Contextual and frequency seriation
Two different variants of seriation have been applied: contextual seriation and frequency seriation (Renfrew and Bahn 1996, pp. 116–117). Whereas contextual seriation is based on the presence or absence of aHistory
Flinders Petrie excavated at Diospolis Parva inThe model
Description of the model
The assumption that design styles follow a bell curve of popularity – starting slowly, growing to a peak and then dying away as another style becomes popular – provides the basis for frequency seriation. It also assumes that design popularity will be broadly similar from site to site within the samePitfalls
The task of identifying design styles i.e. to form groups of objects belonging to the same design style is by no means trivial. Creating a typology frequently is the basis of a seriation. Errors in typology result in errors in seriation: For example, if a certain design style had two peaks in popularity ( bimodal distribution), this design style is not appropriate for seriation and its inclusion in the analysis may result in strange results. Some design styles were used for a very long time as the shape constructed was handy and no improvement or ornament was added. Of course, these design styles are not eligible for chronological seriation. For example, knives in early medieval times in Europe are said to show no chronological variation. In addition to temporal organization, seriation results may reflect assemblage differences in social status, age, sex or those resulting from regional variation (or a combination of two or more of these factors). Shennan (1997, p. 343) presents a seriation result of Danish hoards based on artefact types like daggers, axes, and swords. The result is not a chronological sequence due to the selection of types, the ordering seems to start with extremely male hoards and ends with extremely female ones.Three conditions for chronological seriation
Doran and Hodson (1975, p. 269)Doran, J.E. and F.R. Hodson (1975). ''Mathematics and Computers in Archaeology.'' Edinburgh University Press. . list three conditions that must be satisfied to obtain a chronological seriation result: * Regional variation must be kept to a minimum, i.e. assemblages must best be drawn from one locality. * The objects analyzed must all come from a single cultural tradition. * The traits or attributes included in the seriation must depend on cultural aspects (rather than on function).Statistical methods
Development of seriation methods
Nowadays, seriation results are no longer produced manually as in Petrie's times but by appropriate algorithms. Though according to David George Kendall (1971), Petrie's paper showed already a deep understanding of the mathematics of the seriation problem (Quote: "..in my view Petrie should be ranked with the greatest applied mathematicians of the nineteenth century"). In Baxter's (2003, p. 8) list of landmarks of statistics in archaeology the paper of Robinson (1951) is the first entry. Robinson based his frequency seriation method on a similarity matrix. In 1971, Kendall proposed the use of multidimensional scaling techniques for seriation problems, and this approach has also been used by some other scientists (see Baxter 2003, pp. 202–203). Baxter also presents a review of statistical methods for seriation and a description of these approaches (pp. 202–207). In 1975, Doran and Hodson (pp. 269–281) summarized the state of the art of seriation methods thoroughly, giving detailed descriptions of Kendall's and Robinson's approaches.Correspondence analysis for seriation purposes
Today, the most popular seriation method both for contextual and frequency problems is based on correspondence analysis. The sequence of the first axis of a correspondence analysis is considered the best seriation order (Shennan 1997, p. 342; Lock 2003, p. 127; Jensen & Høilund Nielsen 1997). Using this technique, not only the sequence of the objects but also those of the design styles is established. Note that external evidence is needed to establish the direction of the sequence calculated, i.e. the method does not tell whether the first object in the sequence is the oldest or the youngest object. Kendall (1971) applied multidimensional scaling to the cemetery data of Münsingen. The resulting scatterplot showed the form of a horse-shoe where the graves were arranged on the curve according to their chronological order. Similarly, a mapping of the component scores for the first two axes of the correspondence analysis result will display aExamples
Example 1: Small contextual seriation
The small example below was inspired by Flinders Petrie's serial ordering of Egyptian pottery as published by Renfrew and Bahn (1996, p. 117). The raw data are stored in an unsorted binary contingency table indicating which design style can be found in which context by a star symbol. For example, consider the first column: context 3 contains the design styles ''blackrim'', ''bottle'', and ''handle''. A ''beaker'' is contained in contexts 1 and 2. Contextual seriation sorts the design styles and the contexts in such a way that the star symbols are found as close as possible to the diagonal of the table. Of course, for a small examples like this, no computer programs are needed to find the best ordering, but for larger data sets like the 900 graves studied by Petrie they are extremely helpful.Example 2: Simulated data, seriation and correspondence analysis
