Sherrod and Rolingson's initial study of the Toltec Module focused on distances between key points at the Toltec Mounds site, primarily the edges and centers of the mounds, and the edges and openings in the embankment around the site.  In order to conduct this type of study, the edges and center points of the mounds must first be determined with at least as much precision as the analysis employs.  If the mound edges or center points are mapped inaccurately, the measurements between them will be correspondingly inaccurate.  It is unclear how precisely the mound locations were determined, but the original study employs increments of 50 cm, so we must assume that the locations of the mound edges and centers were demarcated with at least this precision.

            How accurately and precisely, though, can we realistically pinpoint the edges and centers of these large features?  The largest mound at the site (Mound A) is about 95 m long.  Plotting its general position on a map is an easy task, but what about demarcating the exact locations of the edges with sub-meter accuracy?  Even on a 1:1000 scale map (such as the master site map for the Toltec Mounds site), a typical 0.75 to 1 mm wide pencil line covers 75 to 100 cm of width on the ground.  Drawing distances between these lines on this or any similar map would result in an additional margin of error of 1.5 meters at the very least (minimum 75 cm of play on both sides of the measured distance). 

            Like most prehistoric mounds, there are not sharply delineated edges between the sides of the mound and the ground surface at the Toltec Mounds site.  The southern edge of Mound B, for example, does not slope evenly down to the ground surface (Figure 3).  A sharp break in the slope is visible a few meters above the base.  At least some of the fill below the break is almost certainly erosional slope wash from higher up.  Similar erosional deposits are common at the base of mounds at many sites throughout the Southeast.  As Sherrod and Rolingson acknowledge (1987:41), the summits of the mounds at Toltec Mounds site may be truncated from their original heights.  The mounds were subjected to several centuries of natural site formation processes before archaeologists even became aware of the site, experiencing erosion from rain, gravity, tree falls, and the natural mixing of the soil through biological and other means.  For several decades before a formal map of the site was made, the grounds were subjected to repeated plowings, the grazing of animals, foot traffic, and other disturbances.  The locations of mounds that have been leveled (the majority of mounds at the Toltec Mounds site) were inferred through earlier sketch maps and photographs, surface artifact concentrations, and soil stains visible on the surface and through excavation. 

Figure 3.  Mound B at the Toltec Mounds site, facing northeast.  The break in slope angle represents the upper limits of slope wash; the mound has likely been altered both above and below this point.

            How confident, then, can we be in any estimation of mound edges?  The precision undoubtedly varies from site to site, depending on the preservation of the monuments, and the extent and precision of any excavations or surveys of the mounds.  As a hypothetical case, assume we have determined the location of a mound's edge within a margin of error of +/-2 m (the edge may be 2 m either direction from our exact demarcation).  Measuring between any two points, we would need to sum this uncertainty for a total margin of error of +/- 4 m, which is 16.8% of a TM distance.  We should therefore expect about 16.8%, or about one out of every six measurements, to conform to a TM distance by chance alone (even without propagating the margin of error with each multiple). 

            This problem is further compounded when we consider what is meant the by the 'center' of a mound.  Disregarding the theoretical question of why the location of the exact midpoint of an earthen monument would be significant to prehistoric populations, how do we interpolate from edge to center?  Most prehistoric mounds do not present a perfectly round bull's-eye target in plan view.  They may be rectangular, oblong, or irregularly shaped with adjoining mounds, ramps, and other associated features.  Center point determination may be done through simple geographic estimation or with a weighted mean method that takes into account deviations from spherical.  It is also possible to determine a 3-dimensional center taking into account the total volume of a mound.  In addition, many mounds have flat summits that do not perfectly conform to the outline of the base.  It is difficult to quantify the additional margin of error introduced in light of these considerations, even for a single mound.  Clearly, though, different methods will lead to different center points, possibly with significant distances between them.

<-- return to The Quantitative Approach or continue to Statistical Background I -->