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).     

Precision of the genotypic correlation estimated from variety trials conducted in incomplete block designs

 Precise assessment of an association among traits of a crop plant is helpful in developing crop-improvement strategies. Two types of association, genotypic correlation and phenotypic correlation, may be used. An estimate of correlation is required along with a measure of precision in terms of standard error. Methods for the evaluation of the standard errors of genotypic and phenotypic correlations are not available in the literature, and when trials are conducted in incomplete blocks an algebraic evaluation of such correlation is cumbersome. Three methods – simulation, jackknife and bootstrap – have been used to evaluate bias and standard errors of genotypic, phenotypic and environmental correlations. We have evaluated their performance with data on grain yield, days-to-heading, and plant height, in barley genotypes in triple lattices. Simulation and jackknife techniques were found to be closer, compared to bootstrap, and can be recommended for assessing the precision of correlation estimates. Received: 9 December 1996 / Accepted: 2 May 1997     

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.