The data presented in this example was simulated by WinBasp. Initially 60 contexts (called units in WinBasp) were created along with 50 types. The contexts were labeled in chronological order by numbers 01 to 60, the types are labeled in the form T00001 to T00050. If a type is represented by one object only this object is not relevant for the chronological sequence as it does not provide a link to another context. Similarly, contexts containing one object only are irrelevant for seriation. Therefore, the contexts with one or no object and types represented by one object or not at all were eliminated. The resulting raw simulated data consisting of 43 contexts and 34 types are shown on the left. As expected, the dots indicating the occurrence of a type in a context are close to the diagonal of the table. The image on the right hand side shows the result of the seriation for this data set. Note that the dots are even more compact along the diagonal of the table compared to the raw data. This shows a minor problem of seriation: In fact, the intervals of production may be somewhat longer than those calculated by the algorithm. In general, the sequences of contexts and types calculated by a seriation algorithm are not the correct chronological sequences but they are fairly close. The image above shows the scatterplot with the typical parabola shape of the first two axes of a correspondence analysis for the contexts of the simulated data set.Example 3: Ideal data, seriation and correspondence analysis
The contingency table shows 29 contexts with ideal seriation data as created by Kendall and Jensen & Høilund Nielsen (see above). With each new context a new type appears and another type disappears. For this regular data, it seems reasonable to assume constant time intervals for contexts adjacent in time. The correspondence analysis results shown in the figures below were calculated on the basis of 49 contexts with ideal seriation data. The scatterplot of the first two correspondence analysis axes shows the typical parabola shape. The display of the scores on the first and the third axes exhibits points lying on a third degree polynomial curve. Similarly, the plot of the scores on the first and the fourth axes will show a fourth degree polynomial for ideal data – and so on. Note that the distances of the scores for adjacent contexts on the first axis vary: At the beginning and the end, the distances are extremely small, the largest distances in the centre is about 30 times as large as the smallest distance. Hill and Gauch (1979) created a similar contingency table with a regular structure with each context containing six types. They note, too, that the within-context distances are smaller at the ends than in the middle. This was one of the reasons why they proposed an adjustment which is called detrended correspondence analysis. Nevertheless, some archaeologists think that a linear transformation of the scores on the first axis on the basis of some known absolute dates will create good estimates for the unknown absolute dates, and this approach is the basis of the method presented by Groenen and Poblome (see above) to combine relative and absolute dates. This ideal example shows that a linear transformation might not be appropriate in all cases, though a simulation study by van de Velden, Groenen and Poblome comes to the conclusion that the predictions of the approach are quite good. van de Velden, M., Groenen, P. J. F., Poblome, J. (2007). ''Seriation by constrained correspondence analysis: a simulation study.'' Econometric Institute Report EI 2007-40.Archaeological sequence
The archaeological sequence (or sequence) for short, on a specificSee also
* * Archaeological context * *Notes
References
* Baxter, M. (2003). ''Statistics in Archaeology''. London: Arnold. . * Fagan, B. (2005). ''Ancient North America''. London: Thames & Hudson Ltd. * Janssen, U.: Die frühbronzezeitlichen Gräberfelder von Halawa, Shamseddin, Djerniye, Tawi und Wreide am Mittleren Euphrat. Versuch einer Datierung und Deutung sozialer Strukturen anhand multivariater statistischer Verfahren (Korrespondenzanalyse und Seriation). Ugarit Forschungen 34, Münster 2002. * Jensen, C.K. and K. Høilund Nielsen (1997). Burial Data and Correspondence Analysis. In Jensen, C.K. and K. Høilund Nielsen (eds.) ''Burial and Society: The Chronological and Social Analysis of Archaeological Burial Data''. Aarhus University Press, pp. 29–61. . * Kendall, D.G. (1971). "Seriation from abundance matrices". In ''Mathematics in the Archaeological and Historical Sciences''. Edited by F. R. Hodson, D. G. Kendall, and P. Tautu, pp. 215–252. Edinburgh: Edinburgh University Press. . * Lock, G. (2003). ''Using Computers in Archaeology: towards virtual pasts''. London: Routledge. . *O'Brien, Michael J. and R. Lee Lyman (1999). ''Seriation, Stratigraphy, and Index Fossils: The Backbone of Archaeological Dating''. New York: Plenum Press. . *Renfrew, C. and Bahn, P. (1996). ''Archaeology. Theories, Methods, and Practice''. London: Thames and Hudson Ltd. . *Siegmund, F. (2015). ''How to perform a correspondence analysis. A short guide to archaeological practice''. Charleston SC: CreateSpace. 2015. .External links