5.6 Similarity and dissimilarity

In multivariate classification techniques first it is necessary to define a variable to express the degree of (dis)similarity between two sites. There is a large number of these so-called (dis)similarity coefficients. In the present situation, where we have chosen to convert raw numbers of artefacts per type into progressive classes, an ordinal correlation coefficient such as r_s or tau seems at first sight called for. The modified data are not actual rankings and for instance have a great many equal values (ties), making these coefficients less applicable. The data are also not counts, so in the end we have chosen to consider them nominal data and select a correlation coefficient based on Chi².

To illustrate this we have displayed for the sites 52B-168 and 52E-150 the progressive class values side by side in a cross table. For this table a Chi² value of 4.375 is valid. Statistically this absolute value is not high enough and there are too many cells with a low expectation value to indicate a significantly different artefact composition. In principle an increasing Chi² value should indicate increasing dissimilarity. However, the Chi² value is unsuitable as a dissimilarity variable, as it is dependent on the absolute numbers in the cross table. Comparison of two large sites yields a higher Chi² value more easily than comparison of two small sites. A workable variable is obtained by dividing the Chi² value by the numbers of observations (n). This variable Phi has been defined as:

Phi = Ö (Chi²/n)

In this situation, with an r x 2 cross table, Phi equals the Cramer's V-value (Shennan 1988). The minimum value is 0 when both sites are similar and the maximum value of 1 is reached when both sites are completely dissimilar. The absence of an artefact type on both sites does not affect the end result. In this example Phi has a value of 0.468, indicating a reasonable degree of similarity. In spite of the fact that there are far less finds on site 52B-168, the pattern of the artefact types that are present is more or less similar to the pattern of site 52E-150. Relatively abundant types on the 'rich' site 52E-150, such as production debris and scrapers, are precisely the types that occur on the 'poor' site 52B-168. The types that occur only in limited amounts on 52E-150, are those absent from 52B-168.