On finding trend-free block designs

Win Chin Lin, John Stufken

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

We introduce and discuss a new algorithm to convert a given binary block design, if possible, into a linear trend-free block design. The only permissible operation in attempting this conversion is that of reallocating treatments to plots within blocks; the treatment-block incidence structure is not allowed to be changed. We discuss an extension of the algorithm to cases where the trend is thought to be of a higher degree, and establish a relation between the algorithm and the optimal assignment problem, a well-known problem in operations research.

Original languageEnglish (US)
Pages (from-to)57-70
Number of pages14
JournalJournal of Statistical Planning and Inference
Volume78
Issue number1-2
StatePublished - May 1999
Externally publishedYes

Fingerprint

Block Design
Linear Trend
Operations research
Operations Research
Assignment Problem
Convert
Incidence
Binary
Trends

Keywords

  • Optimal assignment problem
  • Search algorithm
  • Time or spatial trends
  • Trend-free designs

ASJC Scopus subject areas

  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Statistics and Probability

Cite this

Lin, W. C., & Stufken, J. (1999). On finding trend-free block designs. Journal of Statistical Planning and Inference, 78(1-2), 57-70.

On finding trend-free block designs. / Lin, Win Chin; Stufken, John.

In: Journal of Statistical Planning and Inference, Vol. 78, No. 1-2, 05.1999, p. 57-70.

Research output: Contribution to journalArticle

Lin, WC & Stufken, J 1999, 'On finding trend-free block designs', Journal of Statistical Planning and Inference, vol. 78, no. 1-2, pp. 57-70.
Lin, Win Chin ; Stufken, John. / On finding trend-free block designs. In: Journal of Statistical Planning and Inference. 1999 ; Vol. 78, No. 1-2. pp. 57-70.
@article{2c9d9667d77a43a5b19ec322c415b602,
title = "On finding trend-free block designs",
abstract = "We introduce and discuss a new algorithm to convert a given binary block design, if possible, into a linear trend-free block design. The only permissible operation in attempting this conversion is that of reallocating treatments to plots within blocks; the treatment-block incidence structure is not allowed to be changed. We discuss an extension of the algorithm to cases where the trend is thought to be of a higher degree, and establish a relation between the algorithm and the optimal assignment problem, a well-known problem in operations research.",
keywords = "Optimal assignment problem, Search algorithm, Time or spatial trends, Trend-free designs",
author = "Lin, {Win Chin} and John Stufken",
year = "1999",
month = "5",
language = "English (US)",
volume = "78",
pages = "57--70",
journal = "Journal of Statistical Planning and Inference",
issn = "0378-3758",
publisher = "Elsevier",
number = "1-2",

}

TY - JOUR

T1 - On finding trend-free block designs

AU - Lin, Win Chin

AU - Stufken, John

PY - 1999/5

Y1 - 1999/5

N2 - We introduce and discuss a new algorithm to convert a given binary block design, if possible, into a linear trend-free block design. The only permissible operation in attempting this conversion is that of reallocating treatments to plots within blocks; the treatment-block incidence structure is not allowed to be changed. We discuss an extension of the algorithm to cases where the trend is thought to be of a higher degree, and establish a relation between the algorithm and the optimal assignment problem, a well-known problem in operations research.

AB - We introduce and discuss a new algorithm to convert a given binary block design, if possible, into a linear trend-free block design. The only permissible operation in attempting this conversion is that of reallocating treatments to plots within blocks; the treatment-block incidence structure is not allowed to be changed. We discuss an extension of the algorithm to cases where the trend is thought to be of a higher degree, and establish a relation between the algorithm and the optimal assignment problem, a well-known problem in operations research.

KW - Optimal assignment problem

KW - Search algorithm

KW - Time or spatial trends

KW - Trend-free designs

UR - http://www.scopus.com/inward/record.url?scp=0033130228&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0033130228&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0033130228

VL - 78

SP - 57

EP - 70

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 1-2

ER -