On Construction of Some Augmented Block Designs

Augmented block designs are frequently used in practice. In this paper procedures of construction of some types of augmented block designs are discussed using the concept of efficiency-balance and partially efficiency-balance.     

Analysis of Triangular Diallel Table for Experiments in Block Designs

In this paper the analysis of genotypes obtained in diallel crossing system, including one set of F₁′s and parents, arranged in triangular table is given. This analysis is presented for data obtained from the experiments laid out in block designs. The analysis of variance, estimators of general and specific combining abilities as well as statistics for testing of hypotheses concerning those parameters are given.     

Analysis of Diallel Table for Experiments in Block Designs

In this paper the analysis of genotypes obtained in diallel crossing system, including parents, one set of F₁s and reciprocal F₁'s, is given. This analysis is presented for data obtained from the experiments laid out in block designs. The analysis of variance, estimator of reciprocal effects, estimators of general and specific combining abilities as well as statistics for testing of hypotheses concerning those parameters are given.     

Experiment with Split-Plot Generated by PBIB Designs

The paper refers to the construction of two-factor experiments carried out in incomplete split-plot design in which levels of both factors occur as treatments in PBIB designs. It presents also the analysis of variance of these experiments based on partial analyses in the so called strata. These strata are connected with the variability between subplots inside wholeplots, between the wholeplots inside blocks and between blocks inside the total experiment.     

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 the E-Optimality of Block Designs with Unequal Block Sizes

In this paper an inequality for the smallest positive eigenvalues of the C-matrix of a block design are derived. This inequality is a generalization of a result by Constantine (1982) to the case of unequal block sizes. On the basis of the above result a certain E-optimality criterium of block designs is given. Furthermore coefficient e_d has been introduced which permits to assess how close the block design is from the optimal one.     

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.     

Some Third-Order Rotatable Designs

Some new third-order rotatable designs are obtained in 5, 6, 7 and 8 dimensions. Many of these designs are of a sequential type and some require fewer experiments than the known designs with minimal number of experiments.     

Searching for Optimal Block Designs when Block Effects are Random

An algorithm that searches for optimal block designs when block effects are random is described. Some situations in which such an algorithm will prove useful are considered. An illustrative example and some discussion are given.     

Analysis of Partially Balanced Incomplete Block Designs with Standards

The paper presents a detailed analysis of variance of PBIB designs supplemented by one or more standard treatments. Comparisons were carried out of treatment effects within the group of standard and test treatments and between the two groups. The analysis is supplemented by an example.     

Application of Partially Balanced Block Designs to Factorial Experiments

In this paper we present partially balanced block designs with F_p and C_p association schemes. These designs play a great role in the experimental theory since they can be applied to factorial experiments. A particular stress is put on the formulation of association schemes _p and C_p, presentation of exemplary constructions of these designs and their analysis of variance. The presented considerations are abundantly illustrated with 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)).     

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.     

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.     

Cylindrically Rotatable Designs of Type 3: Further Considerations

The cylindrically rotatable designs of type 3 are generalised to consider the factors split up into any number of groups. The conditions which must be satisfied by such a design are derived from the moment generating function of the design. A method of construction of second-order cylindrically rotatable designs of type 3 with three or more groups of factors is provided.     

Some Simple Statistics to Test Against Ordered Alternatives in Complete Block Designs

Consider testing the hypothesis of no treatment effects against a postulated ranking of the m treatments, given data from n Complete Blocks. A suitable test statistic is the weighted average rank correlation w = σb_QiC_i where C_i is the correlation between the postulated ranking and the ranking observed within the ith block, Q_i is the rank of the ith block with respect to credibility, and the b_i's are weights such that 0 ≦ b¹ ≦ … ≦ bn. In this paper we introduce some simple statistics: the first extends the signed-rank statistic to m ≦ 3, the second uses a simple measure of correlation based on the antirank, and the third a statistic based on Spearman's footrule. Tables for critical values are provided and the normal approximation is investigated.