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Assessing intrasample variation Analysis of Rapa Nui (Easter Island) museum cranial collections example.

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AMERICAN JOURNAL OF PHYSICAL ANTHROPOLOGY 124:45–58 (2004)
Assessing Intrasample Variation: Analysis of Rapa Nui
(Easter Island) Museum Cranial Collections Example
Vincent H. Stefan*
Department of Anthropology, Lehman College, CUNY, Bronx, New York 10468
KEY WORDS
intrasample variation; Rapa Nui; craniometrics; cranial discrete traits
ABSTRACT
Osteological studies both old and new
have utilized various Polynesian cranial samples, individually or in combination, to assess the racial composition of
prehistoric Polynesians as a group, with regards to other
Pacific populations, or to represent the Polynesian peoples
as a whole in various multivariate analyses of worldwide
populations. However, few of these studies have assessed
the degree of intrasample variation produced when data
derived from skeletal samples from different Polynesian
islands (populations) are pooled to represent “Polynesians” as a whole. A similar argument can be made when
data derived from various museum skeletal samples of the
same Polynesian population are pooled to produce a larger
sample representing that particular Polynesian population (Murrill [1968] Cranial and postcranial skeletal remains from Easter Island; Minneapolis: University of
Minnesota Press; Stefan [2002] Am. J. Phys. Anthropol.
[Suppl.] 34:147). This study examined Easter Island crania curated at various museums in North America, South
America, and Europe to assess whether significant differences exist among the museum collections of Rapa Nui
(Easter Island) skeletal material. A NORM statistical program (Schafer and Olsen [1997] NORM, version 1.01; University Park: Pennsylvania State University) for multiple
Human biological variation within individual
skeletal samples has been assessed with regards to
temporal processes (Jantz, 1973; Key and Jantz,
1981; Konigsberg, 1990; Owsley and Jantz, 1978;
Owsley et al., 1982; Relethford and Crawford, 1995;
Relethford et al., 1997) and between skeletal samples when assessing population relationships
(Konigsberg and Blangero, 1993; Relethford, 1998;
Steadman, 2001). However, relatively few studies
have assessed the degree of intrasample variation
produced when data from various museum samples
are combined into one sample (Sparks et al., 2002;
Stefan, 2002).
Osteological studies both old and new have utilized various Polynesian cranial samples individually or in combination to assess the racial composition of prehistoric Polynesians as a group (Howells,
1990; Katayama, 1987; Pietrusewsky, 1996; Tagaya
and Katayama, 1988), with regards to other Pacific
populations (Brace et al., 1990; Giles, 1973; Howells,
1970; Pietrusewsky, 1970, 1990a,b, 1992, 1994;
Wagner, 1937), or to represent the Polynesian peo©
2004 WILEY-LISS, INC.
imputation of incomplete multivariate datasets was utilized to estimate missing data. A variance comparison
method, which utilizes variance/covariance matrices derived from “hypothesis” and “baseline/reference” samples
(Key and Jantz [1990] Hum. Evol. 5:457– 469; Key and
Jantz [1990] Am. J. Phys. Anthropol. 82:53–59) was used
to compare the Rapa Nui museum samples. This method
is designed to test whether variability in a “hypothesis”
museum sample exceeds “normal within-group variability” represented by the “baseline/reference” sample. The
method was applied to six Rapa Nui museum samples
(AANMW, MNHN-KB, MNHN-NAE, NHM, MH, and
AMNH). The results indicate that the museum “hypothesis,” male and female samples, exhibited little intrasample variability from the “baseline/reference” sample (MAPSE), though the samples were collected at
different times and by different individuals. These results
show the ability of multiple imputation and variance comparison methodologies to predict missing variables while
maintaining the inherent variance/covariance structure
and to discriminate sample variation in artificially assembled samples. Am J Phys Anthropol 124:45–58, 2004.
©
2004 Wiley-Liss, Inc.
ples as a whole in various multivariate analyses of
worldwide populations (Brace and Hunt, 1990; Howells, 1973, 1989, 1995). With regards to the prehistoric Rapa Nui (Easter Islanders), researchers have
Grant sponsor: Easter Island Foundation Research Grants; Grant
sponsor: PSC-CUNY Award, City University of New York; Grant
sponsor: Research, Projects, and Travel Grant, Office of Graduate
Studies, University of New Mexico.
This article was presented at the 71st Annual Meeting of the American Association of Physical Anthropologists at Buffalo, New York,
April 2002.
*Correspondence to: Vincent H. Stefan, Department of Anthropology, Lehman College, CUNY, 250 Bedford Park Blvd. West, Bronx,
NY 10468. E-mail: vstefan@lehman.cuny.edu
Received 14 August 2002; accepted 16 April 2003.
DOI 10.1002/ajpa.10331
Published online 11 August 2003 in Wiley InterScience (www.
interscience.wiley.com).
