Optimization and Experimental Design

Most people only think of statistics when faced with a lot of quantitative information to process. From the common sense perspective, using statistical methods would be comparable to mining. The statistician would be some powerful miner, capable of exploring and processing mountains of numbers and extracting precious conclusions from them. 

As with many things associated with common sense, this is another misconception, or at least an incomplete one. In an experiment, the most important statistical activity is not data analysis, but the actual design of the experimental runs that will produce the data. If this is not properly done, the experiment may yield only a sad bunch of meaningless values, where no statistical wizardry will help. 

Evolution of an empirical study. Knowledge of the system increases as we make our way down the table. 

Yogi Berra, the American baseball legend, was also known for his witticisms, some of them apparently paradoxical. One of them is very apposite here You ve got to be careful if you don t know where you re going cause you might not get there . 

Once we have identified the reaUy significant factors, the next step should be to quantitatively evaluate their influences on the responses of interest, as weU as any possible interactions between them. To do this with a minimum number of experiments, we can employ full factorial designs, treated in Chapter 3. Then, if we want a more detailed 

In Chapter 3 we introduced the idea of a factor, i.e. any aspect of the experimental conditions which affects the result obtained from an experiment. Section 3.9 gave the example of the dependence of a fluorescence signal on the conditions under which a solution was stored. The factor of interest was these storage conditions it was called a controlled factor because it could be altered at will by the experimenter. In another example in Section 4.3, in which salt from different parts of a barrel was tested for purity, the factor of interest, i.e. the part of the barrel from which the salt was taken, was chosen at random, so that factor was called an uncontrolled factor. In both these examples the factors were qualitative since their possible values could not be arranged in nmnerical order. A factor for which the possible values can be arranged in numerical order, e.g. temperature, is a quantitative one. The different values that a factor takes are known as different levels. 

The term experimental design is usually used to describe the stages of  

1 identifying the factors which may affect the result of an experiment  

2 designing the experiment so that the effects of uncontrolled factors are 

3 using statistical analysis to separate and evaluate the effects of the various factors involved. 

---

Statistical Designs, 9941 Rowlett, Suite 6, Houston, TX Software for Experimental Design and Optimization. ... 

Bayne, C.K., and Rubin, I.B. (1986), Practical Experimental Designs and Optimization Methods for Chemists, VCH Publishers, Deerfield Beach, FL. 

Implementing A Robust Methodology Experimental Design and Optimization... 

By executing the steps of the analytical process, we can take advantage of most of the basic methods of chemometrics, e.g., statistics including analysis of variance, experimental design and optimization, regression modeling, and methods of time series analysis. 

For deeper study of the matter the reader can be directed to monographs on experimental design and optimization, e.g. [MORGAN, 1991 DEMING and MORGAN, 1993]. More references on this subject are given in Section 1.8. 

---