Construction and analysis of experimental designs
Creators: name: Alanazi, Talal
Publisher: name: RMIT University
Year: 2024
Subjects: classificationCode: 490509
subject: Statistical theory

description: This thesis seeks to put into focus the analysis of experimental designs and their construction. It concentrates on the construction of fractional factorial designs (FFDs) using various aspects and applications. These dierent experimental designs and their applications, including how they are constructed with respect to the situation under consideration, are of interest in this study. While there is a wide range of experimental designs and numerous dierent constructions, this thesis focuses on FFDs and their applications. Experimental design is a test or a series of tests in which purposeful changes are made to the input variables of a process or system so that we may observe and identify the reasons for changes that may be noted in the output response (Montgomery (2014)). Experimental designs are important because their design and analysis can in uence the outcome and response of the intended action. In this research, analysing experimental designs and their construction intends to reveal how important they are in research experiments. Chapter 1 introduces the concept of experimental designs and their principal and oers a general explanation for factorial experiment design and FFDs. Attention is then given to the general construction and analysis of FFDs, including one-half and one-quarter fractions, Hadamard matrices (H), Balanced Incomplete Block Design (BIBD), Plackett-Burman (PB) designs and regression modelling. Chapter 2 presents an overview of the screening experiments and the literature review regarding the project. Chapter 3 introduces the rst part of the project, which is construction and analysis of edge designs from skew-symmetric supplementary dierence sets (SDSs). Edge designs were introduced by Elster and Neumaier (1995) using conference matrices and were proved to be robust. One disadvantage is that the known edge designs in the literature can be constructed when a conference matrix exists. In this chapter, we introduce a new class of edge designs- these are constructed from skew-symmetric SDSs. These designs are particularly useful, since they can be applied in experiments with an even number of factors, and they may exist for orders where conference matrices do not exist. The same model robustness is archived, as with traditional edge designs. We give details of the methodology used and provide some illustrative examples of this new approach. We also show that the new designs have good D-eciencies when applied to rst-order models, then complete the experiment with interaction in the second stage. We also show the application of models for new constructions. Chapter 4 presents the second part of the project, which is construction and analysis two-level supersaturated designs (SSDs) from Toeplitz matrices. The aim of the screening experiments was to identify the active factors from a large quantity of factors that may in uence the response y. SSDs represent an important class of screening experiments, whereby many factors are investigated using only few experimental runs; this process costs less than classical factorial designs. In this chapter, we introduce new SSDs that are constructed from Toeplitz matrices. This construction uses Toeplitz and permutation matrices of order n to obtain E(s2)- optimal two-level SSDs. We also study the properties of the constructed designs and use certain established criteria to evaluate these designs. We then give some detailed examples regarding this approach, and consider the performance of these designs with respect to dierent data analysis methods. Chapter 5 introduces the third part of the project, which is examples and comparison of the constructed design using real data in mathematics. Mathematics has strong application in dierent elds of human life. The Trends in International Mathematics and Science Study(TIMSS) is one of the worlds most eective global assessments of student achievement in both mathematics and science. The research in this thesis sought to determine the most eective factors that aect student achievement in mathematics. Four identied factors aect this problem. The rst is student factors: age, health, number of students in a class, family circumstances, time of study, desire, behaviour, achievements, media (audio and visual), rewards, friends, parents' goals and gender. The second is classroom environment factors: suitable and attractive and equipped with educational tools. The third is curriculum factors: easy or dicult. The fourth is the teacher: wellquali ed or not, and punishment. In this chapter, we detailed the methodology and present some examples, and comparisons of the constructed designs using real data in mathematics . The data comes from surveys contacted in schools in Saudi Arabia. The data are collected by the middle stage schools in the country and are available to Saudi Arabian citizen. Two main methods to collect real data were used: 1/ the mathematics scores for students' nal exams were collected from the schools; 2/ student questionnaires were conducted by disseminating 16-question questionnaires to students. The target population was 2,585 students in 22 schools. Data were subjected to regression analyses and the edge design method, with the nding that the main causes of low achievement were rewards, behaviour, class environment, educational tools and health. Chapter 6 surveys the work of this thesis and recommends further avenues of research.