On Analysis of Some Augmented Block Designs

Augmented designs are frequently used in practice. In this paper, a simplified procedure of analysis of some types of augmented designs is discussed using the concept of efficiency-balance and partially efficiency-balance.     

A Simple Approach to Analyse Non-Orthogonal Data

The present paper deals with an alternative and simple procedure to analyse the non-orthogonal data. The procedure is general in nature but has some advantages for the non-orthogonal data due to some missing observations. The procedure is applied to (i) two way classification with unequal number of observations per cell; (ii) randomized block designs with some missing observations and (iii) balanced incomplete block designs and also illustrated with the help of numerical examples.     

On the Construction of Balanced and Partially Balanced Ternary Design

A method of constructing balanced and partially balanced ternary designs from balanced and partially balanced incomplete block designs, respectively, and two methods of constructing partially balanced ternary designs from association schemes are obtained. Two new and efficient balanced ternary designs having K < V and R ≦ 20 are obtained by the first method.     

Construction of Partially Balanced Incomplete Block Designs with Nested Rows and Columns

A number of methods of construction of partially balanced incomplete block designs with nested rows and columns are developed and new balanced incomplete block designs with nested rows and columns are obtained as a by-product.     

On C-Property in Block Designs

Block designs having a property described in Caliński (1971) and Saha (1976), referred to herein as C-property, are considered. A necessary and sufficient condition for a block design to have C-property is derived, and some methods of construction of such block designs are presented.     

Construction of Resolvable Designs with Nested Treatment Structure

The construction of resolvable incomplete block and row-column designs is investigated when the treatments have a nested structure. Some theoretical results are derived for lattice designs. Efficient designs for unequal-sized treatment groups are obtained by defining a multiple objective function and carrying out a computer search using an interchange algorithm.     

Construction of resolvable spatial row-column designs

Resolvable row-column designs are widely used in field trials to control variation and improve the precision of treatment comparisons. Further gains can often be made by using a spatial model or a combination of spatial and incomplete blocking components. Martin, Eccleston, and Gleeson presented some general principles for the construction of robust spatial block designs which were addressed by spatial designs based on the linear variance (LV) model. In this article we define the two-dimensional form of the LV model and investigate extensions of the Martin et al. principles for the construction of resolvable spatial row-column designs. The computer construction of efficient spatial designs is discussed and some comparisons made with designs constructed assuming an autoregressive variance structure.     

Rank Tests for Complete Block Designs

In this article a general univariate K-sample rank test for complete block designs with proportional cell frequencies is derived. It is shown that the test statistic has under H₀ and for arbitrary scores asymptotically a X²-distribution with K — 1 degrees of freedom. Special cases of this test are the Kruskal-Wallis test and the Friedman test. The test is compared with the Benard-van-Elteren test, the Mack-Skillings test and a test proposed by Downton. Finally the application of the test is illustrated by two examples.     

Universal Optimality of Nearest Neighbour Balanced Block Designs using Second Order Correlated Models

Block designs for observations correlated in one dimension are investigated. Santharam and Ponnusamy (1995) investigated the universal optimality of Nearest Neighbour balanced block designs (NNBD) using first order correlated models (AR(1), MA(1) and ARMA(1,1)). In this article we have investigated the universal optimality of NNBD using second order correlated models (ar(2), and MA (2)).     

A Simple Procedure for Constructing Experiment Designs with Incomplete Blocks of Sizes 2 and 3

In order to maximize control of heterogeneity within complete blocks, an experimenter could use incomplete blocks of size k = 2 or 3. In certain situations, incomplete blocks of this nature would eliminate the need for such spatial types of analyses as nearest neighbor. The intrablock efficiency factors for such designs are relatively low. However, with recovery of interblock information, FEDERER and SPEED (1987) have presented measures of design efficiency factors which demonstrate that efficiency factors approach unity for certain ratios of the intrablock and interblock variance components. Hence with recovery of interblock information, even incomplete block designs with k = 2 or 3 have relatively high efficiency factors. The reduction in the intrablock error variance over the complete block error variance in many situations will provide designs with high efficiency. A simple procedure for constructing incomplete blocks of sizes 2 and 3 is presented. It is shown how to obtain additional zero-one association confounding arrangements when v = 4 t, t an integer, and for v = pk, k ≤ p. It is indicated how to do the statistical analysis for these designs.     

