APPENDIX A: ANALYSIS OF POTENTIAL ASSEMBLAGE AND SHERD SIZE BIASES


In addition to the issues discussed in Chapter 4, the assemblages selected for analysis in this study could present a biased picture of utility ware pottery technology and use due to the effects of sample size and the size of the sherds themselves. If the samples are not large enough to represent adequately the true range of variation present at the time the assemblages were formed, then both the richness and the relative abundance of different attributes could be distorted. If significant differences exist among assemblages in the size of sherds and the measurement of certain attributes is affected by sherd size, then variation among assemblages could result from differences in sherd size rather than accurate descriptions of technological variation. In this appendix, I evaluate these potential sources of bias, beginning with sherd size and followed by sample size.


Sherd Size


I measured two attributes that provide data on the size of each sherd, maximum length and sherd weight. The distributions of values for both attributes show considerable right skew in all six assemblages. Most of the weight and length values are low, but a few sherds in each assemblage are unusually heavy and long. However, these data can be made to conform more closely to a normal distribution by transforming the data using a Log10 transform. The transformed data from all of the assemblages combined display a significant linear correlation (rp=.948, p<.000) between sherd weight and maximum length. This correlation means that we can rely on only one of the attributes to track variation in sherd size among the six assemblages.


Figure 48 gives the averaged sherd weight in each assemblage with error bars showing the 95% confidence interval around each mean. Assemblages whose error bars do not overlap have significantly different average sherd size at the .05 level. This figure indicates that significant differences exist among the assemblages in the size of sherds. The three assemblages with artifacts recovered from deeply buried contexts (5MT2193, 5MT4671, and 5MT8827) have significantly larger sherds on average than the three assemblages with artifacts from surface or shallow midden deposits. The correlation between recovery context and sherd size indicates that post depositional breakage is the primary cause of variation in sherd size among the assemblages. In addition to introducing possible biases into the data from the six assemblages, these differences in the degree of fragmentation of the pottery reinforce the decision to use the weight rather than the count of pottery to quantify abundance.



Figure 48. Variation in sherd size among the six utility ware assemblages.


With the exception of measurements of the arc and radius of vessel rims, it is difficult to anticipate exactly which attributes will be adversely affected by variation in sherd size. Attributes that monitor features of the interior and exterior surface of the pottery are the most likely to be affected because, as the sherd size increases, the area of the surfaces increases more rapidly than the area of the edge. Consequently, attributes such as forming marks, firing clouds, and use-related alterations could differ among sherds due to differences in sherd size. However, if the sample size from each assemblage is large enough-the subject of the next section-the data from each assemblage as a whole should not be affected. Thus, assemblage-based comparisons should limit, but not necessarily eliminate, the detrimental effects of variation in sherd size. Another way to identify the impact of sherd size is to compare the pattern of variation among assemblages in a given attribute to the pattern of variation in sherd size. Those attributes that match the sherd size pattern should be considered suspect in terms of reflecting biases created by sherd size differences. However, given the correlation between sherd size and depositional context, one must also assess the possibility that the depositional context, rather than sherd size, is responsible for the similar patterns. As I present and discuss the results of my analyses of the six pottery collections in Chapters 5 and 6, I use this approach to identify and evaluate possible sherd size biases.


Sample Size


For some time, archaeologists have recognized that the size of their samples can affect the accuracy and precision of their descriptions in terms of the range (richness) and relative abundance (evenness) of objects and attributes represented (e.g., Beals et al. 1945; Leonard and Jones 1989). A positive correlation between the richness and sample size of assemblages has been used to identify possible sample size biases in a group of assemblages. Among the six utility ware assemblages, there is no consistent correlation between sample size and assemblage richness (Table 21). Assemblages with the lowest number and weight of sherds possess the greatest richness of surface forming marks, exposed coil manipulations, and exposed coil classes. Although the vessel form data may show a minor sample size effect, it is not the primary cause of variation in the richness of vessel forms among the assemblages as discussed in Chapter 6.


