Characteristics for distinguishing among balanced incomplete block designs with repeated blocks
type: Item
instance of: scholarly article
title: Characteristics for distinguishing among balanced incomplete block designs with repeated blocks
zbMATH Open document ID: 0584.62125
DOI: 10.1016/0378-3758(86)90129-1
published in: Journal of Statistical Planning and Inference
publication date: 1986-01-01T00:00:00Z
full work available at URL: https://hdl.handle.net/1813/32927
review text: The class \({\mathcal B}\) of balanced incomplete block designs with parameters v,b,r,k,\(\lambda\) considered here includes designs with repeated blocks. Attention to date has centered on constructing the members of \({\mathcal B}\) and on finding the minimum number of distinct blocks \(d\leq b\). Under the classical model, the usual statistical characteristics do not distinguish among members of \({\mathcal B}\); however, effects related to block totals can be used as distinguishing characteristics. A competing effects model is introduced and is shown to distinguish among members of \({\mathcal B}\). This model is appropriate for intercropping, marketing, and survey investigations. The model is applied to the ten nonisomorphic BIB designs with parameters 7,21,9,3,3. A computer algorithm for obtaining the pairwise treatment by block incidence matrix of this model is given.
Mathematics Subject Classification ID: 62K10
Mathematics Subject Classification ID: 62-04
zbMATH DE Number: 3936284
zbMATH Keywords: optimality
zbMATH Keywords: balanced incomplete block designs
zbMATH Keywords: repeated blocks
zbMATH Keywords: minimum number of distinct blocks
zbMATH Keywords: competing effects model
zbMATH Keywords: intercropping
zbMATH Keywords: marketing
zbMATH Keywords: survey investigations
zbMATH Keywords: nonisomorphic BIB designs
zbMATH Keywords: computer algorithm
author: D. Raghavarao
author: Walter T. Federer
author: Steven J. Schwager
MaRDI profile type: Publication
OpenAlex ID: W2038686072
cites work: On theory and applications of BIB designs with repeated blocks
cites work: Q5815916
cites work: Q5627526
cites work: Q3900813
cites work: Block designs with repeated blocks and \((b,r,\lambda)=1\)
description: scientific article; zbMATH DE number 3936284