balanced incomplete block design

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An experimental design in which t treatments are compared in b blocks of size k, where k<t, and b and k are chosen so that bk is a multiple of t. The balanced nature of the design is reflected in the fact that each treatment appears the same number (r) of times, and every pair of treatments appear together in a block on the same number (λ) of occasions. To satisfy these requirements,

bk=rt  and  λ(t−1)=r(k−1).

An example with four treatments (A–D) and blocks of size 3 is shown below.

Subjects: Probability and Statistics.

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