Microsoft Word - Green, Elizabeth FINAL THESIS.docLiz Green
May 5, 2007
A senior thesis submitted in partial fulfillment of the requirements for the degree of
Bachelor of Arts in Archaeological Studies University of Wisconsin – La Crosse
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CONCLUSIONS ---------------------------------------------------------------------------------------30 REFERENCES CITED-------------------------------------------------------------------------------36 APPENDIX----------------------------------------------------------------------------------------------38
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ABSTRACT
Sampling is an extremely important aspect of archaeological fieldwork, and it can
significantly influence interpretation; therefore, the effects of these processes must be
understood and controlled. Various experimental sampling methods are tested against the
surface recovery data collected from the Pirque Alto site in Cochabamba, Bolivia. The project
addresses the following questions: do results from the sampling methods reflect the total
surface recovery; what method gives the most accurate results for this site and why; and at
what percentage of quadrat (unit) samples taken per method do the results show validity.
Finally, in what way are the methods biased and how can these biases be addressed? The
project has yielded information about how various methods would or would not have affected
the interpretation of the Pirque Alto site, and the results were thn applied to a broader study
and understanding of sampling methods.
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INTRODUCTION
Sampling, a less visible but just as essential tool in archaeology as the trowel, has been
used since the start of the discipline. “Archaeologists have always sampled… archaeologists
have been choosing, among alternatives, where to look for archaeological sites, which sites to
excavate, and where on selected sites to dig” (Hole 1980:217). However, despite the fact that
archaeologists have always sampled, there seems to be a disproportionately small effort put
forth to truly understand and test the methods so heavily relied upon. Sampling exists and is
used for many reasons, including: financial, labor and time restraints and the logistical
necessity of controlling the sheer volume of physical materials and non-physical data
generated by the process of archaeology.
The processes of sampling have far-reaching consequences and influences. For
instance, a sampling of units on the surface of a site can directly affect an archaeologist’s
perception of the site (its function, chronology, scope, etc), as well as directly affecting the
direction of the research questions posed in the future. It is important to know that these
critical procedures and methodologies are the most conclusive possible so that their influence
on the excavation and interpretation of sites is as constructive as possible. “Given that
sampling is essential, we need to ensure that it is carried out in a way that enables us to make
best use of the data that it provides” (Orton 2000:8).
Due to this, it is important that experiments with comparable results be conducted in
order to gain a better understanding of the act of sampling and its effects. The purpose of this
specific project is to do just that — to act as a testing mechanism for common sampling
procedures. The data used in this endeavor comes from the work done at the site of Pirque
Alto, located in the Department of Cochabamba, Bolivia. Details of this site will be discussed
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in the background section to follow; however, it is important to note that the work conducted
at this site included a surface collection of ceramics and lithics of the entire site. Ceramics
bigger than a nickel and all of those featuring paint were collected.
The collected ceramics data act as a control group in testing various sampling methods
with the goal of answering the following questions:
1. Do results from the sampling methods equal or come close to the spatial (ex.
identified ceramic clusters) and numeric results indicated from surface collection?
2. What method gives the most spatially and numerically accurate results for this site
and why?
3. At what percentage of unit samples taken per method do the results show the
greatest spatial and numerical accuracy, (10%, 30%, or 50%)?
4. In what way are the methods of sampling biased, and how can these biases be
addressed or corrected?
The ultimate goal of this project is to determine the validity and precision of common
archaeological sampling methods and identify the most accurate methods. Because the data
being used as the control group comes from a real site, looking at how the sampling methods
would have affected its interpretation help to present the gravity of influence from sampling.
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BACKGROUND THE SITE OF PIRQUE ALTO
During the 2005 field season, archaeological fieldwork was conducted by several
students in the UW-L Archaeological Studies program under the supervision of Dr. Timothy
McAndrews at Pirque Alto, in the Department of Cochabamba, Bolivia. One goal of this
project was to investigate the influence of the Tiwanaku culture in the area through the
cultural remains present at the site, such as ceramics, stone artifacts, and features. Tiwanaku
was a powerful polity operating out of the southern part of the Lake Titicaca Basin that
influenced a broad region throughout the central Andes from A.D. 500 to A.D. 1150 (Janusek
2004:xvii). Now viewed as “the first true state in the south-central Andes,” the Tiwanaku
culture is typified by stratified societal levels, monumental architecture, and sophisticated
material culture (Young-Sanchez 2004:17-18). Their material culture is unique, especially the
ceramics which are “extremely distinctive and rather easy to recognize both in terms of slip
and paint, and in diameter of base and rim,” which allows for easier identification
(Burkholder 1997: 130). The nature of the spread of the Tiwanaku is a topic currently under
fierce debate, and as such this site could help shed light on the presence of the Tiwanaku in
the Cochabamba Valley area.
Through the surface collection of 406 5 x 5 meter units, a total of over 13,200
diagnostic ceramics (rims, bases, handles, painted pieces), and over 52,000 non-diagnostic
(those pieces bigger than a nickel not belonging to the diagnostic category) were collected and
subsequently analyzed. Early conclusions regarding this site indicated that it was a multi-
component site occupied from the Formative Period though Inca times. This site is located on
a bluff (see Figure 1) overlooking the Rio Tapacari and exists in a natural travel corridor
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leading to the Altiplano and Titicaca Basin. Since this site, in terms of location and artifact
assemblage, can offer important addition to the debate concerning Tiwanaku presence in the
Cochabamba Valley, it serves as an excellent case of how sampling would and could affect
site interpretation and how in turn that can affect the archaeology of an entire area
(McAndrews 2006).
HISTORY OF SAMPLING
The history of sampling in archaeology is an interesting one, and the current debates
within the subject showcase the breadth of thought concerning its importance and its
influence, both on the process of archaeology and on archaeologists themselves. One of the
few comprehensive histories of sampling in archaeology is contained in Sampling in
Archaeology, by Clive Orton (2000). In this book, Orton discusses the changes in the actual
sampling themes throughout time but also talks about the changes in archaeologists’ attitudes
towards sampling.