Table 21. The richness of utility ware features in relation to sample size in the six assemblages.
Assemblage N Grams Forming Marks Exposed Coil Manipulation Exposed Coil Classes Vessel Forms
5MT2193 315 2306 5 2 1 3
5MT4671 785 6049 5 4 3 4
5MT3868 1504 7383 6 5 5 4
5MT8371 326 1568 8 6 8 2
5MT1786 918 3344 7 6 3 1
5MT8827 326 3493 7 5 3 1

The presence or absence of a particular feature is less susceptible to sample size biases than the relative abundance of pottery assigned to a category or a specific ratio or interval scale measurement. To assess whether sample size effects appear in the quantitative data, I performed an iterated resampling of each assemblage by randomly selecting sherds at increasing sample sizes. I began with a sample size of 10 randomly selected sherds and increased each subsequent sample by 10 sherds until reaching a sample size of 100, then incremented by 25 sherds until reaching a sample size of 300 and then incremented by 50 sherds until I reached the total sample size of the assemblage. This produced numerous subsamples of each assemblage for which I calculated relative frequencies of categorical data and the mean values of measurements. With these resample data, I can examine how relative frequencies and mean values change with increasing sample size by graphing the values by sample size. Large fluctuations in values between different samples indicates the presence of sample size effects, while stable values indicate measurement redundancy and adequate sample size. As the size of the subsamples come close to the total sample size, the resampled values inevitably begin to converge on the values found in the total sample. This is not necessarily an indication of adequate sample size. Consequently, values must stabilize well before the total sample size to indicate convincingly that the size of a sample is sufficient to avoid the biasing effects of small samples.


To evaluate these sample size effects, I focus on the attributes that play an important role in this study and the three assemblages (5MT2193, 5MT8371, and 5MT8827) with the smallest number of sherds in the total sample. If these three smaller assemblages do not show sample size effects, then it is extremely unlikely that the data from the three larger assemblages are adversely affected by sample size. Fortunately, the three smaller samples also span the temporal range of the assemblages, so the full range of features is represented. If these smaller assemblages do show sample size effects, I then examine the larger assemblages as well.


I begin this assessment with data that have a direct bearing on my reconstructions of how the plain and corrugated vessels were formed. These data include coil application technique, fracture pattern of plain-surfaced pottery, percent coil overlap, exposed coil height, coil junction depth, spacing of coil indentations, and exposed coil classes. I then turn to data on the firing of the pottery including core color patterns and the presence of fire clouds. Finally, I evaluate sample size effects in data related to the use of the pottery including vessel forms, vessel size, and use-related alterations. In each case, I present the resample data in a series of graphs that show the relationship between relative frequencies (percentages) or mean values and sample size.


Pottery Forming Data


Figure 49 shows the resample data on the frequency of pottery with exposed coils relative to plain pottery, and the abundance of filleted and overlapped exposed coils relative to one another in the three smaller assemblages. Although sample sizes below about 100 sherds produce variable quantities, values are sufficiently consistnt above 100 sherds to indicate no sample size effects for these attributes. The frequency of nonrandom fracture patterns relative to random fractures of plain pottery required larger sample sizes (~200 sherds) to reach redundancy, but the total sample sizes appear to be adequate in each of the smaller assemblages (Figure 50).



Figure 49. Change in the percentage of pottery with exposed coils, filleted exposed coils, and overlapped exposed coils with increasing sample size in the assemblages from 5MT2193, 5MT8371, and 5MT8827.



Figure 50. Change in the percentage of nonrandom fracture patterns in plain-surfaced pottery with increasing sample size for the assemblages from 5MT2193, 5MT8371, and 5MT8827.


The mean values of quantitative measurements on exposed coils shown in Figure 51 also indicate no sample size effects for these data, and sample sizes of 150 sherds were sufficient for their precise documentation. Finally, the resample data on the relative frequencies of different exposed coil classes defined in Chapter 5 also show adequate sample sizes in the three smaller assemblages (Figure 52). Samples of 100 to 150 sherds were sufficient to document the two assemblages very few classes represented. However, the assemblage from 5MT8371, which has the greatest variety of classes, required over 250 sherds to reach redundancy. Even then, a few of the very infrequent classes show some fluctuations in relative abundance indicating possible sample size effects on the quantitative data for these rare classes.



Figure 51. Changes in the mean value of metric attributes of exposed coils plotted against increasing sample size for assemblages from 5MT2193, 5MT8371, and 5MT8827.



Figure 52. Changes in the percentages of exposed coil classes with increasing sample size for assemblages from 5MT2193, 5MT8371, and 5MT8827.


Pottery Firing Data


The relative frequencies of core color patterns stabilized after a sample size of 150 - 200 sherds in the three smaller assemblages (Figure 53). Some of the more rare color patterns continue to fluctuate slightly in samples greater than 200 sherds, but the proportions appear to be reliably characterized by the total samples. The presence of fire clouds on the exterior and interior surfaces of pottery shows a relationship to samples size that is similar to that seen in the core color patterns (Figure 54). The proportions of fire clouds become fairly stable in samples greater the 200 sherds, although some slight fluctuations continue. Overall, the effects of sample size on the reliability of the firing data appear to be minimal, except in reducing the reliability of the percentages observed for rare classes.



