Trend-free block designs for higher order trends

Feng Shun Chai, John Stufken

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

For a given number of varieties v, number of blocks b, common treatment replication r and common block size k, rv = bk, 3 ≤ k ≤ 8, k ≤ v, necessary conditions for the existence of p-trend-free equireplicated binary block designs are derived for 2 ≤ p ≤ k - 1. The conditions are also sufficient for complete block designs (where v = k and b = r). For balanced incomplete block designs (BIBDs) that satisfy the necessary conditions, we investigate whether varieties can be ordered within blocks to make the designs p-trend-free. For v ≤ 20 and b ≤ 100, if the necessary conditions are satisfied and if a BIBD exists, we conclude that a p-trend-free BIBD is also available.

Original languageEnglish (US)
Pages (from-to)65-78
Number of pages14
JournalUtilitas Mathematica
Volume56
StatePublished - Nov 1999
Externally publishedYes

Fingerprint

Balanced Incomplete Block Design
Block Design
Higher Order
Necessary Conditions
Replication
Binary
Sufficient
Trends

ASJC Scopus subject areas

  • Applied Mathematics
  • Statistics and Probability

Cite this

Chai, F. S., & Stufken, J. (1999). Trend-free block designs for higher order trends. Utilitas Mathematica, 56, 65-78.

Trend-free block designs for higher order trends. / Chai, Feng Shun; Stufken, John.

In: Utilitas Mathematica, Vol. 56, 11.1999, p. 65-78.

Research output: Contribution to journalArticle

Chai, FS & Stufken, J 1999, 'Trend-free block designs for higher order trends', Utilitas Mathematica, vol. 56, pp. 65-78.
Chai, Feng Shun ; Stufken, John. / Trend-free block designs for higher order trends. In: Utilitas Mathematica. 1999 ; Vol. 56. pp. 65-78.
@article{fa66c070000346c780093b2583d7f1b5,
title = "Trend-free block designs for higher order trends",
abstract = "For a given number of varieties v, number of blocks b, common treatment replication r and common block size k, rv = bk, 3 ≤ k ≤ 8, k ≤ v, necessary conditions for the existence of p-trend-free equireplicated binary block designs are derived for 2 ≤ p ≤ k - 1. The conditions are also sufficient for complete block designs (where v = k and b = r). For balanced incomplete block designs (BIBDs) that satisfy the necessary conditions, we investigate whether varieties can be ordered within blocks to make the designs p-trend-free. For v ≤ 20 and b ≤ 100, if the necessary conditions are satisfied and if a BIBD exists, we conclude that a p-trend-free BIBD is also available.",
author = "Chai, {Feng Shun} and John Stufken",
year = "1999",
month = "11",
language = "English (US)",
volume = "56",
pages = "65--78",
journal = "Utilitas Mathematica",
issn = "0315-3681",
publisher = "Utilitas Mathematica Publishing Inc.",

}

TY - JOUR

T1 - Trend-free block designs for higher order trends

AU - Chai, Feng Shun

AU - Stufken, John

PY - 1999/11

Y1 - 1999/11

N2 - For a given number of varieties v, number of blocks b, common treatment replication r and common block size k, rv = bk, 3 ≤ k ≤ 8, k ≤ v, necessary conditions for the existence of p-trend-free equireplicated binary block designs are derived for 2 ≤ p ≤ k - 1. The conditions are also sufficient for complete block designs (where v = k and b = r). For balanced incomplete block designs (BIBDs) that satisfy the necessary conditions, we investigate whether varieties can be ordered within blocks to make the designs p-trend-free. For v ≤ 20 and b ≤ 100, if the necessary conditions are satisfied and if a BIBD exists, we conclude that a p-trend-free BIBD is also available.

AB - For a given number of varieties v, number of blocks b, common treatment replication r and common block size k, rv = bk, 3 ≤ k ≤ 8, k ≤ v, necessary conditions for the existence of p-trend-free equireplicated binary block designs are derived for 2 ≤ p ≤ k - 1. The conditions are also sufficient for complete block designs (where v = k and b = r). For balanced incomplete block designs (BIBDs) that satisfy the necessary conditions, we investigate whether varieties can be ordered within blocks to make the designs p-trend-free. For v ≤ 20 and b ≤ 100, if the necessary conditions are satisfied and if a BIBD exists, we conclude that a p-trend-free BIBD is also available.

UR - http://www.scopus.com/inward/record.url?scp=0041169396&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0041169396&partnerID=8YFLogxK

M3 - Article

VL - 56

SP - 65

EP - 78

JO - Utilitas Mathematica

JF - Utilitas Mathematica

SN - 0315-3681

ER -