### Abstract

Experiments usually aim to study how changes in various factors affect the response variable of interest. Since the model used most often at present in experimental design is expressed through the effect of each factor, it is easy to understand how each factor affects the response variable. However, since the model contains redundant parameters, a considerable amount of time is often necessary to implement the procedure for estimating the effects. On the other hand, it has recently been shown that the model in experimental design can also be expressed in terms of an orthonormal system. In this case, the model contains no redundant parameters. Moreover, the theorem with respect to the sum of squares for the 2-factor interaction, needed in the analysis of variance (ANOVA) has been obtained. However, 3-factor interaction is often to be considered in real cases, but the theorem with respect to the sum of squares for the 3-factor interaction has not been obtained up to now. In this paper, we present the theorem with respect to the sum of squares for the 3-factor interaction in a model based on an orthonormal system. Furthermore, we can also obtain the theorem for interactions with 4 or more factors by the similar proof. Hence, in any real case, we can execute ANOVA in the model based on an orthonormal system.

Original language | English |
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Title of host publication | Proceedings 2012 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2012 |

Pages | 1990-1995 |

Number of pages | 6 |

DOIs | |

Publication status | Published - 2012 Dec 1 |

Event | 2012 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2012 - Seoul, Korea, Republic of Duration: 2012 Oct 14 → 2012 Oct 17 |

### Publication series

Name | Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics |
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ISSN (Print) | 1062-922X |

### Other

Other | 2012 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2012 |
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Country | Korea, Republic of |

City | Seoul |

Period | 12/10/14 → 12/10/17 |

### Keywords

- Analysis of variance
- Bandlimited function
- Design for experiments
- Estimation
- Fourier transforms
- Sampling theorem

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Control and Systems Engineering
- Human-Computer Interaction

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## Cite this

*Proceedings 2012 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2012*(pp. 1990-1995). [6378030] (Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics). https://doi.org/10.1109/ICSMC.2012.6378030