46
V.H. STEFAN
also analyzed various museum collections to assess
the racial composition of the islanders and their
biological relationship to other Polynesian populations (Baker and Gill, 1997; Brace et al., 1991; Chapman, 1993, 1996, 1998; de Quatrefages and Hamy,
1882; Gill and Owsley, 1993; Gill et al., 1997;
Henckel, 1939; Howells, 1989; Imbelloni, 1951;
Meier, 1975; Meyer and Jablonowski, 1901; Murrill,
1968; Petri, 1936; Pietrusewsky, 1996; Shapiro,
1940; Stefan, 1998, 2000; Stevenson et al., 1998;
Tigner and Gill, 1986; Volz, 1895; von Bonin, 1931;
Zimple and Gill, 1986). However, few of these studies assessed the degree of intrasample variation produced when data derived from skeletal samples from
different Polynesian islands (populations) are
pooled to represent “Polynesians” as a whole. A similar argument can be made when data derived from
various museum skeletal samples of the same
Polynesian population are pooled to produce a larger
sample representing that particular Polynesian population (Murrill, 1968; Stefan, 2002).
Rapa Nui craniometric data were collected on a
sample of 403 individuals from collections in Europe, North and South America, and Rapa Nui. This
skeletal series provides an opportunity to determine
whether significant differences exist between the
various Rapa Nui skeletal samples, and if the differences between these samples can be explained by
temporal shifts in skeletal morphology (Konigsberg,
1990).
The objectives of this study are the following: 1) to
assess the range of variation and differences between various museum Rapa Nui cranial samples;
2) to determine if temporal shifts in Rapa Nui cranial morphology exist; and 3) to determine if pooling
Rapa Nui cranial samples is unwarranted due to
excessive intrasample variation.
RAPA NUI CRANIAL COLLECTIONS
The collection of Rapa Nui skeletal remains for
museums in Europe and North and South America
commenced shortly after the Dutch rediscovery of
the island in 1722 (Ayers, 1995; Imbelloni, 1951; La
Pérouse, 1797; Lavachery, 1935; Murrill, 1965;
Nicoll, 1908; Pinart, 1878a,b; Routledge, 1919; Shapiro, 1935; Thomson, 1891). The majority of Rapa
Nui skeletal material has been dated to the Late
Prehistoric (AD 1680 –1722) and the Protohistoric
(AD 1722–1868) periods (Gill and Owsley, 1993; Gill
et al., 1983; Owsley et al., 1994). Skeletal material
from earlier periods is not available due to the extensive practice of cremation known to have occurred during the 13th century and most probably
through the final phases of ahu use (Shaw, 1996;
Van Tilburg, 1994). The existing skeletal material
was recovered from modified image ahus (Love,
1993), semipyramidal ahu crypts (Stevenson, 1984),
and secondary cave burials (Shaw, 1996). The utilization of image ahus, semipyramidal ahus, and
caves as burial sites began around 1700 and contin-
ued up until the 1860s, when the first missionaries
came to the island.
The Rapa Nui skeletal samples investigated by
this researcher and others, primarily G.W. Gill,
D.W. Owsley, and S.J. Baker, include museum collections from North and South America and Europe
from which craniometric data were collected. Detailed provenience information was gathered for
each sample if available. However, exact provenience information on all Rapa Nui collections was
not available due to the unsystematic manner in
which early expeditions collected the material
(Chapman, 1996). The Rapa Nui skeletal material
utilized in this study is curated at the Anthropologische Abteilung, Naturhistorisches Museum Wien,
Austria; the Museo Nacional de Historia Natural
(MNHN), Santiago, Chile; the Natural History Museum, London, UK; the Musée de l’Homme, Paris,
France; the American Museum of Natural History,
New York, New York; and the Museo Antropológico
Padre Sabastián Englert (MAPSE), Rapa Nui. A
summary of available provenience information and
circumstances of collection for each sample is provided in Table 1.
INTRAGROUP VARIABILITY
There are several measures of intragroup variability available on a univariate level. These include
the coefficient of variation, comparison of ranges
statistic, the variance ratio of Morant (1935), and
the sigma ratio of Howells (1936) (see also Key and
Jantz, 1990a, p. 458). Van Vark (1984) and Howells
(1974) attempted multivariate measures of variability. However, univariate measures suffer from various underlying problems common to univariate statistics (i.e., they do not consider variable
intercorrelation and have problems with simultaneous confidence levels in significance tests) (Key
and Jantz, 1990b, p. 53), and few multivariate methods possess a formal test of the null hypothesis that
the variances are equal. Key and Jantz (1990a) previously attempted several multivariate measures of
intragroup variability, including intrasample discriminant functions, intrasample clustering techniques, and calculating Mahalanobis D2s between
all possible pairs of individuals; however, all these
attempts defied easy interpretation.
Recently, Key and Jantz (1990a,b) employed a
multivariate statistical method, the variance comparison method, which utilizes variance/covariance
matrices derived from hypothesis and reference
samples. It is an adaptation of certain techniques
used in twin research (Bock and Vandenberg, 1968).
The method can be most easily understood with
reference to ordinary discriminant analysis.
The standard discriminant model can be defined
as:
共W ⫺1 ⴱ A ⫺ L ⴱ I兲 ⴱ V ⫽ 0,
where W is the pooled within-group covariance matrix and A is the covariance matrix among groups. In
47
ASSESSING INTRASAMPLE VARIATION
TABLE 1. Male and female museum sample1
Museum
Who collected
Date collected
Rapa Nui provenience
Male
(n)
Female
(n)
Reference
AANMW
Paymaster J.
