Construction of Equi-replicated Balanced Block Designs with Block Sizes Exceeding the Number of Treatments

In this note it is shown that the block design with incidence matrix Ñ = [NN… N], where N = c_1hN_h + c_oh (11′–N_h). c_oh and c_1h are any non-negative integers and N_h,h = 1, 2,…,p, are incidence matrices of balanced incomplete block designs with the same number of treatments t, is a balanced block design with the block sizes exceeding the number of treatments. In derivation the matrix M₀, introduced by CALIński (1971) is utilized.     

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.     

Analysis of Line × Tester Progenies Compared in Orthogonally Supplemented Efficiency Balanced Incomplete Block Design

An analysis of experimental design is suggested for comparing progenies of lineXtester mating system. The line × tester mating system is an expanded top-cross mating system, used frequently in practice. This system is of interest for breeders dealing with estimation and testing of general as well as specific combining abilities. In the suggested design, treatments, i.e. hybrids obtained in crosses, and testers are studied in orthogonally supplemented incomplete block design. Analysis of variance has been presented, estimators of expected values for progenies and for testers have been given, testing of hypotheses concerning contrasts of interest for progenies, lines and testers has been discussed. Estimators of effects of general and specific combining abilities as well as tests permitting for testing the significance of various genetic parameters, have also been given.     

Equi-replicated balanced block designs generated by a balanced matrix

In this paper it is shown that if N= \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^{S_h} $\end{document} c_ihN_ih, where c_ih are some non-negative integer numbers and N_ih are such incidence matrices that A_h = \documentclass{article}\pagestyle{empty}\begin{document}$ \mathop \sum \limits_{i = 1}^{S_h} $\end{document} i N_ih is a balanced matrix defined by SHAH (1959), for h = 1, 2,…, p, then a block design with an incidence matrix Ñ = [N, N,…,N] is an equi-replicated balanced block design. Here the balance of a block design is defined in terms of the matrix M₀ introduced by CALI?SKI (1971).     

Application of the Biased Spring Balance Weighing Design Theory to Estimation of Differences of Line Effects for Legume Content

The incidence matrix of a BIB design for v treatments has been used to construct a biased spring balance weighing design. Conditions under which an optimum biased spring balance weighing design exists are given. It is also shown how this theory may be utilized to obtain treatment and experiment designs to estimate differences in legume content between pair of lines in an experiment overseeded with grass species.     

Optimum Biased Spring Balance Weighing Designs Under Equal Correlations of Errors

The paper deals with the problem of estimating the individual weights of objects under a biased spring balance weighing design with equal correlations of errors in the model. A lower bound for the variance of each of the estimated weights resulting from this biased spring balance weighing design is obtained and a necessary and sufficient condition for this lower bound to be attained is given. The incidence matrix of a BIB design has been used to construct optimum biased spring balance weighing designs.