Multifactorial design

In contrast to common statistical techniques, by modern experimental design influencing factors are studied simultaneously (multifactorial design, MFD). The aim of MFD consists in an arrangement of factors in such a way that their influences can be quantified, compared and separated from random variations. 

According to the number n of included independent variables xb x (influencing quantities, features, factors,. ..) we distinguish one-factorial designs (n = 1) and multifactorial designs (n > 1). According to the number m of recorded response features v i,. .., ym we will get univariate results (m = 1) or multivariate results (m > 1). Therefore we can arrange our numerical results in data matrices with k lines, the experiments, and m... 

Marcobal, A., Martin-Alvarez, P.J., Moreno-Arribas M.V, Munoz, R. (2006a). A multifactorial design for studying factors influencing growth and tyramine production of the lactic acid bacteria Lactobacillus brevis CECT 4669 and Enterococcus faecium BIFI-58. Res. Microbiol, 157, 417-424. 

M0LLER J K S, JAKOBSEN M, WEBER C J, MARTINUSSEN T, SKIBSTED L H and BERTELSEN G (2002), Optimization of colom stability of cured ham during packaging and retail display by a multifactorial design, Meat Science, in press. 

The development of sepsis is complex and multifactorial. The normal host response to infection is designed to localize and control bacterial invasion and initiate repair of injured tissue through phagocytic cells and inflammatory mediators.1 Sepsis... 

Plackett RL, Burman JP (1946) The design of optimum multifactorial experiments. Biometrika 33 305... 

Townsend JP. 2003. Multifactorial experimental design and the transactivity of ratios with spotted DNA microarrays. 

The effects of interference on the flame photometric determination of potassium and sodium can be detected. Quantitative description of these interference effects is possible by empirical modeling on the basis of experimental design, i.e. by applying a multifactorial plan. 

The experimental design, i.e. the combination of multifactorial plans and empirical modeling, is not limited in application to this specific case study. It can be enlarged to encompass other similar problems in the field of analytical chemistry. Other mathematical methods, for instance LMS regression (see Section 9.3.2) or PLS regression (see Section 5.7.2), can also be used for empirical modeling. 

Cordingley HC, Roberts SL, Tooke P, Armitage JR, Lane PW, Wu W, Wildsmith SE. Multifactorial screening design and analysis of SELDI-TOF ProteinChip array optimization experiments. Biotechniques 2003 34 364-365, 368-373. 

Breast cancer has a multifactorial etiology involving numerous genetic, metabolic, and cultural variables. Table I presents a summary of many epidemiological studies designed to identify risk factors for breast cancer (2-8). 

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