Weisser
1877–1879 or
1882
Unknown
6
7
MNHN-KB
1911 and 1918
Unknown
22
18
MNHN-NAE
Dr. Walter Knoche
Padre Bienvenido
de Estella
Thor Heyerdahl
1955–1956
9
10
Murrill (1965, 1968)
NHM
Lord Crawford
Ahu Tepeu, Ahu Hekii, and
Ahu Vinapu
Unknown
28
25
Nicoll (1908)
MH
Katherine Scoresby
Routledge
Alphonse Pinart
AMNH
MAPSE
1903 and
1914–1915
Volz (1895), Petri (1936),
Pietrusewsky (1986),
Jumeau (1997)
Knoche (1925)
Imbelloni (1951)
Routledge (1919)
1877 and
1934–1935
La Pérouse Bay and Vaihu
40
26
Alfred Métraux
Harry L. Shapiro
1935
Ahu Tahai and Ahu Tautira
11
11
George W. Gill
1981–1991
Various
61
47
177
144
Total
Pinart (1878b)
Lavachery (1935)
Chapin (1935),
Shapiro (1935)
Gill (1986),
Gill et al. (1997)
1
AANMW, Anthropologische Abteilung, Naturhistorisches Museum Wien, Vienna, Austria; MNHN-KB, Museo Nacional de Historia
Natural (MNHN), Santiago, Chile, Knoche/Bienvenido collection; MNHN-NAE, Museo Nacional de Historia Natural (MNHN),
Santiago, Chile, Norwegian Archaeological Expedition collection; NHM, Natural History Museum, London, UK; MH, Musée de
l’Homme, Paris, France; AMNH, American Museum of Natural History, New York, NY; MAPSE, Museo Antropológico Padre
Sabastián Englert, Rapa Nui.
the null case, A can be regarded as an estimate of W.
L, the vector of eigenvalues of (W⫺1 * A), provides a
test of the null hypothesis. V is the matrix of eigenvectors of (W⫺1 * A), and can be utilized to define
linear combinations of variables which maximize
distances among groups. I is the identity matrix.
The variance comparison model is defined as:
共W ⫺1 ⴱ H ⫺ L ⴱ I兲 ⴱ V ⫽ 0.
With this model, W is a covariance matrix obtained
from a sample thought to represent normal withingroup variability, which Key and Jantz (1990a,b)
term “baseline variability.” The hypothesis matrix H
will contain a component of baseline variability represented by W, plus an unknown component A. The
statistics of interest are the eigenvalues and eigenvectors of the asymmetric product matrix W⫺1 * H,
which provides a test of the null hypothesis that A ⫽
0. The results of this test can indicate whether there
are significant differences between the baseline
sample and the hypothesis samples, and to determine whether there are unknown forces producing
excessive variation between samples. Key and Jantz
(1990a,b) utilized a ␹2 test statistic for evaluating
the statistical significance of the test, following Bartlett (1951). This method tests the overall heterogeneity present, as well as residual heterogeneity remaining after successively removing each
eigenvalue. It also tests the cumulative contribution
of each eigenvalue to the overall heterogeneity.
However, Petersen (1998, 2000) recently criticized
their methods and suggested that an F-test would be
more appropriate when dealing with small sample
sizes. He also noted that Key and Jantz (1990a,b)
utilized the wrong number of degrees of freedom (df)
for the ␹2 test. These problems would have the result
of increasing the probability of committing a type I
error. To account for these difficulties, this research
utilized both the ␹2 test and the F-test, and the
F-test statistic calculated in accordance with (Rao,
1973).
MATERIALS AND METHODS
Measurements
This study incorporates measures of the cranial
vault, face, and interorbital region as defined by
Bass (1995), Gill et al. (1988), Howells (1973), and
Martin and Saller (1957). The list of 49 standardized
measurements collected is provided in the Appendix. To take these measurements, five instruments
were used: a pair of sliding calipers, a pair of spreading calipers, a head spanner, a simometer, and a
palatometer. The complete dataset of 49 variables
was reduced to 30 variables (Table 2) following the
univariate ANOVA procedure, discussed below, to
identify those variables which were significantly different among museum samples and more likely to
reflect excessive intrasample variation.
Museum collections utilized
The methodologies of missing data estimation and
intrasample variance comparisons could only be applied to the Anthropologische Abteilung, Naturhistorisches Museum Wien, Vienna, Austria, Weisser
collection; the Museo Nacional de Historia Natural,
Santiago, Chile, Knoche/Bienvenido collection and
the Norwegian Archaeological Expedition collection;
the Natural History Museum, London, UK, Lord
Crawford/Katherine Scoresby Routledge collection;
48
6
7
22
18
9
10
28
25
40
26
11
11
61
47
321
Percentage of sample in parentheses.
