Discrete variations and systematic errors

In Chapter 3 it was discussed how the presence of a random error can be handled by statistical tools. The precautions which must be taken by the experimenter not to violate the assumption of independencies of the experimental error is randomization, which allows certain time-dependent systematic errors to be broken down and turned into random errors. There are, however, sources of error which can be suspected to produce systematic deviations which cannot be counteracted by randomization. In such cases, forseeable sources of systematic variation can be brought under control by dividing the whole set of experiments into smaller blocks which can be run under more homogeneous conditions. By a proper arrangement of these blocks, the systematic variation can be isolated through comparison of the between-block variation. Some examples where splitting the series of experiments into blocks is appropriate are  

Their contents may differ slightly and this may produce a systematic variation. 

The objective is to select the one which seems most promising for further development of the procedure. In this case it is highly probable that the influence of experimental variables will be modified by the nature of the reagent, i.e. there are interaction effects between the type of reagent and the experimental variables. 

two examples will be discussed to illustrate some principles. The general problem of how to split large designs into smaller blocks has been the subject of considerable interest over the years. It is beyond the scope of this book to go into details on this. Readers who are interested in more thorough discussions on this subject should consult the specialized text-books given in the list of references.[13] 

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