Quantitative Analysis of the Balance Property in Factorial Experimental Designs 2 4 to 2 8

Ricardo Ramírez-Tapia, Armando Javier Ríos-Lira (), Yaquelin Verenice Pantoja-Pacheco, José Antonio Vázquez-López and Edgar Augusto Ruelas-Santoyo
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Ricardo Ramírez-Tapia: Doctorado en Ciencias de la Ingeniería, Tecnológico Nacional de México en Celaya, Celaya 38010, Guanajuato, Mexico
Armando Javier Ríos-Lira: Tecnológico Nacional de México/Instituto Tecnológico de Celaya, Celaya 38010, Guanajuato, Mexico
Yaquelin Verenice Pantoja-Pacheco: Tecnológico Nacional de México/Instituto Tecnológico de Celaya, Celaya 38010, Guanajuato, Mexico
José Antonio Vázquez-López: Tecnológico Nacional de México/Instituto Tecnológico de Celaya, Celaya 38010, Guanajuato, Mexico
Edgar Augusto Ruelas-Santoyo: Tecnológico Nacional de México/Instituto Tecnológico de Celaya, Celaya 38010, Guanajuato, Mexico

Mathematics, 2022, vol. 10, issue 20, 1-17

Abstract: Experimental designs are built by using orthogonal balanced matrices. Balance is a desirable property that allows for the correct estimation of factorial effects and prevents the identity column from aliasing with factorial effects. Although the balance property is well known by most researchers, the adverse effects caused by the lack or balance have not been extensively studied or quantified. This research proposes to quantify the effect of the lack of balance on model term estimation errors: type I error, type II error, and type I and II error as well as R 2 , R 2 adj , and R 2 pred statistics under four balance conditions and four noise conditions. The designs considered in this research include 2 4 –2 8 factorial experiments. An algorithm was developed to unbalance these matrices while maintaining orthogonality for main effects, and the general balance metric was used to determine four balance levels. True models were generated, and a MATLAB program was developed; then a Monte Carlo simulation process was carried out. For each true model, 50,000 replications were performed, and percentages for model estimation errors and average values for statistics of interest were computed.

Keywords: design of experiments; design matrix; balance; orthogonality; general balance metric (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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