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).     

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.     

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.     

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.     

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.