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balanced incomplete block design
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balanced incomplete block design

mathematics
Also known as: BIB design
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Quick Summary

A balanced incomplete block (BIB) design is a mathematical structure used in statistics and combinatorics. It involves a set of treatments (objects) and a collection of blocks (subsets of treatments). In a BIB design, each block contains a fixed number of treatments, and each treatment appears in a fixed number of blocks. Crucially, every pair of distinct treatments appears together in a specific number of blocks. These designs are characterized by parameters (v, b, r, k, λ), representing the number of treatments, blocks, replications of each treatment, size of each block, and the number of blocks in which any pair of treatments occurs, respectively. The term "incomplete" signifies that blocks contain fewer treatments than the total number available.1

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2 Britannica Sources
  1. combinatorics - BIB (balanced incomplete block ) designs
  2. combinatorics - PBIB ( partially balanced incomplete block ) designs

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