### Abstract

Experiments usually aim to study how changes in various factors affect the response variable of interest. Since the response model used most often at present in experimental design is expressed through the effect of each factor, it is straightforward to ascertain how each factor affects the response variable. However, since the response model contains redundant parameters, we must calculate the degrees of freedom defined by the number of independent parameters in the analysis of variance. In this paper, we show that through a description of experimental design based on an orthonormal system, the response model can be expressed using only independent parameters. Hence, we do not have to calculate the degrees of freedom defined by the number of independent parameters.

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

Pages | 2181-2185 |

Number of pages | 5 |

DOIs | |

Publication status | Published - 2011 |

Event | 2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011 - Anchorage, AK Duration: 2011 Oct 9 → 2011 Oct 12 |

### Other

Other | 2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011 |
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City | Anchorage, AK |

Period | 11/10/9 → 11/10/12 |

### Fingerprint

### Keywords

- analysis of variance
- Fourier transform
- mean square
- sum of squares

### ASJC Scopus subject areas

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

### Cite this

*Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics*(pp. 2181-2185). [6084000] https://doi.org/10.1109/ICSMC.2011.6084000

**A note on the degrees of freedom in an experimental design model based on an orthonormal system.** / Ukita, Yoshifumi; Matsushima, Toshiyasu; Hirasawa, Shigeichi.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics.*, 6084000, pp. 2181-2185, 2011 IEEE International Conference on Systems, Man, and Cybernetics, SMC 2011, Anchorage, AK, 11/10/9. https://doi.org/10.1109/ICSMC.2011.6084000

}

TY - GEN

T1 - A note on the degrees of freedom in an experimental design model based on an orthonormal system

AU - Ukita, Yoshifumi

AU - Matsushima, Toshiyasu

AU - Hirasawa, Shigeichi

PY - 2011

Y1 - 2011

N2 - Experiments usually aim to study how changes in various factors affect the response variable of interest. Since the response model used most often at present in experimental design is expressed through the effect of each factor, it is straightforward to ascertain how each factor affects the response variable. However, since the response model contains redundant parameters, we must calculate the degrees of freedom defined by the number of independent parameters in the analysis of variance. In this paper, we show that through a description of experimental design based on an orthonormal system, the response model can be expressed using only independent parameters. Hence, we do not have to calculate the degrees of freedom defined by the number of independent parameters.

AB - Experiments usually aim to study how changes in various factors affect the response variable of interest. Since the response model used most often at present in experimental design is expressed through the effect of each factor, it is straightforward to ascertain how each factor affects the response variable. However, since the response model contains redundant parameters, we must calculate the degrees of freedom defined by the number of independent parameters in the analysis of variance. In this paper, we show that through a description of experimental design based on an orthonormal system, the response model can be expressed using only independent parameters. Hence, we do not have to calculate the degrees of freedom defined by the number of independent parameters.

KW - analysis of variance

KW - Fourier transform

KW - mean square

KW - sum of squares

UR - http://www.scopus.com/inward/record.url?scp=83755206435&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=83755206435&partnerID=8YFLogxK

U2 - 10.1109/ICSMC.2011.6084000

DO - 10.1109/ICSMC.2011.6084000

M3 - Conference contribution

AN - SCOPUS:83755206435

SN - 9781457706523

SP - 2181

EP - 2185

BT - Conference Proceedings - IEEE International Conference on Systems, Man and Cybernetics

ER -