### Abstract

One of the main features that distinguish split-plot experiments from other experiments is that they involve two types of experimental errors: the whole-plot (WP) error and the subplot (SP) error. Taking this into consideration is very important when computing measures of adequacy of fit for split-plot models. In this article, we propose the computation of two R^{2}, R ^{2}-adjusted, prediction error sums of squares (PRESS), and R ^{2} -prediction statistics to measure the adequacy of fit for the WP and the SP submodels in a split-plot design. This is complemented with the graphical analysis of the two types of errors to check for any violation of the underlying assumptions and the adequacy of fit of split-plot models. Using examples, we show how computing two measures of model adequacy of fit for each split-plot design model is appropriate and useful as they reveal whether the correct WP and SP effects have been included in the model and describe the predictive performance of each group of effects.

Original language | English (US) |
---|---|

Pages (from-to) | 272-284 |

Number of pages | 13 |

Journal | Journal of Quality Technology |

Volume | 41 |

Issue number | 3 |

State | Published - Jul 2009 |

### Fingerprint

### Keywords

- Model adequacy checking
- Press
- R -adjusted
- R
- R-prediction
- Residual analysis
- Subplot error
- Whole-plot error

### ASJC Scopus subject areas

- Industrial and Manufacturing Engineering
- Safety, Risk, Reliability and Quality
- Strategy and Management
- Management Science and Operations Research

### Cite this

*Journal of Quality Technology*,

*41*(3), 272-284.

**Checking the adequacy of fit of models from split-plot designs.** / Almimi, Ashraf A.; Kulahci, Murat; Montgomery, Douglas.

Research output: Contribution to journal › Article

*Journal of Quality Technology*, vol. 41, no. 3, pp. 272-284.

}

TY - JOUR

T1 - Checking the adequacy of fit of models from split-plot designs

AU - Almimi, Ashraf A.

AU - Kulahci, Murat

AU - Montgomery, Douglas

PY - 2009/7

Y1 - 2009/7

N2 - One of the main features that distinguish split-plot experiments from other experiments is that they involve two types of experimental errors: the whole-plot (WP) error and the subplot (SP) error. Taking this into consideration is very important when computing measures of adequacy of fit for split-plot models. In this article, we propose the computation of two R2, R 2-adjusted, prediction error sums of squares (PRESS), and R 2 -prediction statistics to measure the adequacy of fit for the WP and the SP submodels in a split-plot design. This is complemented with the graphical analysis of the two types of errors to check for any violation of the underlying assumptions and the adequacy of fit of split-plot models. Using examples, we show how computing two measures of model adequacy of fit for each split-plot design model is appropriate and useful as they reveal whether the correct WP and SP effects have been included in the model and describe the predictive performance of each group of effects.

AB - One of the main features that distinguish split-plot experiments from other experiments is that they involve two types of experimental errors: the whole-plot (WP) error and the subplot (SP) error. Taking this into consideration is very important when computing measures of adequacy of fit for split-plot models. In this article, we propose the computation of two R2, R 2-adjusted, prediction error sums of squares (PRESS), and R 2 -prediction statistics to measure the adequacy of fit for the WP and the SP submodels in a split-plot design. This is complemented with the graphical analysis of the two types of errors to check for any violation of the underlying assumptions and the adequacy of fit of split-plot models. Using examples, we show how computing two measures of model adequacy of fit for each split-plot design model is appropriate and useful as they reveal whether the correct WP and SP effects have been included in the model and describe the predictive performance of each group of effects.

KW - Model adequacy checking

KW - Press

KW - R -adjusted

KW - R

KW - R-prediction

KW - Residual analysis

KW - Subplot error

KW - Whole-plot error

UR - http://www.scopus.com/inward/record.url?scp=68249122364&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=68249122364&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:68249122364

VL - 41

SP - 272

EP - 284

JO - Journal of Quality Technology

JF - Journal of Quality Technology

SN - 0022-4065

IS - 3

ER -