLS) for the same treatments. All the emanating designs are found to be connected, only the designs in nine blocks are both variance- and efficiency-balanced and offer gain in efficiency but lead to about 46 percent loss of information.     

On the block structure of proper block designs

In this paper we consider proper block designs and derive an upper bound for the number of blocks which can have a fixed number of symbols common with a given block of the design. To arrive at the desired bound, a generalization of an integer programming theorem due to Bush (1976) is first obtained. The integer programming theorem is then used to derive the main result of this paper. The bound given here is then compared with a similar bound obtained by Kageyama and Tsuji (1977).     

On the equivalence of two approaches to simplicity in the analysis of block designs and some related results

Two seemingly different approaches to simplicity in the analysis of connected block designs, and their relationship to the concepts of balance are discussed.     

A note on generalized binary proper efficiency-balanced block designs

Some methods of construction of generalized binary proper efficiency-balanced block (GB-EB) designs with two different replications are derived and the solution of the unknown designs given by Das and Kageyama (1991) are obtained.     

Optimum chemical balance weighing designs for estimating the total weight

This deals with chemical balance weighing designs which attain a lower bound for the variance of the estimated total weight, The results extend those of Chacko Dey (1978).     

Type a incomplete multi-response designs

Srivastava considered the problem of designing and analysis of incomplete multi-response experiments, The main characteristics of the analysis given by her are investigated and a general class of incomplete multiresponse designs (Type A) is obtained on the basis of these investigations.     

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

Several authors have investigated conditions for a binary block design, D, to be maximally robust such that every eventual design obtained from D by eliminating r_[υ]−1 blocks is connected, where r_[υ] is the smallest treatment replication. Four new results for the maximal robustness of D with superior properties are given. An extension of these results to widen the assessment of robustness of the planned design is also presented.     

Simple pilot procedures for the avoidance of disconnected experimental designs

Summary.  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.     

Measures of non orthogonality in block designs

Orthogonality is an important concept in block design. Necessary and sufficient condition for a connected block design to be orthogonal is well known. However, when a design is not orthogonal, it is not clear how much it deviates from orthogonality. In this paper, an attempt has been made to first define the measures of or indices to non orthogonality in block design and then to characterize designs possessing minimum non orthogonality indices. It is shown that a Balanced Incomplete Block Design (BIBD) and a Balanced Block Design (BBD), if exist, possess this property.     

The robustness of chain block designs and coat-of-mail designs

Chain block designs are relatively vulnerable to loss of information when missing values or outliers may occur. An alternative class of designs, coat-of-mail designs, are proposed and the relative robustness of the two types of design are compared.     

Mixture designs with orthogonal blocks

Constructions of blocked mixture designs are considered in situations where BLUEs of the block effect contrasts are orthogonal to the BLUEs of the regression coefficients. Orthogonal arrays (OA), Balanced Arrays (BAs), incidence matrices of balanced incomplete block designs (BIBDs), and partially balanced incomplete block designs (PBIBDs) are used. Designs with equal and unequal block sizes are considered. Also both cases where the constants involved in the orthogonality conditions depend and do not depend on the factors have been taken into account. Some standard (already available) designs can be obtained as particular cases of the designs proposed here.     

Information in an observation in robust designs

We consider the Information contained 1n each observation in a given design robust with respect to the estlmability of parameters and against the unavailability of observations. We compare the observations in various 1-, 2- and 3- dimensional designs on the basis of their informations.     

Remove unwanted variation retrieves unknown experimental designs

Remove unwanted variation (RUV) is an estimation and normalization system in which the underlying correlation structure of a multivariate dataset is estimated from negative control measurements, typically gene expression values, which are assumed to stay constant across experimental conditions. In this paper we derive the weight matrix which is estimated and incorporated into the generalized least squares estimates of RUV-inverse, and show that this weight matrix estimates the average covariance matrix across negative control measurements. RUV-inverse can thus be viewed as an estimation method adjusting for an unknown experimental design. We show that for a balanced incomplete block design (BIBD), RUV-inverse recovers intra- and interblock estimates of the relevant parameters and combines them as a weighted sum just like the best linear unbiased estimator (BLUE), except that the weights are globally estimated from the negative control measurements instead of being individually optimized to each measurement as in the classical, single measurement BIBD BLUE.     

Hypercubic designs and applications

In this paper we develop relatively easy methods for constructing hypercubic designs from symmetrical factorial experiments for t=v ^m treatments with v=2, 3. The proposed methods are easy to use and are flexible in terms of choice of possible block sizes.     

A note on circular neighbor balanced designs

ABSTRACT

This paper describes some methods of constructing circular neighbor balanced and circular partially neighbor balanced block designs for estimation of direct and neighbor effects of the treatments. A class of circular neighbor balanced block designs with unequal block sizes is also proposed.     

On the analysis of multivariate repeated measures designs

The relationship between the mixed-model analysis and multivariate approach to a repeated measures design with multiple responses is presented. It is shown that by taking the trace of the appropriate submatrix of the hypothesis (error) sums of squares and crossproducts (SSCP) matrix obtained from the multivariate approach, one can get the hypothesis (error) SSCP matrix for the mixed-model analysis. Thus, when analyzing data from a multivariate repeated measures design, it is advantageous to use the multivariate approach because the result of the mixed-model analysis can also be obtained without additional computation.     

On the recovery of intra- and interblock information in n-ary designs

This note presents an extension of Q-method of analysis for binary designs given by Rao (1956) to n-ary balanced and partially balanced block designs. Here a linked n-ary block (LNB) design is defined as the dual of balanced n-ary (BN) design. Having a note on Yates’ (1939, 1940) method of P-analysis, we further extend the expressions for binary linked block (LB) designs given by Rao (1956) to linked n-ary block (LNB) designs which admit easy estimation of parameters for these type of all n-ary designs.     

On the construction of group divisible incomplete block designs

In this paper a method of constructing group-divisible incomplete block designs has been suggested. A series of balanced incomplete block designs has also been obtained.