Figure 53. Changes in the percentages of different core color patterns with increasing sample size for assemblages from 5MT2193, 5MT8371, and 5MT8827.



Figure 54. Changes in the percentages of fire clouds with increasing sample size for assemblages from 5MT2193, 5MT8371, and 5MT8827.


Pottery Use Data


Information on the use of pottery comes from vessel morphology and use-related alterations. Evidence of the shape and size of vessels is most readily obtained from rim pieces. Consequently, only a small subset of sherds in any sample actually provides useful information on vessel morphology. This can make vessel morphology data particularly susceptible to sample size effects. Only three assemblages, 5MT2193, 5MT4671, and 5MT3868, contained a variety of vessel forms. Only one vessel form occurred in the other three assemblages making sample size effects inconsequential given the large number of sherds analyzed. For the three assemblages with a variety of vessel forms, I compared the relative abundance of different vessel forms to sample size using the two ways of quantifying vessel shape: sherd weight and degrees of rim arc. Subsamples with zero percent for all vessel form categories included no sherds for which vessel form data were generated. Figure 55 presents the results for 5MT2193, Figure 56 for 5MT4671, and Figure 57 for 5MT3868.



Figure 55. Changes in the percentages of different vessel forms, using two quantification techniques, with increasing sample size for the assemblage from 5MT2193.



Figure 56. Changes in the percentages of different vessel forms, using two quantification techniques, with increasing sample size for the assemblage from 5MT4671.



Figure 57. Changes in the percentages of different vessel forms, using two quantification techniques, with increasing sample size for the assemblage from 5MT3868.


The relatively small assemblage from 5MT2193 shows considerable fluctuation in the relative frequencies of vessels forms for both quantification methods throughout the range of sample sizes. In this case, the total sample size does not adequately document the abundance of vessel forms in the assemblage, and consequently, the relative frequencies of different vessel forms are unreliable. However, the rank order of different vessel forms is probably accurately documented because, although the values continue to fluctuate, the lines do not cross one another. The other two assemblages, with much larger total sample sizes, did reach redundancy resulting in reliable relative frequency data. The percentages of vessel forms in the assemblage from 5MT4671 stabilized above sample sizes of 600 sherds, and the values from 5MT3868 stabilized after samples of 1000 to 1100 sherds.


I used the estimated radius of the arc of vessel rims to measure the size of vessels and the degrees of arc covered by the rim segment to quantify abundance. I estimated rim radii in 1 cm intervals with actual values falling between 3 and 22 centimeters. Figure 58 shows changes in the relative frequencies of wide-mouth and indeterminate jars in each of the 1-cm radius intervals with increases in sample size for the assemblages from 5MT2193 and 5MT4671. Figures 59 and 60 present the same data for the assemblages from 5MT3868 and 5MT8371, and 5MT1786 and 5MT8827, respectively. In the smaller assemblages, the relative frequencies of different vessel sizes continue to fluctuate over most of the range of sample sizes. Only as resample size come close to the total sample size do the values begin to stabilize. These results indicate that the percentages of pottery in different vessel sizes may be unreliable. However, another possibility is that the 1 cm interval is too fine and falls below the precision of the measurement technique. Consequently, the fluctuations in percentages derive from a combination of sample size effects and measurement error. In two of the larger assemblages, 5MT3868 and 5MT4671, the vessel size values did stabilize, but values from 5MT1786 did not reach redundancy until almost the entire sample was included. Taken together, these results suggest that the data on the relative frequencies of vessel sizes should be used with caution, but the rank orders of different sized vessels is probably fairly reliable.



Figure 58. Changes in the percentages of rim radii with increasing sample size for the assemblages from 5MT2193 and 5MT4671.



Figure 59. Changes in the percentages of rim radii with increasing sample size for the assemblages from 5MT3868 and 5MT8371.



Figure 60. Changes in the percentages of rim radii with increasing sample size for the assemblages from 5MT1786 and 5MT8827.


Finally, the relative frequencies of three forms of use-related alterations-spalling, interior surface pitting-and soot accumulation, are reliably documented with the current sample sizes. Figure 61 shows the changes in percentages of these three attributes with increasing sample size for the three smaller assemblages, 5MT2193, 5MT8371, and 5MT8827. The values in each assemblage stabilized in samples above about 200 sherds.



Figure 61. Changes in the percentages of different use-related alterations with increasing sample size for the assemblages from 5MT2193, 5MT8371, and 5MT8827.


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