SZ. BURGER ALICE: LATE ROMAN MONEY CIRCULATION IN SOUTH-PANNONIA / Régészeti Füzetek II/22. (Magyar Nemzeti Múzeum Budapest, 1981

THE METHODS OF THE ANALYSIS

Time intervall (determined by the LRBC code at the Phase A and by the RIC code at the Phases B and C) Site Mint Avers Officina Emission marks (at the later Phases only) The number of the coins with the same characteristics has been coded as well. An example of the coding of coins from the Phase A and Phase B can be seen on p. 12. The next step of the work has been to develop a program to ask questions about the stored data. The query program written directly for this investigations has used some ideas of relational data bases (namely the techniques of multi aspect binary search trees). The program has been able to classify the whole data or a given part of them into groups according to the characteristics and generate tables of two or more dimensions, like the most basic ones containing the frequencies mints versus sites or the tables with years versus mints versus Emperors. The three dimensional tables have been printed out after slicing them by one dimension. The tables has given the input of the figures containing only some specific groups of coins, too. When working with the tables containing time dimension we have found a problem in the using of the time intervalls given by the LRBC or RIC catalogues. Let's see an example: in the coinage we have found a certain type of coins That is, an average of four coins falls into each year of the first period and five coins into each year of the second period, which gives nine coins altogether in the year 330. In order to avoid this disturbing preponderance the 327 - 330 intervall is proposed to mean only the years 327, 328, 329 - in the evaluations by the computer we have followed this obvious correction. The length and vast print-outs of the computer aided data processing emerged the need of using some mathematical methods for revealing the relationships in the data. The speed of the computer allowed the application of not only the traditional methods of statistical tests of checking hypothesises coming from the experts of a given field but to start with the search for all the relations of a given type. We have done so in the hope that new, statistical evidence can be generated to the statements accepted by the scientists, and the mathematical methods draw attention to some relationships unnoticed till now. The method we have used will be illustrated by an example of mints versus sites: the table containing the quantity of coins minted in a specific mint and found in a specific site gives no concise information about the similarities or dissimilarities of the coinage found in two sites concerning the representation of the mints. The above-mentioned question has a dual one concerning the similarities or dissimilarities of the coinage minted by two specific mints and distributed into sites with more or less similar distributions. The statistical tests for deciding whether two distributions are similar to each other are of everyday use. Since in our case the frequencies have been rather different we decided to use some clustering techniques instead of the classical methods using khi-squares. The essence of this technique is that the relative frequencies of the distribution determine the coordinates of a point in a multi-dimensional space. Two distributions are similar to each other if the corresponding points are near each other. After the computation of the distances the clustering program forms the groups (clusters) step by step. At the very beginning each point in itself represents a cluster containing only this point, at the end of the process all the points are contained in one cluster only. In the middle of the process the clusters contain two-four points in general. Due to the multi-dimensional nature of the approach no graphical means helps to clarify the situation. ABOUT THE QUERY PROGRAM A.D. 327 - 330 A. D. 330 - 335 16 coins 30 coins. THE CLUSTERING OF THE FREQUENCY DISTRIBUTIONS 9