Figure 1 Site of Pirque Alto as viewed from opposite valley wall
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At the turn of the twentieth century, there was more attention directed towards
sampling; however, without the later developments that statistics would bring, “it would not
be reasonable to expect more than an informal approach” (Orton 2000:112). Preliminary
attempts at sampling were carried out in a rather intuitive way. For instance, if there appeared
to be a large amount of sherds, you took what you believed to be “representative.” It was not
until the developments of the 1940s that sampling procedures became more concrete and
statistically representative. The developments in statistical theory came about as a result of the
need for quality control in response to industrial growth but eventually became incorporated
into the sampling of shell middens. This helped to cut down on the tedium of going through
mountains of low grade data. At first glance, the beginning of sampling in archaeology would
seem to suggest a rather haphazard approach designed to make archaeological evaluation
easier and less tedious.
It was during the 1950s and 1960s that more formal sampling methods, which Orton
describes as “samples selected from well-defined populations according to rigorous statistical
procedures,” became more commonplace (Orton 2000:1-2). Vescelius was the first to discuss
the use of probabilistic sampling, and he directed his attention towards finding a way to
estimate artifact proportions compared to all others within a site (Vescelius 1960:457-470).
However, “no other single article has altered more radically the recent course of archaeology
than Lewis Binford’s 1964 consideration of research design” (Hole 1980:218).
Lewis Binford contributed greatly to the field of archaeology, especially in relation to
field methodology and research design, which included sampling. Although Binford’s regard
to sampling was directed regionally rather than at a site level, he instituted tremendous
changes in the way archaeology was carried out. Orton describes there being three major
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changes advocated by Binford: “the promotion of the region to the position of primary unit of
archaeological research, the explicit design of archaeological research programs, and the
explicit use of sampling theory as the way of linking the two” (Orton 2000:4).
Though Binford’s contributions to the field of archaeology cannot be underestimated,
such an enforcement and indoctrination of sampling methods caused a severe backlash that
emerged in the 1970s. Sampling appeared as an evil necessity that one would never escape
and as a compromise with the constraints of real life. This feeling increased with the
development of sieving methods at the feature level, which created even more data which
required sampling from (Orton 2000:4). Part of this backlash was to criticize sampling itself
rather than how it was being carried out, as though sampling was something impressed upon
archaeology by fields that had nothing to do with archaeology.
Though the 1970s are characterized by a backlash against sampling, they were also a
time of reflection on the progress of sampling due to the publication of the San Francisco
Symposium (which was the first formal gathering to discuss sampling) and Kent Flannery’s
Early Mesoamerican Village (Flannery 1970). James Mueller, one of the big names in
sampling theory, describes this reactionary period as extremely varied. “The responses and
reactions have been varied – categorical rejection, blind acceptance, and skeptical
positivism,” the last which seems to dominate in the 1970s (Mueller 1975: xi).
This evaluation of the progress of sampling had the curious result of bringing
viewpoints regarding it back full circle to a more intuitive process. “By the 1980s in the USA
and the 1990s in the UK, sampling had become firmly entrenched in the methodology of the
‘contract’ wing of archaeology” and had become something almost instinctive among
archaeologists (Orton 2000:6). Though sampling has again become something rather intrinsic
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to archaeology, “[it] is still on the agenda even if it is not discussed as openly or explicitly as
it was, say, in the 1970s and 1980s” (Orton 2000: 207).
DEBATES WITHIN SAMPLING
Due to the importance of sampling, there exists a great deal of controversy throughout
the literature. The debates range from the general importance of sampling (Rootenberg 1964)
to the proper methods while conducting sampling (Schiffer, Sullivan and Klinger 1978) to the
correct math and proportions (Plog and Hegmon 1993, Nance 1981). According to Bonnie
Laird Hole, “Despite the widespread availability of understandable presentations of the theory
of sampling and the powerful potential of its appropriate application in archaeological
research, its contributions to archaeological knowledge have been disappointing” (Hole
1980:217).
Articles run the gamut from math-entrenched to highly theoretical and behavioral. It is
interesting to note that within most of the literature there exists a great deal of disagreement
expressed through journal publications. At times some archaeologists would rather attack one
another through publication than to correspond directly. Though opinions are varied, it is
important to mind the theoretical milieu from which the disagreements arise.
A great debate going on in sampling right now is the degree to which post-
depositional factors contribute to the bias of a sample. Many in the Processual archaeology
group bypassed looking at this question by examining things which were the least affected.
The Cultural History school of thought also tended to ignore the issue. (Orton 2000:43). This
debate continues today, especially in regards to issues like the value of the number of
identified specimens over the minimum number of individuals.
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A debate more relevant to this project is the degree to which surface remains reflect
the subsurface, and “is a key issue for the practice of archaeological survey, at both the
regional and the site level. Opinions, both as expressed and as implicit as fieldwork practices,
seem to vary widely” (Orton 2000:57). For the site of Pirque Alto, the clusters of certain
identified phases are so distinct and identifiable that they are assumed to represent a reliable
indication of the subsurface.
Obviously, these are hardly the only ongoing debates within sampling, and more
research is being conducted in order to present specific debates concerning individual
sampling methods; i.e. random vs. judgmental, etc. Some of these disagreements will be
explored later in the paper as they relate to the results of the project.
DESCRIPTIONS OF THE SAMPLING METHODS USED IN THIS PROJECT
Below are basic descriptions of the types of sampling methods relied upon in this
project. Information concerning the experimental procedures will be discussed in the
methodology section of this paper. Lastly, more specific pros and cons for each method will
be discussed in the results section as they correlate directly. Archaeological sampling methods
can be roughly divided into two categories: probabilistic and non-probabilistic. Archaeology
employs probabilistic sampling methods as an “attempt to improve the probability that
generalizations from the sample will be correct” (Renfrew and Bahn 2000: 76). Charles
Redman describes probabilistic sampling methods as “good for estimated total population
values for common artifacts or features… probability sampling is poor for locating rare
feature or artifacts, dealing with clustered distributions, or illuminating contiguous spatial
patterns” (Redman 1987: 251). Non-probabilistic methods, described subsequently, are
generally looked upon less favorably.
