Page 48 - Kennemerland VOC ship, 1664 - Published Reports

NAUTICAL ARCHAEOLOGY, 4.2
class IV (clay pipes) separate maps are drawn up for the three sub-classes.
The problem is now to correlate these 11 distribution maps; the techniques used are borrowed from the discipline of numerical taxonomy (Sneath & Sokal, 1973). Borrowing procedures from this source is conimon in conventional archaeology (Clarke, 1968). However, the nature of the subject is such that there are no firm rules specifying the most appropriate methods to use in any given situation. For this reason a couple of alterna- tive approaches are presented below, in the hope that this may initiate some further tests to identify the most appropriate methods for our purposes.
The first method is one which seeks to simplify the data by transforming the num- bers of items in each class in each square into three basic categories; absent, present, and abundant. The more orthodox approach is to consider only presence or absence, but in this case tests using such a division indicate that virtually all discrimination between classes is lost. Introducing the abundance category gives considerably more satisfactory results. The measure of abundance used is whether the figure for that square is greater than the mean figure for that particular class of artefact over the whole site (i.e. the figure given in row d, column 6 in Table 1). In cases where the mean is less than one (i.e. classes Ill, IVb, etc.) this means that all squares where the items occur register as abundant ; these classifications have reverted to presence/absence ones. The next step is to transfer this data onto a master matrix, as shown in Fig. 3, for easy visual corrdation. To facilitate reference, each square is given a number according to the code given in Fig. 4, the numbers running strictly from left to right and from top to bottom to aid scanning. Thus the body of the matrix consists of symbols indicating the status of the class heading that column in the square indicated at the left-hand margin; that status is either absence (a blank), presence (X), or abundance (0).In order to abbreviate
the matrix, all those squares which contained no artefacts of any class are totally omitted; there are 17 such squares, and they are indicated in Fig. 4 by italic underlined numbers.
Since our interest is in the relationships between the classes of artefact, the next step is t o calculate coefficients of similarity between each pair of columns in this matrix. However, there are innumerable ways of calculating these coefficients; in this instance. two particularly promising approaches are used (Sneath & Sokal, 1973: 129-37). The first approach uses the Coefficient of Jaccard. in which, for the pair of classes under consideration, the numerator is the number of occasions on which they are both present in the same state (i.e. the number of rows containing either X X or 0 0 for those two columns), while the denominator is the number of occasions on which either class is present in some state (i.e. the number of rows containing X or 0,OX or XO or 00 or XX for the two columns). In other words, this coefficient expresses the proportion of oc- casions when the two classes involved are present in identical states out of the total number of occasions on which at least one of these classes is present. It thus ignores com- pletely all occasions on which both classes are absent (i.e. when there are two blanks): consequently, the omission of all totally empty squares from Fig. 3 is of no conse- quence. For ease of presentation and inter- pretation, these coefficients are displayed in a similarity matrix (Fig. 5). The alternative coefficient used is the Simple Matching Coefficient; the matrix displaying the results is given in Fig. 6. This coefficient is generated by taking as the numerator the number of occasions when the two classes under con- sideration are identical (i.e. 0 0 , XX or two blanks), while the denominator is the total number of possible correlations, in other words, the total number of rows (in this case 90). This coefficient simply correlates total similarity, in any form, with the overall total. The omission of the 17 totally blank rows is thus relevant; 17 has to be added to both the numerator and the denominator in each case. One minor advantage of this coefficient in practical terms is that calculations and inspection are easier because the denominator is always 90.
Brief inspection of Figs 5 and 6 will show that the choice of coefficient makes a great difference to the similarity values reached. An
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