### 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, in the analysis of variance we must calculate the degrees of freedom defined by the number of independent parameters. In this letter, we propose the idea of calculating the degrees of freedom over the model based on an orthonormal system for the first time. In this way, we can easily obtain the number of independent parameters associated with any component, which reduces the risk of mistakes in the calculation of the number of independent parameters and facilitates the implementation of estimation procedures.

Original language | English |
---|---|

Pages (from-to) | 658-662 |

Number of pages | 5 |

Journal | IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences |

Volume | E96-A |

Issue number | 2 |

DOIs | |

Publication status | Published - 2013 Feb |

### Fingerprint

### Keywords

- Analysis of variance
- Fourier transform
- Mean square
- Sum of squares

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Computer Graphics and Computer-Aided Design
- Applied Mathematics
- Signal Processing

### Cite this

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

Research output: Contribution to journal › Article

*IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences*, vol. E96-A, no. 2, pp. 658-662. https://doi.org/10.1587/transfun.E96.A.658

}

TY - JOUR

T1 - A study 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 - 2013/2

Y1 - 2013/2

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, in the analysis of variance we must calculate the degrees of freedom defined by the number of independent parameters. In this letter, we propose the idea of calculating the degrees of freedom over the model based on an orthonormal system for the first time. In this way, we can easily obtain the number of independent parameters associated with any component, which reduces the risk of mistakes in the calculation of the number of independent parameters and facilitates the implementation of estimation procedures.

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, in the analysis of variance we must calculate the degrees of freedom defined by the number of independent parameters. In this letter, we propose the idea of calculating the degrees of freedom over the model based on an orthonormal system for the first time. In this way, we can easily obtain the number of independent parameters associated with any component, which reduces the risk of mistakes in the calculation of the number of independent parameters and facilitates the implementation of estimation procedures.

KW - Analysis of variance

KW - Fourier transform

KW - Mean square

KW - Sum of squares

UR - http://www.scopus.com/inward/record.url?scp=84873349094&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84873349094&partnerID=8YFLogxK

U2 - 10.1587/transfun.E96.A.658

DO - 10.1587/transfun.E96.A.658

M3 - Article

AN - SCOPUS:84873349094

VL - E96-A

SP - 658

EP - 662

JO - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

JF - IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences

SN - 0916-8508

IS - 2

ER -