# Connections between Two-Level Factorials and Venn Diagrams

Dennis K.J. Lin, Amy W. Lam

Research output: Contribution to journalArticle

4 Citations (Scopus)

### 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) 49-51 3 American Statistician 51 1 https://doi.org/10.1080/00031305.1997.10473588 Published - Jan 1 1997

Venn diagram
Factorial Design
Logic
Algebra
Diagrams

### All Science Journal Classification (ASJC) codes

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

### Cite this

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In: American Statistician, Vol. 51, No. 1, 01.01.1997, p. 49-51.

Research output: Contribution to journalArticle

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AB - 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.

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