Frequency profile analysis

Frequency profile analysis consists in comparing a series of attribute frequency profiles. These profiles are of two types: index profiles and assemblage profiles. An index profile is an `ideal' profile which analytically identifies a phase. Let us say that our ceramic analysis involves a single attribute with three possible states. A phase index profile consists of the percentages of each of those attribute states in a given phase. So the index profile of Phase 1 would be in the form A-B-C, where A is the percentage of attribute state A, B the percentage of attribute state B, and C the percentage of attribute state C in an unmixed Phase 1 assemblage. Thus a possible Phase 1 index profile would be 30-60-10, meaning that in Phase 1 assemblages 30% of sherds have attribute state A, 60% have attribute state B, and only 10% have attribute state C.

An assemblage profile consists of the relative frequencies of possible attribute states within a given empirical assemblage, such as the ceramics from a surface collection or excavation locus. The assemblage profile therefore represents an empirical frequency distribution, as opposed to the ideal frequency distribution of the index profile.

The method of frequency profile analysis is to generate a series of hypothetical assemblage profiles - one for every possible combination of the predefined index profiles. In the case of my surface collection ceramic analysis, the index profiles represented the various ceramic phases defined for the region, and the hypothetical assemblage profiles were every possible mixture of these phases, ceramically defined. The empirical assemblage profile is then compared to the full range of hypothetical assemblage profiles. The closest match is found and this is taken to indicate the specific mixture of ceramic phases represented in a particular empirical assemblage. Matching between the hypothetical and empirical assemblage profiles is accomplished automatically by computer using a simple recursive algorithm. The algorithm attempts to minimize the quantity $d$:

  
$d=\frac{abs(H_{1}-E_{1})+abs(H_{2}-E_{2})+...+abs(H_{n}-E_{n})}{n}$




where E = empirical assemblage profile 


H = hypothetical assemblage profile

Thus, the best match is the hypothetical assemblage profile with the lowest average departure from the frequencies recorded for the empirical assemblage profile. The short program I have written for the analysis of the surface collection materials - which performs this operation - is included as Appendix C.