Optimal complete block designs to adjust for interplot competition with a covariance analysis

Optimal complete block designs are given for variety trials with interplot competition. In the paper, competition is modeled using height differences between neighboring varieties. When variety heights are known at the design stage, a simulated annealing algorithm is proposed. The optimal designs tend to reduce height differences between neighboring varieties. When variety heights are not known in advance, neighbor-balanced designs at distances 1 and 2 are shown to have optimality properties.     

Some Bounds on Parameters of Efficiency-Balanced Block Designs

Bounds on the eigenvalue of the C -matrix with respect to R and the number of blocks for efficiency-balanced block designs are given. AMS 1970 Subject Classification: 62K10     

A model-independent approach to the theory of experimental designs and a special discussion of bib. i general definition and designs with one or two block factors

Experimental designs are definded by introducing an assignment matrix Z. It is shown by block designs and double block designs that using Z or an operator on Z otherwise defined, well known designs can be got as special cases. Till now we didn' find an experimental design which could not be defined by our matrix Z. The definitions of properties of experimental designs can be given independently of the model of the statistical analysis. This is shown for the property of balance of block designs.     

Maximin D-optimal designs for longitudinal mixed effects models

In this article, the optimal selection and allocation of time points in repeated measures experiments is considered. D-optimal cohort designs are computed numerically for the first- and second-degree polynomial models with random intercept, random slope, and first-order autoregressive serial correlations. Because the optimal designs are locally optimal, it is proposed to use a maximin criterion. It is shown that, for a large class of symmetric designs, the smallest relative efficiency over the model parameter space is substantial.     

Optimality of Some Class of Incomplete Block Designs

A class of incomplete block designs called C-design, was considered by Caliński (1971), Saha (1976), Ceranka (1983) and Ceranka , Kozłowska (1983, 1984). In this paper we extend the theory of block designs having the C-property. We consider optimality of C-designs with respect to any criterion of a described form. Das and Kageyama (1991) considered a class of E-optimal proper efficiency balanced designs (strictly speaking, Das and Kageyama considered E_R-optimality of some class of block designs). Hence we consider E_R, A_R, D_R optimality of C-designs.     

Are neighbour methods preferable to analysis of variance for completely systematic designs? 'Silly designs are silly!'

It is shown that the usual analysis of a complete-block designis weakly valid under a range of assumptions but that more sophisticatedanalyses of systematic block designs may not be.     

Robust and efficient design of experiments for the Monod model

In this paper the problem of designing experiments for the Monod model, which is frequently used in microbiology, is studied. The model is defined implicitly by a differential equation and has numerous applications in microbial growth kinetics, environmental research, pharmacokinetics, and plant physiology. The designs presented so far in the literature are local optimal designs, which depend sensitively on a preliminary guess of the unknown parameters, and are for this reason in many cases not robust with respect to their misspecification. Uniform designs and maximin optimal designs are considered as a strategy to obtain robust and efficient designs for parameter estimation. In particular, standardized maximin D- and E-optimal designs are determined and compared with uniform designs, which are usually applied in these microbiological models. It is demonstrated that maximin optimal designs are substantially more efficient than uniform designs. Parameter variances can be decreased by a factor of two by simply sampling at optimal times during the experiment. Moreover, the maximin optimal designs usually provide the possibility for the experimenter to check the model assumptions, because they have more support points than parameters in the Monod model.     

On the PBB Designs for Multiresponse Experiments

We present the idea of using multiresponse incomplete block designs when not all responses can be observed in all experimental units. For a special class of such designs, in which partial designs are PBB designs, a method for estimating natural treatment contrast is given. We also consider the problem of testing the hypotheses concerning the natural and any estimable treatment contrasts. For testing this hypothesis the Wald statistics, being asymptotically chi-square distributed, is proposed.     

A New Class of Matrices with Application in Experimental Designs

A very general class of balanced matrices is defined in this paper. These matrices are generalisations of the balanced orthogonal designs of Rao (1970) and generalised balanced matrices of Dey and Midha (1976). Some methods of construction of these balanced matrices are discussed. An application of these matrices in experimental designs is also given.     

Group Divisible Second Order Rotatable Designs

The Group Divisible Rotatable (GDR) designs are the designs in which the factors get divided into groups such that for the factors within group, the designs are rotatable. In the present paper we have obtained a series of Group Divisible Second Order Rotatable designs, by decomposing the v-dimensional space corresponding to v-factors under consideration into three mutually orthogonal spaces. We have given the least squares estimates of the parameters, the analysis and construction of such designs.