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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 a parabola if the design styles considered are controlled by one factor only (like chronology).
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.
Hill and Gauch (1980) presented a method to remove this effect.
In 2003, Groenen and Poblome adapted the correspondence analysis algorithm to combine seriation with absolute dates and stratigraphic relationships.
Contextual seriation is often used for reconstructing the chronological sequence of graves as only the presence or absence of a design style or type is important.
Frequency seriation is applied in case of large quantities of objects belonging to the same style.
He found that the graves he was uncovering contained no evidence of their dates and their discrete nature meant that a sequence could not be constructed through their stratigraphy. 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.
Petrie listed the contents of each grave on a strip of cardboard and swapped the papers around until he arrived at a sequence he was satisfied with. It also assumes that design popularity will be broadly similar from site to site within the same culture.
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. 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.
Though according to David George Kendall (1971), Petrie's paper showed already a deep understanding of the mathematics of the seriation problem (Quote: ".my view Petrie should be ranked with the greatest applied mathematicians of the nineteenth century"). 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. 269–281) summarized the state of the art of seriation methods thoroughly, giving detailed descriptions of Kendall's and Robinson's approaches.
This is called the arch effect by Hill and Gauch (1980).