On finding trend-free block designs

Win Chin Lin; John Stufken

doi:10.1016/s0378-3758(98)00206-7

On finding trend-free block designs

Win Chin Lin, John Stufken

Arizona State University

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

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 language	English (US)
Pages (from-to)	57-70
Number of pages	14
Journal	Journal of Statistical Planning and Inference
Volume	78
Issue number	1-2
DOIs	https://doi.org/10.1016/s0378-3758(98)00206-7
State	Published - May 1999

Keywords

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

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

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10.1016/s0378-3758(98)00206-7

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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",

note = "Funding Information: Research Supported by NSF grants DMS-9504882 and DMS-9803684. ",

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AU - Stufken, John

N1 - Funding Information: Research Supported by NSF grants DMS-9504882 and DMS-9803684.

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

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ER -

On finding trend-free block designs

Abstract

Keywords

ASJC Scopus subject areas

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