Connections between Two-Level Factorials and Venn Diagrams

Dennis K.J. Lin; Amy W. Lam

doi:10.1080/00031305.1997.10473588

Connections between Two-Level Factorials and Venn Diagrams

Dennis K.J. Lin, Amy W. Lam

Statistics

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

4 Scopus citations

Abstract

The Venn diagram is widely used in many textbooks to illustrate relationships in logic, algebra and probability events. Most applications are limited to k = 2 or 3 sets. Attempts have been made to construct Venn diagrams for many sets. This paper illustrates the connection between Venn diagrams and the well-known two-level factorial designs. Such a connection provides: (1) a simple way to construct a Venn diagram for any k sets, and (2) a graphical understanding of two-level factorials. Examples are given for k = 2, 3, 4, and 5.

Original language	English (US)
Pages (from-to)	49-51
Number of pages	3
Journal	American Statistician
Volume	51
Issue number	1
DOIs	https://doi.org/10.1080/00031305.1997.10473588
State	Published - Feb 1997

All Science Journal Classification (ASJC) codes

Statistics and Probability
Mathematics(all)
Statistics, Probability and Uncertainty

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10.1080/00031305.1997.10473588

Cite this

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title = "Connections between Two-Level Factorials and Venn Diagrams",

abstract = "The Venn diagram is widely used in many textbooks to illustrate relationships in logic, algebra and probability events. Most applications are limited to k = 2 or 3 sets. Attempts have been made to construct Venn diagrams for many sets. This paper illustrates the connection between Venn diagrams and the well-known two-level factorial designs. Such a connection provides: (1) a simple way to construct a Venn diagram for any k sets, and (2) a graphical understanding of two-level factorials. Examples are given for k = 2, 3, 4, and 5.",

author = "Lin, {Dennis K.J.} and Lam, {Amy W.}",

note = "Funding Information: Dennis K. J. Lin is Associate Professor, Department of Management Science and Information Systems, Pennsylvania State University, University Park, PA 16802. Amy W. Lam is Senior Research Assistant, Office of Institutional Research, University of Tennessee at Knoxville, Knoxville, TN 37916. The authors thank the editor, associate editor, and two referees who suggested several improvements to the manuscript. Dennis Lin was supported in part by a Professional Development Award at the University of Tennessee and by National Science Foundation Grant DMS-9204007.",

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Connections between Two-Level Factorials and Venn Diagrams

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