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The most basic probabilistic sampling method is a simple random sample, in which
numbers are assigned to the quadrats and those to be sampled are chosen through a random
number chart till a predetermined number or percentage of units is sampled. “It implies that
an equal probability of selection is assigned to each unit of the frame at the time of sample
selection” (Binford 1964:141).
Systematic random sampling involves the sectioning out of a site grid into groups of a
predetermined number of quadrats, and then randomly selecting quadrats within each section
(Drennan 1996: 246). The general advantage of this method is that it ensures there will be
broader coverage across the entire site; “Systematic sampling ensures an equal dispersion of
sample units” (Binford 1964:153).
Next there is stratified random sampling, where the site is divided into its natural
zones (or strata) and like before, random numbers are chosen. However, in this method the
squares are proportional to the natural zones; 85% forest equals 85% of the samples are taken
from that area (Renfrew 2000: 77).
Judgmental sampling, which is not representative of the whole, is a non-probabilistic
form of sampling and is associated with similar methods including haphazard sampling, grab
sampling, and purposive sampling. “Non-probabilistic sampling is regarded as intuitive,
inductive, and unstated” (Hole 1980: 219). All of these terms represent a method referring to
“explicit or implicit application of a variety of nonrandom selection criteria” (Drennan
1996:88). In judgmental sampling, samples are “selected by looking over the range of
elements in a population and specifically deciding to include certain elements in the sample
and exclude others” (Drennan 1996:88). Obviously, this method has a large degree of bias.
It was important to include due to the current instinctive feeling of archaeological sampling.
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METHODOLOGY
The first step of this process was to become familiar with the literature concerning
sampling. This was an important step because it helped to frame the concerns and debates
within sampling and helped to provide a general understanding of the subject. Another
familiarization step was to become comfortable with the computer programs necessary for
this project, including Microsoft Access and Excel, and Surfer by Golden Software, a map
generating program. After sufficient skills with these programs had been developed the
sampling experiments could be carried out.
Sampling experiments were carried out at three percent intervals (10%, 30%, and
50%) with five trials each. Originally, these experiments were to be carried out for the total
ceramics data and for the identified Tiwanaku phase ceramics. However, a different
approach has been considered and decided on instead. Each of the trials will take into
account the total ceramics data, yet the data will show the percent levels for three identified
ceramic phases: Formative, Early Intermediate, and Tiwanaku. These percents will be
compared to the total percents for each of the ceramic phases. For example, if a 10% random
sample shows 13% of sherds belonging to the Tiwanaku phase ceramics, this will be
compared to the percent of Tiwanaku phase ceramics for the entire site.
The sampling experiments focus on four types of sampling commonly relied upon by
archaeologists: random sampling, systematic sampling, stratified sampling, and judgmental
sampling. For the random sampling experiments, Microsoft Access was used to randomly
sample units according to the percent level specified. For the systematic sample, the site is
divided into as many 25 x 25 meter groups as possible.
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The units within these groups are then selected randomly according to percent. See
Figure 2 for systematic group distributions.
For the stratified random sample, the site is broken up into three areas related to their
relative elevation: highest part of the sites, middle and lowest. Grids are then selected
randomly according to percent level. See Figure 3 for the stratified group distributions.
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Figure 2 Stratified Group Distributions
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Since the judgmental sample is a non-probabilistic method, it was carried out
differently than the previous methods. Three students in the Senior Thesis class (ARC 499)
who did not attend the 2005 field school at Pirque Alto were given a site map with general
information such as the physical layout of the site, areas of higher artifact concentration (like
one would see on a pedestrian survey). They were then asked to indicate which areas based on
the information they had been given would be their choice for sampling. Size of the sampled
areas was equal to the percent levels used for the other three sampling methods. For example,
the first student was given enough units to equal a 10% sample of the site to lay out as they
see fit; for the second student, 30% and so on. Though this method differs significantly and
will not be able to be compared in exactly the same way, it is an important avenue to explore.
After the experiments were carried out, the information was plotted onto a site map
using Surfer by Golden Software. This allows for a clear illustration of the differences
between the sampling methods and their visual results. A series of descriptive statistics
(mean and standard deviation) were generated and will be used in comparison to the visual
results. T-tests were also carried out to determine if there was a statistically significant
difference between the samples and the full dataset in terms of the relative proportions of
different periods of ceramics. It was determined that there was not a statistically significant
difference; meaning all samples may be considered numerically representative of the whole.
Armed with both the visual representations of the sampling experiments created using
Surfer and the statistics generated from the samples, a comprehensive comparison of the
methods will then occur. The relative success or failure of the various sampling methods will
be viewed in regards to their implications for interpretations of the site and then applied on a
larger scale to view the effect of sampling on the field of archaeology.
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RESULTS
In addition to the main goal of determining the validity and precision of common
archaeological sampling methods, this thesis also sought to address four specific questions:
1. Do results from the sampling methods equal or come close to the spatial (ex.
identified ceramic clusters) and numeric results indicated from surface collection?
2. What method gives the most spatially and numerically accurate results for this site
and why?
3. At what percentage of unit samples taken per method do the results show the
greatest spatial and numerical accuracy, (10%, 30%, or 50%)?
4. In what way are the methods of sampling biased, and how can these biases be
addressed or corrected?
These questions will be addressed throughout this portion of the paper, which is itself
broken up into three different sections. In the first section, results in terms of the individual
methods (random, systematic, etc) will be discussed. This will be followed by a section
describing the results on each percent interval, including the spatial representations of each
sample method and the statistics and ceramic phase percentages. This is done to illustrate the
benefits and problems associated with each method and provide more detailed information at
the sample size level. General comments about the various methods and their results will
comprise the last section. On the following page, Figure 4 shows the overall distributions of
all ceramics over the entire site for reference. Maps for the Formative, Early Intermediate,
and Tiwanaku Ceramics can be found at the end of the document.
