An algorithm to minimize the number of blocks in incomplete block designs

  • Justin A. MacDonaldEmail author
  • Michael C. Hout
  • Joseph Schmidt


Incomplete block designs are experimental designs in which a subset of treatments are included in each block. The researcher must decide which conditions are assigned to each block. This design concept is quite general. At the level of the experiment, a treatment is a condition in an experiment, blocks are different groups of subjects, and the researcher must decide how to assign a subset of conditions to each block of subjects. At the level of the subject, the treatments correspond to individual stimuli, blocks correspond to experimental trials, and the researcher must decide which subset of stimuli to include in each trial. In this article, we present an efficient algorithm that assigns treatments to blocks in an incomplete block design according to two criteria: Each pair of treatments must appear together in at least one block, and the number of blocks in the experiment is minimized. We discuss details and applications of the algorithm and provide software and a web application to generate designs according to the needs of the researcher.


Experiment design Incomplete block dezsigns Randomized block designs Set cover problem 



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Copyright information

© The Psychonomic Society, Inc. 2019

Authors and Affiliations

  • Justin A. MacDonald
    • 1
    Email author
  • Michael C. Hout
    • 1
  • Joseph Schmidt
    • 2
  1. 1.New Mexico State UniversityLas CrucesUSA
  2. 2.University of Central FloridaOrlandoUSA

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