Since any measurement depends on an extremely large number of variables, the analytical signal will always have a random character with a distribution described by a certain limit theorem. When the fluctuations of the analytical signal, which always include the background noise, are described by the Liapunov-Lindeberg central limit theorem, the distribution of frequencies will be normal.Fig. 1 presents in a simplified form an analytical system with a detection function and a determination function. The detection function of an analytical system consists in providing both measurement data and the criterion for decision between the two possible hypotheses: H0 --the component sought is not present or H1 --the component sought is present. Once the decision is made, an amount of information of one bit will be obtained, evidently with a certain probability [I=log2 (2/1)=~ bit]. The determination function of the analytical system consists of estimating the content of the component sought and this corresponds to an amount of information which exceeds one bit. Fig. 2 gives a schematic representation of the random character of measurement results, whether it is the background noise (c = 0) or the analytical signal (c > 0).The simplest model for the dependence between concentration and analytical signal is the case in which the signal y is normally " Dedicated to Professor M. K. Zacherl on his 70th birthday.
mathematical methodology is being used. Use of such data not only aids in "debugging" the necessary procedures, it trains the researcher's intuition and may help reveal potential problems and limitations of the methodology used.
COMPUTATIONSAll calculations required for this study were carried out on the University of Washington Academic Computer Center's CDC6400/CYBER73 dual mainframe system. The programs used in this study are currently being added to our data analysis system ARTHUR; we hope to make this expanded system available early in 1977.
The goal of analytical processes is to acquire chemical information and therefore the amount of information, according to Shannon, is the most adequate measure in the evaluation of an analytical process. The procedure of evaluating the amount of information In analytical processes as well as the utilization of this quantity as a criterion in solving many analytical problems is discussed; the problems are: selecting one method out of several methods, the optimal combination of several methods to solve an analytlcal problem, coding of information, and chemical classificatbn. The analogy between the systems of Information transmisslon and analytical measuring systems allows the adaptation of information theory notions (entropy, amount of information, coding, decoding, perturbatlons, etc.) to chemical analysis. This represents the generalized basis of analytical chemistry.(60-63).
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