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54 92 105135151168 87 180 82 0 162 190 267 216216159157 61 26 51 20
20 89 80 134122130 202 102 137 171 233 315 239 239101 47 89 139 70 69 47 83
26 31 53 44 74 38 82 137 58 127 37 21 16 11 97 342309179 119 100 51 53
23 0 25 57 44 94 44 67 11 49 139 118 106 67 36 272285244 172 106 117 61
30 30 12 54 83 110 18 173 145 324 155 94 87 224194162 80 150 59 75 66 180 75
21 53 92 121108339129 289 230 198 695 135 118 20 69 212177266184 81 48 340 284 0
67 19 74 101 78 161139 99 212 221 299 78 75 28 87 157239120181 125 0 263 185
55 33 123132179264164 141 197 333 283 145 41 69 48 109 59 156620 146 328 123 468
28 30 86 264277143148 135 145 143 8 95 44 212 97 59 87 43 235 219 555 400
14 32 125140203242165 95 45 64 145 189 200 259 178124 62 89 259 172 198
23 40 41 135140112128 112 65 161 150 148 122 134 113 68 109122199 296 323
27 20 114234116 74 112 241 200 236 117 0 42 90 204107 65 88 178 249
22 65 99 161 93 47 121 95 211 170 131 249 46 79 129150157255150 147
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RANDOM SAMPLING
Without a doubt, random sampling produced the most varied results, most notably
within the spatial distributions. At odds with this is that the statistical and phase percentage
results gave a representative sample. The circled areas on the maps indicate areas of high
frequency identified ceramic phase clusters that would have been missed by the sample. For
the 10% random sample (see Figure 5), the circled upper right-hand and lower section contain
the two largest clusters of Tiwanaku ceramics on the site. As one of the goals of the Pirque
Alto project was to gather information about the Tiwanaku influence at the site, missing these
clusters would have drastically affected our understanding of the site.
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The above map was generated from the 10% sample level, and it can be seen that is
performs poorly in locating the major clusters of identified ceramics. For this sample type,
this trend continues through the 30% samples. Figure 6 shows that even at three times the
previous sample size a large chunk of the site was not sampled.
For the random sample, the most reliable sample size level was 50%, (see Figure 7).
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Table 1 shows the numeric results for all three maps shown above. Despite the large
spatial differences between all three intervals, the random samples produced the most reliable
and representative numeric results compared to both the systematic and the stratified samples.
However, when viewed in conjunction with their spatial distributions, random sampling
comes up quite short. For a statistician random sampling would be the most ideal, but for the
archaeologist who deals spatially and numerically, random sampling has little to offer. “In an
archaeological context, simple random sampling will not work” (Rootenberg 1964:182).
Table 1 Random Sample Numeric Results
Whole Site RS 10% (Trial 2) RS 30% (Trial 4) RS 50% (Trial 2) Number of Units Sampled 406 41 121 203 Mean ceramics per unit 128.81 119.22 138.66 126.98 Formative Phase % 4.46% 3.85% 5.26% 3.99% Early Intermediate Phase % 0.90% 0.94% 0.84% 0.96% Tiwanaku Phase % 18.99% 19.33% 18.47% 18.70% Diagnostic Ceramics % 25.24% 24.96% 25.30% 24.54% Non-Diagnostic Ceramics % 74.76% 75.04% 74.70% 75.46%
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SYSTEMATIC RANDOM SAMPLING
The systematic random sampling method provided the most consistent results of all
three probabilistic sampling methods spatially and numerically, and therefore it was difficult
to choose certain trials. Of all the percent levels, 50% provides the most solid results, but
logistically speaking a 30% sample is more attainable. However, even at the 10% level the
systematic random sample still performs beautifully. At the beginning stage of an
archaeological investigation, surface sampling is crucial to provide instruction as to which
areas of the site may be significant. Due to this importance, systematic random sampling
dominates its competitors as a way to provide archaeologists with a far-reaching distribution
of samples, providing an overall better knowledge of the site. “This procedure has a number
of advantages. Classes may be established with regard to different variables that one whish to
control, which makes possible the reliable evaluation of variability in other phenomena with
respect to the class-defined variables” (Binford 1964: 142).
At the 10% level, the phase percentage information is rather representative (see Figure
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Figure 8 Systematic Random Sample 10% (Trial 1)
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8). The 10% sample also provides a rather good physical distribution of units throughout the
site (see map on following page with circled Tiwanaku ceramic clusters). Compared to the
10% random sample results, systematic random sampling provides a tremendously improved
method. For the site of Pirque Alto, a 10% systematic sample returned results representative
to the whole and would have been a useful method to employ.
The 30% systematic random sample does an excellent job of displaying representative
numerical results and gives excellent physical coverage. The circled areas on Figure 9
represent key Tiwanaku ceramic clusters.
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Figure 9 Systematic Random Sample 30% (Trial 1)
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At the 50% level, the systematic random sample provides extremely close numeric results for
all five trials. When spatially represented, this sample gives a very clear picture of areas of
ceramic occupation on the site. In Figure 10, the Tiwanaku clusters have been circled.
Table 2 shows the numeric results for all the systematic random trials shown above.
Table 2 Systematic Random Sample Numeric Results
Whole Site SRS 10% (Trial 1) SRS 30% (Trial 1) SRS 50% (Trial 5) Number of Units Sampled 406 49 130 211 Mean ceramics per unit 128.81 119.92 128.56 124.25 Formative % 4.46% 4.61% 4.28% 3.96% Early Intermediate % 0.90% 0.82% 0.94% 0.76% Tiwanaku % 18.99% 19.84% 18.11% 19.00% Diagnostic Ceramics % 25.24% 25.85% 24.24% 24.67% Non-Diagnostic Ceramics % 74.76% 75.80% 75.76% 75.33%
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Systematic Random Sample 50% (5)
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24
STRATIFIED RANDOM SAMPLING
If random samples were the least spatially reliable in terms of finding identified
clusters of ceramics, and systematic random samples were the best overall, stratified random
sampling was firmly in the middle. Visually, the stratified samples performed better than the
random samples (except at the 50% level, where they are roughly equal), but significantly less
well than the systematic samples. You can see that, like the random sample at 10%, the
stratified random sample tends to miss key clusters or cover them only very slightly. It is not
until the 30% and especially 50% stratified sample level does this tend to correct itself
slightly. Despite a fairly good coverage, there are still clusters of sampled units. However,
Figure 11 for the most part offers a good spatial distribution.