1
MAPSE
Total
AMNH
MH
NHM
MNHN-NAE
MNHN-KB
15
0
0
0
0
0
0
0
0
0
0
0
1 (0.091)
1 (0.016)
2 (0.043)
4 (0.012)
0
0
0
0
0
0
0
1 (0.040)
0
0
0
0
2 (0.033)
1 (0.021)
4 (0.012)
14
13
12
1 (0.167)
0
0
0
0
2 (0.094)
0
1 (0.056)
0
0
0
0
2 (0.071) 1 (0.036)
0
1 (0.040)
0
0
0
0
0
0
0
1 (0.091)
2 (0.033) 4 (0.066)
1 (0.021) 3 (0.064)
6 (0.019) 13 (0.04)
0
0
0
0
0
0
0
1 (0.040)
0
0
0
0
1 (0.016)
0
2 (0.006)
11
10
0
0
1 (0.045)
0
0
0
0
0
0
0
0
1 (0.091)
0
1 (0.021)
3 (0.009)
0
0
0
1 (0.056)
0
0
0
1 (0.040)
1 (0.025)
0
0
0
0
1 (0.021)
4 (0.012)
9
8
0
0
2 (0.091)
0
0
0
0
0
1 (0.025)
0
1 (0.091)
0
2 (0.033)
1 (0.021)
7 (0.022)
0
0
1 (0.045)
0
0
0
3 (0.107)
0
1 (0.025)
0
0
0
3 (0.049)
1 (0.021)
9 (0.028)
7
6
Number of missing variable
0
0
0
1 (0.056)
1 (0.111)
1 (0.100)
2 (0.071)
2 (0.080)
0
1 (0.038)
0
0
4 (0.066)
2 (0.043)
14 (0.044)
0
0
1 (0.045)
0
0
0
3 (0.107)
2 (0.080)
1 (0.025)
2 (0.077)
0
0
0
2 (0.043)
11 (0.034)
0
0
0
0
1 (0.111)
0
0
2 (0.080)
1 (0.025)
1 (0.038)
0
2 (0.182)
2 (0.033)
2 (0.043)
11 (0.034)
1 (0.167)
0
0
1 (0.056)
0
1 (0.100)
1 (0.036)
3 (0.120)
0
2 (0.077)
0
0
3 (0.049)
4 (0.085)
15 (0.047)
0
0
4 (0.182)
2 (0.111)
1 (0.111)
2 (0.200)
3 (0.107)
3 (0.120)
5 (0.125)
1 (0.038)
2 (0.182)
1 (0.091)
4 (0.066)
8 (0.170)
36 (0.112)
0
2 (0.286)
3 (0.136)
3 (0.167)
1 (0.111)
1 (0.100)
1 (0.036)
3 (0.120)
7 (0.175)
3 (0.115)
2 (0.182)
2 (0.182)
18 (0.295)
6 (0.128)
52 (0.162)
4 (0.667)
5 (0.714)
8 (0.364)
10 (0.556)
5 (0.556)
5 (0.500)
12 (0.429)
6 (0.240)
23 (0.575)
16 (0.615)
6 (0.545)
3 (0.273)
15 (0.246)
12 (0.255)
130 (0.405)
Male
Female
Male
Female
Male
Female
Male
Female
Male
Female
Male
Female
Male
Female
5
TABLE 2. Number of individuals missing variable data1
4
3
2
1
0
Sex
Sample
AANMW
Total
V.H. STEFAN
the Musée de l’Homme, Paris, France, Alphonse Pinart/Alfred Métraux collection; the American Museum of Natural History, New York, Shapiro collection; and Museo Antropológico Padre Sabastián
Englert (MAPSE), Rapa Nui, G.W. Gill collection,
due to the limitations imposed by the NORM program. Table 1 contains the sample breakdowns as to
number of individuals analyzed and number of
males and females in each museum sample. In this
study, males and females were analyzed separately.
The vast majority of crania in the collections examined were isolated, with no associated postcranial
elements. Therefore, sex determination methods
which assess pelvic morphology and age determination methods which assess pubic symphysis morphology and/or sternal rib end morphology could not
be utilized in this study. An accurate, reliable, and
proven method for assessing the age of Polynesian/
Rapa Nui crania was not available. The sex of each
cranium was determined utilizing standard anthroposcopic techniques of assessing cranial morphology
(Bass, 1995; Buikstra and Ubelaker, 1994), taking
into account that Rapa Nui females tended to appear more robust than European females or females
of other populations (Baker and Gill, 1997). Any
crania with ambiguous or indeterminate sex were
not included in the analyses conducted. Inaccuracies
in sex assessment, if present, would be a methodological error present in all the museum sample data
and would not affect any single pariwise comparison. Cranial metric data were collected only from
adult individuals, as evidenced by a fused sphenooccipital sychondrosis (Krogman and Iscan, 1986),
and only the most complete crania were selected for
data collection. Age determination beyond that of
being an “adult” was not assessed or deemed necessary for the analyses that were to be conducted, as
justified below.
It was noted that significant differences in some
cranial measurements occur among different age
cohorts of a population (Israel, 1973; MooreJansen, 1989; Ruff, 1980). Ruff (1980) examined
16 craniofacial dimensions of an Indian Knoll,
Kentucky sample and found six dimensions (nasion-basion, basion-bregma, glabella-opisthocranion, bizygomatic breadth, basion-prosthion length,
and bigonial angle) that were significantly larger
in a 35–50-year age group than in a 20 –34-year
age group. A few of these dimensions (basionbregma, glabella-opisthocranion, and basion-prosthion length) were found to have increased by 2 mm
or more. Ruff (1980) argued that if skeletal samples
with potentially different demographic structures
are compared, the observed differences might be due
to the age characteristics of the samples, and not to
genetic or environmental differences.
Imbedded within the total range of morphological
variation observed within a given skeletal sample is
variation produced by sex and age effects. In order
for a skeletal sample to adequately represent the
underlying population from which it was drawn, it
ASSESSING INTRASAMPLE VARIATION
needs to document all the variation present within
that population, including aspects of individual, sex,
and age variation. The more comprehensive the
sample, the greater the probability that the sample
will represent its parent population. A sample biased towards individuals of a particular age cohort
may not reflect the total range of variation present
in the parent population, and analyses utilizing that
sample may produce erroneous results.
