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Magic Square Designs

  1. Richard J. Martin

Published Online: 15 JUL 2005

DOI: 10.1002/0470011815.b2a16037

Encyclopedia of Biostatistics

Encyclopedia of Biostatistics

How to Cite

Martin, R. J. 2005. Magic Square Designs. Encyclopedia of Biostatistics. 4.

Author Information

  1. University of Sheffield, Sheffield, UK

Publication History

  1. Published Online: 15 JUL 2005


An n by n magic square with entries 1 to n2 has all row and column sums equal. If n has k factors, then a factorial design with n2 runs and up to 2k factors can be obtained from this for which the main effects and at least some of the two-factor interactions are linear-trend-free (their estimates are unaffected if there is a straight line trend over time). An unconnected experimental design called a magic Latin square is a Latin square with additional blocking obtained from structured rows and columns.


  • factorial experiment;
  • gerechte designs;
  • Graeco-Latin square;
  • Latin square;
  • magic Latin square;
  • trend-free design