55 33 123
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0 10 20 m
14 to 47 47 to 70 70 to 112 112 to 150 150 to 468.1
Stratified Random Sample 10% (5)
Figure 11 Stratified Random Sample 10% (Trial
25
Figure 12 displays the visual distribution of the 30% sample level. The 30% sample level
performed better in all trials than did the 10%.
At the 50% level, (see Figure 13) the stratified sample, much like the systematic and the
159
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Stratified Random Sample 30% (4)
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Stratified Random Sample 50% (5)
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26
random become somewhat the same. While the high percentage guarantees a broad ranging
recovery, it also starts to become redundant.
Table 3 displays the numeric results for all of the samples shown above.
Table 3 Stratified Random Sample Numeric Results
Whole Site Strat. 10% (Trial 5) Strat. 30% (Trial 4) Strat. 50% (Trail 5) Number of Units Sampled 406 41 122 203 Mean ceramics per unit 128.81 109.24 121.28 121.39 Formative Phase % 4.46% 6.30% 4.85% 5.18% Early Intermediate Phase % 0.90% 1.05% 0.95% 0.98% Tiwanaku Phase % 18.99% 18.15% 21.85% 22.82% Diagnostic Ceramics % 25.24% 26.35% 28.47% 29.91% Non-Diagnostic Ceramics % 74.76% 73.65% 85.00% 70.09%
27
JUDGMENTAL SAMPLING
Numeric figures from all three judgmental samples (10, 30, and 50%) all provided
representative results. (See table 4).
Table 4 Judgmental Sample Numeric Results
Whole Site Judgmental 10% Judgmental 30% Judgmental 50% Number of Units Sampled 406 41 122 203 Mean ceramics per unit 128.81 130.63 148.63 131.04 Formative Phase % 4.46% 4.66% 4.66% 4.94% Early Intermediate Phase % 0.90% 0.93% 0.93% 0.86% Tiwanaku Phase % 18.99% 19.02% 19.02% 18.89% Diagnostic Ceramics % 25.24% 25.54% 25.54% 25.59% Non-Diagnostic Ceramics % 74.76% 74.46% 74.46% 74.41%
The judgmental samples had extremely varied spatial results. At the 10% level, the
student chose a systematic sample approach and managed to cover the site rather uniformly.
(See Figure 14).
8826205
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35
290 300 310 320 330 340 350 360 370 380 390 400 410
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Judgmental Sample 10%
28
At the 30% level, the student chose a transect approach and cut the site into sections
using three long corridors of sampled units. This student arranged the transects to intersect
high, middle and low artifact areas, as well as to cover the visible features. (See Figure 15).
At the 50% level, the student again took a systematic approach; however, she avoided a
property divider lined with cactus and thorny shrubbery. (See Figure 16).
67 159 23
26782 162105 2160151168 87
2182 342309179 119 5112753 44 5838
1069444 36 272285 611726757 24423 49
194162 150 7518 173 668330
0212 4820 69 177266 81 284
18515728 120181 263078
165242 172896217845 200 198140
134 323199148 1091501611281401354140 112
24947 15025515715079161 14799 121 211 170
19 205 40882178436 24993274185104147
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Figure 16 Judgmental Sample 50%
128
59
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61
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Judgmental Sample 30%
29
Visually, the 10% and 50% samples are quite similar. The 30% sample, featured in
Figure 5 again with Tiwanaku clusters circled, presents a completely new method of sampling
— transecting. Judgmental sampling has an extremely useful function in archaeology as it
allows the field to become more flexible. Depending on the results of a systematic sample for
example, judgmental sampling allows the archaeologist to redirect the project and investigate
potential areas otherwise excluded through sampling.
PERCENT INTERVAL
The most effective percent interval: 50%
The most realistic percent interval: 30%
Despite claims in the literature to the contrary, it is this author’s belief that a 10%
sample with any method is normally not conclusive or representative enough. What is being
studied is comprised of many parts, some more measurable than others, and a 10% sample
does not allow much leeway for the discovery of lesser reflected materials. However, should a
10% sample be the only available course of action, a systematic random sample should be the
used, as at the 10% level its results were the most acceptable.
GENERAL COMMENTS
Unfortunately, due to the nature and scale of this project, the role statistics and
statistical estimations play in conjunction with sampling was not able to be explored. If
someone were to continue the work begun by this project, the next logical step would be to
conduct various statistical calculations (such as Chi square testing) to fully determine the
statistical extent of the sample procedures.
30
CONCLUSIONS
At the start of this project, I found myself trying to straddle a line between the
hardcore samplers with very complex math equations and those like Hole who saw sampling
and statistics in archaeology as something that had focused too much energy on “probing the
method instead of the ground” (Hole 1980: 219). After conducting my experiments and taking
into account numeric and spatial representations and keeping in mind the various opinions
within the literature, I still found myself straddling the line.
Through the process of conducting the experiments for this project and reading
through the literature discussing the problems, concerns and benefits of sampling, it was
possible to see how these factors played out within my experiments. At the end of this
process, I had several more questions than answers and had grown immensely more cynical
about math and sampling in regards to archaeology. I wrestled (on a much smaller scale) with
all the issues mentioned in most of the journals and books I had read.
First, how does one go about choosing the appropriate sample size? “The optimum
sample can be summarized as being small enough to yield statistically representative,
significant, and accurate results at the minimum cost of labor” (Rootenberg 1964:186). For
me, the choice was a relatively arbitrary one. I wanted to choose values that were both
realistically applied archaeologically and that would give a varied enough result to draw
conclusions about the various methods employed. However, when I examined the literature
on determining appropriate sample size, there were many conflicting methods. Many were
somewhat arbitrary, such as my own, i.e. believing or deciding that a 10% sample would be
representative or a 20% sample, etc.
