Fundamental Concepts and Recent Applications of Factorial Statistical Designs

Abstract

Factorial designs have been increasingly used in scientific investigations and technological development. The designs, through the use of matrices with all the treatment combinations, have been capable to effectively characterize the relationships between the variables of multi-factor experiments, assess the experimental variabilities, and derive mathematical functions that represent the behavior of the responses. Factorial designs were fractionalized, which substantially reduced the number of treatments without the loss of relevant information. The addition of central and star points to the factorial arrays has given them the orthogonality and rotatability characteristics, frequently used to fit models with curvature and identify critical regions of interest. Literature reports indicated that factorial designs, also called factorial experiments, were successfully applied in different types of investigations, including in cost evaluations and time-series studies. They were capable to estimate important features of the experiments, like the individual and combined effects of factors, the magnitude of residuals, additionally to express the relationships of the variables in polynomial equations, draw response surface and contour plots, and determine optimal combinations of parameters. In this review, the fundamental aspects of the Complete, Fractional, Central Composite Rotational and Asymmetrical factorial designs were conceptualized, and recent applications of these powerful tools were described.

The Effect of Authentic Learning Approaches and Assessment Techniques on Students' Statistics Basic Test Results by Intelligence Control

“…The method used to conduct this research is an experimental method with a 2x2 factorial design. (Mainardi & Bidoia, 2022) (Ditzhaus & Smaga, 2022) The treatment factors are (1) learning approach and (2) authentic assessment technique, each of which has two levels of treatment, and the response variable is the results of the Basic Student Statistics test. Before the implementation of this research, the researcher obtained the intelligence value data first, which was also used by the researcher as a covariate or covariate in applying the linear model.…”

Ecotoxicological response surface analysis of salt and pH in textile effluent on Bacillus subtilis and Lactuca sativa

“…The approach can be used to obtain a comprehensive analysis of the factors, including their interactions, and assess the experimental variabilities using a cost-effective number of experiments (Mason et al, 2003). The RSM, moreover, can be used to express the relationships of the variables in polynomial mathematical equations, thus, draw response surface plots that simplify the interpretation of empirical results (Mainardi and Bidoia, 2022).…”