The purpose of this study was to investigate
whether independent Rapa Nui hypothesis samples
possess greater-than-expected variation as compared to a reference, baseline sample which represents the underlying population. If the baseline
sample encompasses the total range of morphological variation of the underlying population, it will
include individuals of all age cohorts. Therefore,
even if an individual hypothesis sample is biased
toward a specific age cohort, that sample would not
be expected to have a variance/covariance structure
exceeding that of the baseline sample. If the baseline
sample is biased toward a specific age cohort, then
comparisons with the hypothesis samples would
produce results indicating “greater than” (not observed in this study; see Results) or “less than/equal
to” variance, depending on whether the hypothesis
sample is or is not similarly biased. The likelihood of
finding independent skeletal samples, collected by
different individuals at different times, each with
the same age cohort bias, is in my opinion low. The
exact demographic/age cohort structure of a single
population’s samples is irrelevant if the results of
intrasample variability assessment analyses fail to
reject the null hypothesis of no differences between
the baseline reference and each hypothesis sample.
The collections examined in this study do not appear to be biased towards individuals of any particular age cohort, and appear to have the similar
demographic structures. Crania spanning the range
of “younger” adults with complete dentition to edentulous “older” adults were observed in each collection. The individuals who personally gathered or
commissioned the gathering of the crania of their
collections were more intent on the collection of intact complete crania (personal opinion). Because
this study examined each sample as a “whole” and
each sample was a composite of individuals from all
age cohorts, further division of the various museum
samples into age-specific cohorts was not performed.
Of the 403 total crania for which data were available, only 355 were from the museum samples under
investigation and had reliable determination of sex.
The new dataset, comprised of 355 individuals and
30 variables, had 15.6% missing data. In order to
minimize the amount of missing data, individuals
missing data for more than 15 of the 30 variables
were eliminated from the dataset. The “pruned”
dataset, comprised of 321 individuals and 30 variables, had only 9.5% missing data. A detailed summary of the number of individuals missing a certain
number of missing variables for each sample is given
49
in Table 2. As is evident from Table 2, 83.8% (n ⫽
269) of the individuals of the total sample have data
for 24 or more of the 30 variables, while only 16.2%
of the individuals of the total sample have data for
only 15–23 of the 30 variables. Though any given
individual could have 50.0% missing data (4 individuals, 1.2% of total sample), the overall percentage of
missing data was significantly reduced. It is the
“pruned” dataset that will be utilized in the missing
data estimation procedures and the intrasample
variability assessment.
The Museo Antropológico Padre Sabastián Englert (MAPSE) Rapa Nui Gill collection will serve as
the baseline sample. The justification for this selection is founded on a number of points. First, it is a
well-documented sample comprising individuals
from various sites from all regions of the island and
spans the period of the Late Prehistoric through the
Protohistoric (Gill and Owsley, 1993; Gill et al.,
1983). Second, the sample is the single largest collection of Rapa Nui crania in the world. Third, it
represents a population which existed prior to the
island population having been reduced to approximately 111 individuals as a result of civil conflict,
slavery, exploitation, and disease (Bahn and Flenley, 1992). The Gill collection is the best approximation of the island’s breeding population, against
which the other samples will be compared. The Anthropologische Abteilung, Naturhistorisches Museum Wien, Museo Nacional de Historia Natural,
Natural History Museum, Musée de l’Homme, and
American Museum of Natural History samples will
serve as the hypothesis samples to be tested.
Data analysis
Interobserver error. In order to utilize the Rapa
Nui data collected by Gill, interobserver error rates
were calculated. The author measured 30 individual
crania measured by Gill (28, Marquesas Island; 2,
Rapa Nui), with interobserver error rates tested via
pairwise t-tests and a method error statistic across
all variables. Bonferroni and Dunn-Šidák methods
for calculating the experimentwise error rate for
multiple comparisons, ␣⬘, was utilized to determine
the significance levels of each comparison (Šidák,
1967; Ury, 1976). The chances of committing a type
I error (rejecting a null hypothesis that is correct)
increase with the number of tests performed. In
order to minimize the chance of committing a type I
error, an experimentwise error rate, ␣⬘ ⫽ 1 ⫺ (1 ⫺
␣)1/k, was calculated, where ␣ is the desired experimentwise error rate, and k is the number of pairwise
comparisons to be made. The experimentwise error
rate lowers the probability of making a type I error
for each comparison, so that the probability of making any type I error in the entire series of tests does
not exceed ␣ (Sokal and Rohlf, 1995). To maintain an
experimentwise error rate of ␣ ⫽ 0.05, with 49 variable comparisons being conducted, each comparison
was determined to be significant only if the P-value
for t-tests was less than the ␣⬘ ⫽ 0.001 level.
50
V.H. STEFAN
The method error statistic (Solow, 1966; Utermohle and Zegura, 1982), which tests for random
error within replicate data, with high values of the
statistic indicating greater measurement error, was
also calculated to assess methodological differences
between myself and other researchers. The method
error statistic (S), also known as the technical error
measurement, is calculated as follows:
S ⫽
冑
冘 共x
N
1i
⫺ x 2i 兲 2
i⫽1
2N
where x1 is the original measurement value, x2 is
the repeated measurement value, and N is the sample size. The size of S is a function of the scale of the
measurements, which in this study were millimeters
(mm).