31
On the other end of the spectrum, I found some archaeologists recommended very
complex mathematical or statistical equations in order to figure out the appropriate size.
Looking at the math required, it seems likely that few archaeologists, without the help of a
professional mathematician or statistician, will be able to do (and understand the implications
of) the math required to determine sample size through these means. Approaching the topic as
a realist, we need to work within our field to create methods that are logistically and
practically applicable for the majority of individuals within our discipline.
The second issue I dealt with was if there is really any way to know that your sample
is representative since archaeology deals with a seemingly indefinite population. Due to the
nature of my thesis, I knew what my population was; I knew how many sherds total, I knew
what phases, and I knew where. In the real world, no archaeologist has this advantage. The
question that arose in my mind was this: is it worse to base your idea of what is representative
on a complex mathematical equation, or draw upon similar archaeological sites combined
with your knowledge of the area? Or is it better instead to use a combination, to rely upon
your own judgment and knowledge of the area and then relate that to sampling and statistics
as a way to aid you through the rest of the process, while still not being afraid to change your
approach based on judgment?
The last of my four specific questions mentioned in the introduction dealt with the bias
in sampling and if this was something able to be addressed or corrected. At the completion of
this project, it occurred to me that the most damaging bias within sampling currently is the
belief that with the right sampling method and the right sample size, a region or a site will be
able to tell all. It is reflected in the literature that many put faith into these sampling methods
that they no longer put into themselves. While Orton does allude to the field having returned
32
to a more instinctive style of sampling, the effect that the explicit samplers has had on the
field is irreversible (Orton 2000:6).
Is the way we conduct sampling intrinsically biased? To this I have to answer a
resounding yes. Deciding the size of sample, the size of a unit, the boundaries of a site – all
are typically made based upon the archaeologist’s judgment. Even if they are based with the
most stringent of mathematics and statistics, you cannot simply cut and paste methods from
one discipline into another. Statistics and sampling from any other field cannot be expected to
operate in the same capacity within archaeology. “None of the sampling and estimation
schemes currently in common use in archaeology take into account fully the spatial
component in the data” (Hole 1980: 230). This is obviously something that needs to change.
Bias is not necessarily a horrible thing, as long as we acknowledge it as a field, and adapt our
methodology to take this into consideration.
For example, many site reports will simply state what percent sample was taken of the
site, with very little regard to the process leading to that decision. If that discussion was
included in the final site report, so that anyone who read it could understand why a 10%, or a
30% sample was chosen, or why a stratified approach was taken, then the harmful bias of
sampling would be lessened. If you can legitimately explain your sampling strategy and how
you came to that decision, the bias you have worked within becomes objective; consistency
and specificity are crucial.
Based on the results of the sampling experiments conducted during this project and a
careful review of the literature on the subject, the following conclusions have been reached:
the most spatially and numerically representative sampling method is a systematic sample of
at least 10% (though this author prefers a 30% sample). Numerically this method was not
33
always as accurate as the random samples, however; it consistently at all percent levels
provided a very even coverage of the site. As the results of surface recovery can be somewhat
dubious (though it was decided at Pirque Alto the surface was a good indication of the
subsurface) a systematic random sample approach on the subsurface would also prove
extremely beneficial. At the beginning of an archaeological investigation, it would give you
the best vantage point through which to view the site as a whole.
It is from this point that a judgmental sample is the next logical step. After the
systematic random sample has provided wide-spread even coverage, the judgmental sample
allows for the archaeologist to reevaluate the site, his or her research questions, and allows
them the flexibility to decide where and how to proceed. This method should not be looked
down upon or regarded as less effective or legitimate. The idea that all archaeology must be
backed up by sophisticated mathematics and estimation statistics to be considered legitimate
is rather insulting. “Without accurate assessment of the personal element, archaeology will be
reduced to a set of mechanically applied approaches practiced by a series of competent but
disinterested researchers, a grim prospect for the discipline” (Redman 1987: 262).
Sampling (and to some extent, statistics) within archaeology should be used as follows:
1. A method through which to locate archaeological sites on a regional scale.
2. A method through which to perform archaeology realistically, taking into account the
current curation crisis, as well as monetary, labor and time constraints.
3. An aid in the analysis of collected data, not as a means to do far too much with way too
little. “Given the usual money and time restrictions, the minimum is far too often taken
to be the maximum” (O’Neil 1993: 523).
34
4. A way to operate both spatially and numerically in a way to produce the most contextual
results.
Though it is displeasing to end this thesis in a contradictory fashion, I find that it is
where my experimental results and own personal conclusions lead. Sampling within
archaeology is both at once a useful and dangerous tool. It allows us to work realistically
within a world of constraints; however, it also has the propensity for great abuse. While my
experiments concluded that a certain method of sampling at a certain percent was the most
accurate and beneficial approach for the site of Pirque Alto, this does not mean that this is the
approach that will work for every site; it would be naïve to think so.
Instead, the new direction of sampling in archaeology should be one of judgmental
enforced flexibility. Sampling should continue to be relied upon, and the basic guidelines and
the statistical analysis associated with it should be followed. However, it is extremely
important that archaeologists expand on their methods, become far more specific about their
decision making process, and not be afraid to rely on their own judgment. Archaeology is a
complex, multifaceted field which requires more than an explicit methodology.
35
ACKNOWLEDGEMENTS
I would first like to thank Drs. Tim McAndrews and Connie Arzigian for their
guidance throughout this project. Without them I would not have had a clue where to begin or
how to proceed. I would also like to thank Dr. Jim Theler for redirecting my thoughts and
questions. Thanks to the other members of the 2005 Bolivia Field School for helping to
collect the raw data. Thanks to the Undergraduate Research Committee for funding this
project. I would like to thank my mother and father Denise and Al Green for listening to me
describe this project and giving me their support even though they are interested not in the
slightest. I would like to acknowledge my friends, in particular Beth Plunger, Chris Salinas
and Beth Boe for keeping me company throughout this process and offering their advice over
much needed drinks. Lastly, I’d like to thank Phil Lee for his amazing proof reading abilities.
