More Thoughts on Mound Size Variability

This post begins to explore additional patterning in mound size, refining some of my earlier observations and offering some hypotheses for evaluation. Suppose mound-building groups occupied stable territories over the span of several generations or longer. Within the territory held by such groups, they built burial mounds. Many burial mounds within a given area may thus have been produced by the same group or lineage. Under these circumstances, burial mounds located in close proximity should be more likely to be the product of a single group or lineage. If the group traits that influenced mound volume were also relatively stable through time, burial mounds located near to each other should be similar in size. As an initial attempt to evaluate these claims, I looked at the relationship in mound size between mounds that were nearest neighbors and between randomly-paired mounds.

Recall that most mounds have been affected by modern plowing and other disturbances, but some mounds have been largely spared such damage. The museum records that I used characterized these undamaged mounds as “whole”. The museum records documented 287 whole mounds. To make sure that the comparisons were fair, I limited the sample of nearest neighbors to just those whole mounds that had another whole mound as its nearest neighbor. I eliminated duplicate pairings, so each pair of nearest neighbors was only considered once. The imposition of these constraints shrunk the nearest neighbor sample size to 49. Finally, I ran a simple linear regression to evaluate the relationship between the size of the mounds in these nearest neighbor pairings. Because the distribution of mound volume can be modeled as an exponential distribution, I used the log of mound volume in the regression analysis. Without this transformation, any relationship in
mound size between the nearest neighbors would be unlikely to be well approximated by a straight line.

I then sampled without replacement from the 287 whole mounds to obtain 49 randomly-selected pairs. As with the nearest neighbors, I performed a simple linear regression, using log volume. I repeated this procedure 500 times. The repeated sampling and analysis allowed me to develop a null hypothesis for the values of the regression coefficients.

I expected that the randomly-selected pairs would not have a meaningful relationship. The slope of the regression line should be close to zero for these samples. In contrast, the size of the nearest neighbor pairs should be positively correlated, so the slope of the regression line should be significantly larger than zero. The following two figures show the distribution of the regression coefficients, the intercept and slope, for the randomly-selected pairs.

20130629-183701.jpg

20130629-183806.jpg
Notice, in particular, that the distribution of the slope clusters near zero as predicted. This result indicates that the randomly-selected pairs do not have a meaningful relationship with each other, at least with respect to size.

These distributions contrast with the regression coefficients calculated for the nearest neighbors. The intercept is 0.90, and the slope is 0.75. These values are completely beyond the range of values estimated for the randomly-selected pairs. This experiment shows that the size of nearest neighbors is significantly and positively correlated. The results lend some support to the notion that stable groups produced these mounds. At the very least, the results provide encouragement to further explore the relationship between mound size and mound spatial distribution. Such work should probably make use of the spatial analysis tools available in GIS programs.

© Scott Pletka and Mathematical Tools, Archaeological Problems, 2013.

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