Optimal a\(\times b\) connected designs with \(a+b\) observations
type: Item
instance of: scholarly article
title: Optimal a\(\times b\) connected designs with \(a+b\) observations
zbMATH Open document ID: 0732.62071
DOI: 10.1016/0378-3758(91)90058-M
author: Yadolah Dodge
author: David S. Birkes
published in: Journal of Statistical Planning and Inference
publication date: 1991-01-01T00:00:00Z
review text: In an experiment to investigate the effect of factor 1, with a levels, and factor 2, with b levels, on a response variable Y, suppose that only n observations can be afforded, where n is a small number such as \(a+b-1\) or \(a+b\). The problem of determining the best design for placing these n observations is here considered under the usual two-factor model without interaction. The designs constructed by placing a observations at a single level of factor 2 and b observations at a single level of factor 1 will be said to be perpendicular. For the problem of determining optimal \(a\times b\) two-factor designs with only \(a+b\) observations, the present paper shows that, when \(a\neq 3\), the A-optimal designs are those constructed by placing \(a+b-1\) observations in a perpendicular pattern so that a observations are at a single level of factor 2 and b observations are at a single level of factor 1, and then adding one more observation. These designs are also optimal under a modification of the E-criterion.
reviewed by: Sanpei Kageyama
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62K15
zbMATH DE Number: 4211309
zbMATH Keywords: connected designs
zbMATH Keywords: E-optimal design
zbMATH Keywords: loop in an incidence matrix
zbMATH Keywords: response variable
zbMATH Keywords: two-factor model without interaction
zbMATH Keywords: two-factor designs
zbMATH Keywords: A-optimal designs
MaRDI profile type: Publication
cites work: Spanning sets for estimable contrasts in classification models
cites work: Q5345410
cites work: D–optimality of a class of saturated main–effect plans and allied results
full work available at URL: 0378-3758(91)90058-m
OpenAlex ID: W2059998092
description: scientific article; zbMATH DE number 4211309