## Abstract

If an experiment has orthogonal block structure then linear combinations of the data can be allocated to various strata, in such a way that combinations in different strata are uncorrelated and all normalized combinations in a single stratum have the same variance. The analysis of the experiment is computationally and conceptually simple if the design has the property of general balance, introduced by Nelder: that is, there is an orthogonal basis for the space of treatments, such that, in any stratum in which they are both estimable, the estimators of any pair of basis elements are uncorrelated.

More recent results show that general balance is related to commutativity of certain matrices. It is possible that neither computational simplicity nor abstract commutativity has anything to do with practical experiments in these days of high computer power. A contrary argument says that general balance aids interpretation and that the design which is generally balanced with respect to meaningful contrasts may be superior to a technically optimal design.

More recent results show that general balance is related to commutativity of certain matrices. It is possible that neither computational simplicity nor abstract commutativity has anything to do with practical experiments in these days of high computer power. A contrary argument says that general balance aids interpretation and that the design which is generally balanced with respect to meaningful contrasts may be superior to a technically optimal design.

Original language | English |
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Title of host publication | Proceedings of the International Conference on Linear Statistical Inference LINSTAT '93 |

Editors | T. Cali'nski, R. Kala |

Place of Publication | Dordrecht |

Publisher | Kluwer Academic Publishers |

Pages | 171-184 |

Number of pages | 14 |

ISBN (Print) | 0 7923 3136 2 |

Publication status | Published - 1994 |

### Publication series

Name | Mathematics and its Applications |
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Volume | 306 |

## Keywords

- basic contrasts
- efficiency
- general balance
- incomplete-block designs
- optimality
- orthogonal block structure
- strata