Univariate analysis. An analysis of variance
(ANOVA) procedure was undertaken, with Scheffé
post hoc analysis, to determine if significant differences existed for each variable within the male and
female museum collections and to determine which
of the museum samples were the most different for
each significant variable. As with interobserver error rate analyses, an experimentwise error rate for
multiple comparisons, ␣⬘, was calculated by the
Scheffé test to determine the significance levels of
each pairwise comparison, in order to maintain an
overall error rate of ␣ ⫽ 0.05 (SAS Institute, 1990, p.
942–945). The interobserver error and univariate
analyses reported here were performed in SAS (version 6) (SAS Institute, 1990).
Missing data estimation. Multivariate analysis
procedures require that there be no missing data:
every observation must have a value for each variable entered into the analysis; otherwise, the observation is eliminated. Deleting observations results
in large amounts of information being lost, and the
remaining completely observed cases would be unrepresentative of the population which they were
intended to reflect. In order to optimize the number
of observations utilized from each Rapa Nui museum collection, the problem of missing variable values needs to be addressed. Considerable attention
has been given to the problems of missing data estimation and of the most appropriate procedures for
estimating missing data (e.g., Droessler, 1981). Traditionally, three options have been available to anthropological researchers for estimating missing
data: substitution of group means, substitution of
grand means, or prediction of missing measurements by means of multiple regression. These alternatives have their associated advantages and disadvantages (Droessler, 1981, p. 80 – 84).
Substitution of group means for missing data has
the effect of decreasing variance within groups,
while concurrently increasing intergroup distances
based on comparisons of within-group and between-
group variances. Substitution of means over all
groups (grand means) increases within-group variance while decreasing between-group differences.
When working with a null hypothesis of no difference among groups, the use of the grand mean would
be a more conservative procedure than the use of
individual group means. However, the use of either
the group or grand means has one additional problem.
Many multivariate techniques involve the consideration of each observation as a composite of interrelated
morphological variables, where proportion as well as
size is represented by these measurements (Droessler,
1981). When mean values are substituted for missing
values into particularly large or small individuals,
there may be inconsistencies in size with the existing
measurements.
The estimation of missing data through multiple
regression is a much more complicated and timeconsuming procedure than the substitution of
means. The technique has several advantages. Predicting missing values from existing variables overcomes the problem of maintaining consistency in the
size of cranial dimensions within observations. Additionally, within-group variation will be affected to
a lesser extent with regression estimates than that
which will result from mean substitution. Regression-based estimates will also result in less alteration of within-group variances than results from
either group or grand mean estimates (Droessler,
1981). However, imputing predicted values from regression models tends to inflate observed correlations (Schafer, 1997). Regression predictions can
also compound sampling error when missing data
are predicted for small groups and when relatively
few complete observations are available for generating the regression equations.
Another potential problem when utilizing imputed
datasets as if they were real in any standard statistical method is that any standard errors, P-values,
and other measures of variability calculated could
be misleading because they would fail to reflect any
uncertainty due to missing data (Schafer, 1997).
This research will utilize the NORM statistical program (Schafer and Olsen, 1997) for multiple imputation of incomplete multivariate datasets and techniques described by Schafer (1997) to assess the
validity in combining point estimates and covariance matrices to be utilized in the intragroup variability analyses discussed below. These methods
will minimize the problems inherent in missing
value estimations discussed above.
NORM utilizes an expectation-maximization (EM)
algorithm, a computational method for finding maximum-likelihood estimates of parameters from an
incomplete dataset, and data augmentation (DA), a
Marchov chain Monte Carlo (MCMC) technique that
can be used to generate multiple imputations of
missing data. Multiple imputation, utilizing EM and
DA, solves an incomplete-data problem by repeatedly solving the complete-data version. In multiple
imputation, the unknown missing data are replaced
51
ASSESSING INTRASAMPLE VARIATION
by simulated values. Each of the completed datasets
is analyzed by standard complete-data methods. The
variability among the results of analyses provides a
measure of the uncertainty due to missing data,
which, when combined with measures of ordinary
sample variation, leads to a single inferential statement about the parameters of interest (Schafer,
1997).
For each individual male and female Rapa Nui
museum sample, five imputed datasets were generated with their associated variance/covariance matrices. Average variance/covariance matrices were
then generated from the imputed matrices. A test
statistic, D,
៮ ⫺ Q 0 兲/k,
៮ ⫺ Q 0 兲⬘T̃ ⫺1 共Q
D ⫽ 共Q
and its associated P-value were calculated to ensure
that the averaged variance/covariance matrix was
not significantly different from the original museum
dataset with missing variables (Schafer, 1997, p.
112–114). The test statistic is assessed utilizing an
F-distribution. This test assessed the two sources of
variance produced by the multiple imputation process: 1) the within-imputation variance, which is the
average of the complete-data variance estimates,
and 2) the between-imputation variance, which is
the variance of the complete-data point estimates.
These two sources of imputation variance serve to
imitate the normal sample variation (J.W. Graham,
personal communication) observed with complete
datasets. This statistical procedure will utilize the
NORM 2.03 statistical program (Schafer, 1999) for
multiple imputation of incomplete multivariate
datasets and techniques described by Schafer
(1997).
Intrasample variability assessment. As discussed above, the variance comparison model was
defined as:
共W ⫺1 ⴱ H ⫺ L ⴱ I兲 ⴱ V ⫽ 0,
and the statistics of interest were the latent roots
and vectors of the asymmetric product matrix W⫺1 *
H. However, these values cannot be calculated directly, since some of the eigenvalues may be imaginary. Therefore, the following procedures were used.