36
Binford, Lewis 1964 A Consideration of Archaeological Research Design. American Antiquity 29:425-441. Burkholder, JoEllen. 1997 Tiwanaku and the Anatomy of Time: A New Ceramic Chronology
From the Iwawi Site, Department of La Paz, Bolivia. New York: Binghamton University.
Drennan, Robert D. 1996 Statistics for Archaeologists: A Common Sense Approach. New York: Plenum Press. Flannery, Kent. 1970 The Early Mesoamerican Village. New York: Academic Press. Hole, Bonnie Laird 1980 Sampling in Archaeology: A Critique. Annual Review of Anthropology 9:217-234. Janusek, John Wayne 2004. Identity and Power in the Ancient Andes: Tiwanaku Cities
Through Time. New York: Routledge. McAndrews, Timothy 2006 Preliminary Results from the Multicomponent Site of Pirque Alto in Cochabamba,
Bolivia. Poster presented at the 71st annual meetings of the Society for American Archaeology in San Juan, Puerto Rico. Tim McAndrews, Claudia Rivera, Carla Jaimes.
Mueller, James. 1975 Sampling in Archaeology. Tucson: The University of Arizona Press. Nance, Jack 1981 Statistical Fact and Archaeological Faith: Two Models in Small-Sites Sampling.
Journal of Field Archaeology 8:151-165. O’Neil, Dennis 1993 Excavation Sample Size: A Cautionary Tale. American Antiquity 58:523-529. Orton, Clive. 2000 Sampling in Archaeology. Cambridge: Cambridge University Press. Plog, Steven and Michelle Hegmon 1993 The Sample Size-Richness Relation: The Relevance of Research Questions, Sampling
Strategies, and Behavioral Variation. American Antiquity 58:489-496.
37
Plog, Steven, Fred Plog, and Walter Wait 1978 Decision Making in Modern Surveys. In Advances in Archeological Method and
Theory. Volume 1, edited by Michael Schiffer. pp. 383-421. Academic Press, Inc., New York.
Redman, Charles 1987 Surface Collection, Sampling and Research Design: A Retrospective. American
Antiquity 52:249-265. Renfrew, Colin, and Paul Bahn. 2000 Archaeology: Theories, Methods and Practice. Third ed. New York: Thames &
Hudson. Rootenberg, S. 1964 Archaeological Field Sampling. American Antiquity 30:181-188. Schiffer, Michael, Alan P. Sullivan, Timothy Klinger 1978 The Design of Archaeological Surveys. World Archaeology 10:1-28. Thompson, S.K. and G.A.F. Seber. 1996 Adaptive Sampling. (New York: John Wiley and Sons). Vescelius, G.S. 1960 Archaeological Sampling: A Problem of Statistical Inference. In Essays in the Science
of Culture: In Honor of Leslie White, edited by Gertrude E. Dole and Robert Carnerio. pp. 457-470. Crowell, New York.
Young – Sanchez, Maraget 2004 Tiwanaku: Ancestors of the Inca. University of Nebraska Press, Lincoln.
38
APPENDIX
29
54 40 109 59 128 66 118 39 15
207153 72 96 208 39 95 73 85 5
148 127 80 181183189145 35 113 26 14 6
88 53 129 65 243 197 145 162 194348317 71 101 90 119 136 12 0 18
54 92 105 135 151 168 87 180 82 0 162190267216216159 157 61 26 51 20
20 89 80 134 122 130 202 102 137 171 233315239239101 47 89 139 70 69 47 83
26 31 53 44 74 38 82 137 58 127 37 21 16 11 97 342 309 179 119 100 51 53
23 0 25 57 44 94 44 67 11 49 139118106 67 36 272 285 244 172 106 117 61
30 30 12 54 83 110 18 173 145 324 155 94 87 224194162 80 150 59 75 66 180 75
21 53 92 121 108 339 129 289 230 198 695 135118 20 69 212177 266 184 81 48 340 284 0
67 19 74 101 78 161 139 99 212 221 299 78 75 28 87 157239 120 181 125 0 263 185
55 33 123 132 179 264 164 141 197 333 283 145 41 69 48 109 59 156 620 146 328 123 468
28 30 86 264 277 143 148 135 145 143 8 95 44 212 97 59 87 43 235 219 555 400
14 32 125 140 203 242 165 95 45 64 145 189200259178124 62 89 259 172 198
23 40 41 135 140 112 128 112 65 161 150 148122134113 68 109 122 199 296 323
27 20 114 234 116 74 112 241 200 236 117 0 42 90 204107 65 88 178 249
22 65 99 161 93 47 121 95 211 170 131 249 46 79 129150157 255 150 147
19 78 117 147 104 185 274 93 128 169 205 53 36 26 84 217 88 40 249
103 182 159 102 213 261 275 156 448 162 104 245 97 224197267196 133 124
