## Abstract

In the 1920s, R. A. Fisher, at Rothamsted Experimental Station in Harpenden, recommended Latin squares for agricultural crop experiments. Frank Yates became his assistant in 1931, and head of Statistics when Fisher left two years later.

In the early 1930s, Fisher and Yates developed sets of mutually orthogonal Latin squares (MOLS). They also introduced what are effectively the duals of finite Abelian groups for the construction of designs for factorial experiments.

In 1938, Fisher and Yates published their famous Statistical Tables for Biological, Agricultural and Medical Research (STBAMR). In the same year, R. C. Bose published what became the standard method of constructing both factorial designs and mutually orthogonal Latin squares, using finite fields.

In 1942, Fisher pointed out that the complete set of 9 × 9 MOLS in STBAMR is not isomorphic to that constructed by Bose. The explanation in STBAMR shows how they are constructed from an elementary Abelian group.

In the early 1930s, Fisher and Yates developed sets of mutually orthogonal Latin squares (MOLS). They also introduced what are effectively the duals of finite Abelian groups for the construction of designs for factorial experiments.

In 1938, Fisher and Yates published their famous Statistical Tables for Biological, Agricultural and Medical Research (STBAMR). In the same year, R. C. Bose published what became the standard method of constructing both factorial designs and mutually orthogonal Latin squares, using finite fields.

In 1942, Fisher pointed out that the complete set of 9 × 9 MOLS in STBAMR is not isomorphic to that constructed by Bose. The explanation in STBAMR shows how they are constructed from an elementary Abelian group.

Original language | English |
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Title of host publication | Research in history and philosophy of mathematics |

Subtitle of host publication | the CSHPM 2021 volume |

Editors | Maria Zack, David Waszek |

Place of Publication | Cham |

Publisher | Birkhäuser |

Pages | 213-233 |

Number of pages | 21 |

ISBN (Electronic) | 9783031214943 |

ISBN (Print) | 9783031214936, 9783031214967 |

DOIs | |

Publication status | Published - 12 May 2023 |

Event | Joint Meeting of the British Society for the History of Mathematics and the Canadian Society for the History and Philosophy of Mathematics - University of St Andrews, St Andrews, United Kingdom Duration: 12 Jul 2021 → 16 Sept 2021 http://www.mcs.st-andrews.ac.uk/bshm-cshpm/index.shtml |

### Publication series

Name | Annals of the Canadian Society for History and Philosophy of Mathematics/ Société canadienne d’histoire et de philosophie des mathématiques |
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ISSN (Print) | 2662-8503 |

ISSN (Electronic) | 2662-8511 |

### Conference

Conference | Joint Meeting of the British Society for the History of Mathematics and the Canadian Society for the History and Philosophy of Mathematics |
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Country/Territory | United Kingdom |

City | St Andrews |

Period | 12/07/21 → 16/09/21 |

Internet address |