First, the covariance matrices, W and H, were
calculated from the baseline and hypothesis samples, respectively, for each sex. W was inverted, and
R found, the Cholesky half-root decomposition of
W⫺1. The latent vectors (V) of the symmetric matrix
RHR⬘ were then calculated, and the eigenvectors
maximizing the variation among individuals in the
hypothesis sample were identified via the equation
X ⫽ R⬘ * V. The latent roots (L), the vector of eigenvalues of RHR⬘, were then calculated, which provided a test of the null hypothesis that A ⫽ 0, i.e., no
variability above the baseline was present. Both the
␹2-test and F-test statistics were calculated. The
statistical analyses reported here were performed on
SAS and SAS IML (version 6) (SAS Institute, 1990).
TABLE 3. Interobserver error rates and method error statistics
Variable
GOL
NOL
XCB
XFB
WFB
ZYB
BBH
BNL
FRC
PAC
NPH
NAL
ASB
BPL
STB
JUB
FOL
OBB
OBD
OBH
EKB
NLB
NLH
FMB
AUB
WCB
AUR
PBH
NAR
SSR
PRR
BPH
MXB
MXS
ZOB
ZOS
ALB
ALS
WNB
ZMB
SSS
MDH
MDB
WMH
IML
XML
PAD
MAB
MAL
t-test P-value
Mean deviation
(in mm)
Method error
statistic
0.4235
1.0000
0.4146
0.7687
0.1608
0.4238
0.1034
0.0502
0.3259
0.0961
0.1033
0.5365
0.7287
1.0000
0.2339
0.1613
1.0000
0.7450
0.2827
0.2641
0.2703
0.4892
0.3256
0.1070
1.0000
0.3788
0.0033
0.0001*
0.0098
0.0003*
0.0001*
1.0000
0.5732
0.0006*
0.2246
0.0830
0.0881
0.0501
0.0431
0.3757
0.0296
0.8012
1.0000
0.0089
0.1610
0.5309
0.1101
0.1033
0.0431
⫺0.1290
0.0000
⫺0.1935
⫺0.0645
⫺0.2581
0.1333
⫺0.2857
⫺0.5000
0.0667
⫺0.3333
⫺0.2667
⫺0.1333
0.2069
0.0000
0.5161
0.2963
0.0000
⫺0.0645
0.3226
⫺0.2000
0.5000
0.1333
⫺0.0645
⫺0.5806
0.0000
⫺0.3448
⫺1.1333
⫺1.2667
⫺0.6207
⫺0.9333
⫺1.3571
0.0000
0.1379
0.7143
⫺0.6897
0.2222
0.5714
0.5185
⫺0.2857
⫺0.2143
0.5714
0.0645
0.0000
0.5161
0.8276
0.4828
⫺0.4444
⫺0.2581
⫺0.5714
0.3162
0.3216
0.4655
0.4282
0.3651
0.3216
0.3333
0.4907
0.1313
0.3939
0.3216
0.4152
1.1260
0.2722
0.8563
0.3922
0.3086
0.3873
0.5916
0.3474
0.8498
0.3714
0.1291
0.7188
0.2582
0.7440
0.7987
0.7071
0.4818
0.5571
0.7577
0.3922
0.4629
0.4303
1.0856
0.2402
0.6383
0.5000
0.2722
0.4513
0.5092
0.5000
0.4472
0.4082
1.1339
1.4577
0.5189
0.3162
0.5443
* Significant at experimentwise error rate of ␣⬘ ⱕ 0.001.
RESULTS
Interobserver error
The results of interobserver error analyses (Table
3) indicate that four variables were significantly different between the data collected by the researcher
and those collected by Gill (␣⬘ ⱕ 0.001): porionbregma P ⫽ 0.0001, porion-subspinale P ⫽ 0.0003,
porion-prosthion P ⫽ 0.0001, and maxillofrontal
subtense P ⫽ 0.0006. Despite their significance,
however, the mean differences between the data
were no greater than ⫾1.5 mm (porion-bregma,
⫺1.2667 mm; porion-subspinale, ⫺0.9333; porionprosthion, ⫺1.3571 mm; and maxillofrontal subtense, 0.7143 mm). The method error statistics for
these variables were: porion-bregma, 0.7071; porion-
52
V.H. STEFAN
TABLE 4. Male and female museum sample significant
variables
Variable
GOL
NOL
XCB
XFB*
ZYB*
JUB*
AUB
BNL
BPL
FRC*
NPH*
NAL
ASB
WCB*
OBB*
OBD*
OBH
EKB
FMB*
AUR*
NAR
SSR*
PRR*
MXS*
ALB*
ALS*
SSS
WMH
IML*
MAL*
Male P-value
Female P-value
0.0250
0.0140
0.2764
0.0295
0.0059*
0.0103*
0.0216
0.0137
0.0374
0.0052*
0.0132*
0.0235
0.0276
0.0002*
0.0019*
0.0013*
0.0120
0.0496
0.0046*
0.0086*
0.0258
0.0002*
0.0163*
⬍0.0001*
0.0851
0.7085
0.0217
0.0316
0.0020*
0.0198*
0.5542
0.4364
0.0278
⬍0.0001*
0.2626
0.0234
0.3194
0.1748
0.5463
0.9894
0.6796
0.7200
0.0206
0.0007*
0.1133
0.3126
0.3389
0.3451
0.2249
0.2910
0.0358
0.4164
0.6052
⬍0.0001*
⬍0.0001*
0.0005*
0.8860
0.7765
0.7348
0.0892
* Significant pairwise differences found with Scheffé’s post hoc
comparisons.
subspinale, 0.5571; porion-prosthion, 0.7577; and
maxillofrontal subtense, 0.4303. Due to this fact, it
is not unreasonable to pool the data collected by this
researcher and those collected by Gill and associates.