54 81 145 132 117 109 75 139 155 117 104 51 163230
64 35 136 125 68 79 79 19 60 70 44 47
61 0
290 300 310 320 330 340 350 360 370 380 390 400 410
240
250
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310
320
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350 0 to 53 53 to 93 93 to 135 135 to 196 196 to 695.1
Total Ceramics
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39
0
2 2 10 6 18 14 16 2 0
11 1 6 10 27 0 0 7 9 0
15 17 8 10 4 6 26 5 9 0 1 2
2 4 23 8 17 11 7 6 9 20 13 3 23 12 30 15 0 0 3
5 6 0 8 7 10 2 14 3 0 6 11 12 13 26 23 17 5 7 1 1
0 2 1 3 7 1 7 9 2 5 11 13 0 10 6 2 2 8 5 7 4 11
1 3 2 1 6 2 5 6 2 11 0 1 0 1 6 92 23 19 12 6 2 5
2 0 4 1 2 5 3 2 1 3 3 4 3 3 3 46 20 26 29 12 4 6
1 5 1 1 1 5 2 4 0 12 6 2 7 2 12 12 7 17 3 4 2 16 2
1 0 5 4 9 7 0 4 4 4 7 0 4 2 1 13 14 35 12 4 1 9 5 0
2 1 6 1 1 3 0 2 3 8 1 6 0 2 2 3 6 7 9 1 0 4 2
3 0 0 5 4 10 0 5 15 5 0 2 1 2 0 4 2 1 0 6 4 12 31
0 0 1 1 5 1 4 3 3 1 0 0 0 2 0 2 0 2 5 14 37 62
0 1 1 3 7 2 2 0 5 8 3 4 7 8 3 5 5 5 18 9 59
0 1 1 0 11 3 3 0 1 4 3 5 4 1 0 5 6 0 4 15 31
1 1 1 4 5 0 4 3 2 3 3 0 0 2 5 1 0 1 1 8
4 6 5 5 5 3 3 0 2 7 1 1 0 0 2 3 4 3 6 4
3 1 0 3 3 0 0 4 7 6 9 0 2 2 3 3 1 0 5
8 6 3 3 5 3 6 0 10 3 3 4 4 10 6 7 4 2 4
4 4 1 11 9 4 2 0 0 0 2 0 0 4
2 2 7 5 2 4 1 1 2 5 4 0
2 0
290 300 310 320 330 340 350 360 370 380 390 400 410
240
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290
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310
320
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350 0 to 1 1 to 3 3 to 5 5 to 9 9 to 92.01
Formative Phase
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0
0 0 0 0 0 2 1 0 0
2 0 0 0 1 0 0 0 0 0
0 0 0 4 0 0 0 0 0 0 0 0
0 0 2 0 0 1 0 1 1 3 0 0 0 0 0 0 0 0 0
0 0 1 0 2 2 5 2 3 0 0 4 0 0 0 0 0 0 0 0 0
0 0 1 0 0 0 2 1 0 6 1 2 0 0 0 0 0 0 0 0 0 0
0 0 1 0 2 0 1 1 0 0 1 0 0 0 4 0 1 0 0 0 0 0
0 0 1 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 2 0 2
2 0 0 0 1 0 0 1 0 2 0 0 0 3 0 0 0 0 1 0 0 1 0
0 1 1 1 1 0 4 0 3 3 3 0 1 0 1 0 0 0 0 0 0 0 0 0
1 0 1 0 1 0 1 2 3 0 1 1 0 1 4 2 2 2 1 2 0 1 1
0 0 0 1 0 8 3 3 5 1 1 0 4 0 0 1 3 0 1 1 1 1 2
1 1 2 0 5 4 1 0 4 1 0 3 1 6 2 1 0 0 4 0 2 2
0 0 2 2 2 0 0 0 0 1 2 3 3 1 0 0 0 0 20 3 3
2 0 0 2 2 2 3 2 0 0 2 1 0 0 3 2 0 2 2 4 1
2 0 2 1 0 1 4 3 5 5 2 0 0 0 0 1 1 4 4 1
0 0 1 1 0 5 0 1 2 6 4 4 2 1 6 0 0 0 5 1
0 1 0 6 2 6 2 1 7 10 16 0 0 0 2 0 1 0 3
1 0 4 2 1 0 3 3 1 3 3 2 1 0 0 0 2 2 0
0 0 1 4 0 3 1 3 0 4 0 0 6 1
0 0 2 1 1 0 0 0 0 0 0 1
5 0
290 300 310 320 330 340 350 360 370 380 390 400 410
240
250
260
270
280
290
300
310
320
330
340
350 0 to 1 1 to 2 2 to 3 3 to 4 4 to 20.01
Early Intermediate Phase
41
5
22 12 6 7 22 17 21 2 1
65 42 34 12 10 0 0 12 12 2
42 22 29 64 60 21 21 7 20 6 1 1
8 2 9 11 43 24 65 62 33 104108 10 19 16 30 30 3 0 0
2 11 16 20 36 37 17 26 28 0 50 88 115 77 33 25 37 15 4 3 2
7 4 6 11 18 15 23 13 15 39 50 105 84 80 24 3 7 29 18 21 11 4
6 2 5 4 21 3 19 17 10 65 4 3 5 2 25 33 33 27 14 13 20 8
5 0 1 8 9 18 5 11 3 9 28 29 33 11 3 15 15 32 43 20 21 12
4 7 2 2 10 16 7 24 14 79 44 14 24 30 24 10 4 15 5 8 17 63 22
6 7 25 19 18 43 38 40 43 52 94 41 31 6 14 43 39 49 18 16 17 72 80 0
17 4 9 16 20 31 34 27 46 47 65 8 17 6 21 35 46 29 32 32 0 90 39
7 0 29 27 23 75 42 32 41 66 76 36 1 4 8 33 19 10 60 30 99 40 87
2 6 19 29 43 26 36 22 34 39 1 11 15 17 15 11 21 8 45 35 67 47
2 5 26 24 38 52 42 33 10 16 53 32 30 26 23 16 10 12 30 27 35
2 6 6 25 22 24 26 22 16 47 30 23 16 32 25 18 18 47 31 48 42
0 0 23 18 11 13 15 34 48 53 31 0 11 12 72 25 13 16 32 44
5 4 11 11 9 14 26 24 41 46 24 50 7 9 20 55 46 47 32 40
2 6 17 18 9 39 48 19 19 43 19 8 7 1 17 52 25 0 43
22 34 40 18 27 42 24 24 49 31 9 21 15 36 49 31 41 33 38
9 15 26 22 16 13 9 24 37 7 8 9 29 44
10 13 46 42 6 7 13 1 24 8 3 8
6 0
290 300 310 320 330 340 350 360 370 380 390 400 410
240
250
260
270
280
290
300
310
320
330
340
350 0 to 7 7 to 15 15 to 24 24 to 39 39 to 115.1
Tiwanaku Phase
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