Unequal Block Sizes Research Articles

PCGEN: A FORTRAN IV program to generate paired-comparison stimuli

selecting stimulus sets. First, with an odd numb~r. of stimuli there are (N - I)/2 blocks, each containing N pairs of stimuli. With an even number of stimuli, there are N/2 blocks; one of these contains only N/2 pairs of stimuli, and the rest contain N pairs. !abl~ I illustrates a simple case with an odd number of stimuli; a similar table is easily constructed for the even case. The unequal block sizes for the even case is s?met~es undesirable, such as when subjects are being given

Inequality for equireplicated n-ary block designs with unequal block sizes

It is shown that certain inequalities known for binary, equireplicated, equiblock-sized block designs remain valid for equireplicated n-ary block designs with unequal block sizes. The approach used here is based on the spectral expansion of the C-matrix of the block design. The main theorems include some useful and combinatorially interesting results.

Balanced block designs with unequal block sizes

Balanced block designs with unequal block sizes

Balanced Designs with Unequal Replications and Unequal Block Sizes

Using two distinct BIB designs with the same number of treatments, a method of construction of balanced binary and ternary designs with unequal block sizes and unequal replications is given. The method is a generalization of the method of construction of balanced designs, given by John [6].

The 2-adjugate mod 2 class of designs

In this paper we define a 2-adjugate mod 2 class of designs obtained by application of process of 2-adjugation to the incidence matrix of given design and subsequently reducing to modulo 2. General properties of such designs are discussed and its application to the class of unreduced Balanced Incomplete Block Designs is investigated in detail. It is found that in this case we obtain a class of generalized partially balanced incomplete block designs with 2 associate classes and with triangular association scheme, but with unequal block sizes.

Symmetrical Unequal Block Arrangements with two Unequal Block Sizes

This paper deals with the analysis and constructions of Symmetrical Unequal Block (SUB) arrangements with two unequal block sizes. The analysis of these designs is obtained on the assumption of equal intrablock error variances for blocks of different sizes. Various methods of constructing these arrangements from known incomplete block designs are considered in this paper. The method of constructing SUB arrangements by the method of finite differences is also considered in this paper.

An Analysis of Rectangular Lattices with Unequal Block Sizes, Using Inter-Block Information

THE square lattice design (2) and the three-dimensional cubic lattice design (7) are available for variety trials and experiments with large numbers of treatments; both designs permit recovery of inter-block information. Yates (6) has also given the design and analysis of a rectangular lattice for pq varieties, using blocks of unequal sizes, but without recovery of inter-block information. The present paper extends the analysis to recover this information, using the assumption that the inter-block and intra-block components of variance are little affected by the unequal block sizes. In practice p and q need seldom differ by more than one, and when q = p + 1 the rectangular lattice design with blocks of equal size, developed by Harshbarger (4), is preferable, using the method of analysis given by Cochran and Cox (1), (cf. also Grundy, 3). The unequal block design may, however, be useful in some cases where the difference between p and q exceeds unity, but is neither greater than 5 nor greater than 10% of pq.