Basic Notions and Ideas

In such statistically designed experiments one wants to exclude the random effects of a limited number of features by varying them systematically, i.e. by variation of the so-called factors. At the same time the order in which the experiments are performed should be randomized to avoid systematic errors in experimentation. In another basic type of experiment, sequential experiments, the set-up of an experiment depends on the results obtained from previous experiments. For help in deciding which design is preferable, see Section 3.6. In principle, statistical design is one recommendation of how to perform the experiments. The design should always be based on an exact question or on a working hypothesis. These in turn are often based on models. 

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 

Chemometrics in Environmental Analysis. IW. Einax, H. W. Zwanziger, S. GeiC Copyright 1997 WILEY-VCH Verlag GmbH ISBN 3-527-28772-8 

The design matrix in a preliminary form is then given by  

Each experiment can also be called a treatment. It refers to a defined combination of fixed levels of the factors. Repeated (multiple) measurements of such a combination are said to be members of one and the same class, sometimes called a cell. In our above example, we may then have performed four replicate analyses, so that in each cell we have four members (objects, measurements), e.g. in class 11 , yn,i Tn,2, Jit,3, Jit,41-Analysis of variance (see also Section 3.3.9) then can be used to evaluate the results. 

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Before analysing systematically the various types of initiation, we wish to introduce some basic notions and ideas concerning the characteristics and properties of the various starting components which make up a system the ways in which these chemicals an interact and how certain physical parameters can influence the course of initiation our present knowledge or hypotheses on the different types of intermediates formed as a result of these interactions and, finally, the advantages and drawbacks of the experimental techniques presently available for carrying out fundamental studies on these processes. 

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