Multifactorial experiments

Multifactorial experiments are used in analytical chemistry for diverse applications, e.g., checking up significant influences before optimization procedures, recognizing matrix effects, and testing the robustness of analytical procedures (Wegscheider [1996]). 

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

A final source of variation in microarray experiments is derived from measurement errors. Measurement errors may occur during the processes of image acquisition and normalization or during the multifactorial data analysis required to extract biological relevance from the collected data. The effect of measurement error can be minimized by ensuring consistency in all aspects of microarray experimentation. If possible, experiments should be performed by the same technician, and subsequent data analyses be applied to all datasets consistently. 

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... 

The influence of water components on the flame photometric determination of potassium and sodium can be detected by factorial experiments. By application of multifactorial plans according to PLACKETT and BURMAN the qualitative determination of the influence of various variables is possible with relatively few experiments [SCHEFFLER, 1986]. For mathematical fundamentals see Chapter 3. 

The measurements were performed with a FLAPHO 4 flame photometer (Carl Zeiss Jena) using a propane-air flame. The influence of sulfate, chloride, and phosphate ions and the mutual influence of alkali metal ions on the determination of potassium and sodium ions were investigated. Anions were selected on the basis of previous experiments to determine their interference properties. The multifactorial plan was realized in the concentration levels represented in Tab. 10-4. 

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. 

The simplest experiments are those in which one treatment (factor) is applied at a time to the samples. This approach is likely to give clear-cut answers, but it could be criticized for lacking realism. In particular, it cannot take account of interactions among two or more conditions that are likely to occur in real life. A multifactorial experiment (Fig. 10.4) is an attempt to do this the interactions among treatments can be analysed by specialized forms of analysis of variance. 

Multifactorial experiments are economieal on resources because of hidden replication . This arises when two or more treatments are given to a subject because the result acts statistically as a replicate for eaeh treatment. Choice of relevant treatments to combine is important in multifactorial experiments for instance, an interaction may be present at certain concentrations of a chemieal but not at others (perhaps because the response is saturated). It is... 

Fig. 10.4 Design of a simple multifactorial experiment. Factors A and B have effects a and b when applied alone. When both are applied together, the effect is denoted by a + b + c.

Diabetes mellitus (DM) is a metabolic carbohydrate disorder that results from either insufficient insulin (type 1 DM) or the body s inability to recognize available insulin (type 2 DM). DM is a multifactorially inherited disorder this means that although people can inherit a propensity toward this condition, environment and diet can trigger onset of the actual disease. People who suffer from DM experience abnormally high blood... 

---