Univariate analysis
The results of ANOVA analyses are presented in
Table 4. There were 27 variables that were statistically significant for males and nine variables for
females, with six variables in common for males and
females at the ␣ ⫽ 0.05 level. The results of Scheffé
post hoc comparisons are presented in Table 5. Of
the 30 variables that were significant at the ␣ ⫽ 0.05
level, 17 variables had significant pairwise differences, and only two had significant comparisons for
both the male and female samples (WCB and MXS).
Though not all 30 variables had significant pairwise
comparisons in Scheffé post hoc comparisons, all will
be utilized in further analyses. The ANOVA analysis
noted some degree of difference between the male
samples and female samples, though these differences could not be identified through Scheffé post
hoc comparisons.
Missing data estimation
For each museum sample utilized, five imputed
datasets were created for males and females separately. An average imputed dataset and variance/
covariance matrix were then calculated. Each aver-
aged imputed dataset was then compared to the
original dataset without missing value estimates, to
determine if the two datasets were significantly different. The D-statistic and its associated P-value for
each museum/sex sample comparison are listed in
Table 6. The D-statistic was assessed utilizing an
F-distribution. As is evident, no average imputed
dataset was significantly different from its original
dataset with missing values.
Intrasample variability assessment
Tables 7 and 8 contain the ␹2-test and F-test statistics and their associated P-values for comparisons
between the Museo Antropológico Padre Sabastián
Englert male and female samples with the Anthropologische Abteilung, Naturhistorisches Museum
Wien, Museo Nacional de Historia Natural, Natural
History Museum, Musée de l’Homme, and American
Museum of Natural History male and female samples, respectively. With the exception of the male
and female Anthropologische Abteilung, Naturhistorisches Museum Wien samples and the male
American Museum of Natural History sample, analyses of the latent roots/eigenvalues of the collections
indicate that there is no excessive heterogeneity
within the remaining collections, and indicate that
there are no significant differences between the hypothesis samples and the baseline sample. It is also
evident that the F-test provides a slightly more conservative test of significance as compared to the
␹2-test, though this does not significantly change the
interpretation of results.
Examination of the ␹2-test and F-test statistics for
the male and female Anthropologische Abteilung,
Naturhistorisches Museum Wien (AANMW) samples (Tables 7 and 8) indicated greater levels of
variability than the baseline male and female samples within these samples. For the male AANMW
sample, after the first three latent roots/eigenvalues
were removed for the ␹2-test and the first two latent
roots/eigenvalues for the F-test, no significant variation remained. For the female AANMW sample,
after the first two latent roots/eigenvalues were removed for the ␹2-test and the first latent root/eigenvalue for the F-test, no significant variation remained. The cause of this excessive variability may
due to temporal changes (the AANMW sample was
collected in 1882; the baseline sample was collected
from 1981–1991) or to the small sizes of these hypothesis samples (male, n ⫽ 6; female, n ⫽ 7). The
investigation of the cause will be discussed below.
Upon examination of the ␹2-test and F-test statistics for the male American Museum of Natural History sample (Table 7), it is evident that there is at
least one significant eigenvector. These results indicate that variability significantly greater than baseline exists in this sample, though not to the extent
seen in the AANMW samples. No significant variability remains after removing the first latent root/
eigenvalue. Again, the possible cause of the excessive variability may be temporal changes, but is
ASSESSING INTRASAMPLE VARIATION
53
TABLE 5. Male and female museum sample Scheffé post hoc comparisons significant variables1
Variable
XFB
ZYB
JUB
FRC
NPH
WCB
OBB
OBD
FMB
AUR
SSR
PRR
MXS
ALB
ALS
IML
MAL
Male pairwise comparison
Female pairwise comparison
MAPSE—MNHN-KB, MH, NHM
MAPSE—MNHN-KB
MAPSE—MNHN-KB
MAPSE—MNHN-KB
MNHN-KB—MH
MAPSE—MNHN-KB
MNHN-KB—NHM
MNHN-KB—MH, NHM
MAPSE—MNHN-KB
MAPSE—MNHN-KB
MAPSE—MNHN-KB, MH, NHM
MNHN-KB—NHM
MH—MNHN-NAE
MAPSE—MNHN-KB, MH
MH—MAPSE, MNHN-KB, MNHN-NAE; MNHN-NAE—NHM, AANMW
MAPSE—NHM
MAPSE—NHM
MAPSE—MNHN-KB
MAPSE—MNHN-KB
1
AANMW, Anthropologische Abteilung, Naturhistorisches Museum Wien, Vienna, Austria; MNHN-KB, Museo Nacional de Historia
Natural (MNHN), Santiago, Chile, Knoche/Bienvenido collection; MNHN-NAE, Museo Nacional de Historia Natural (MNHN),
Santiago, Chile, Norwegian Archaeological Expedition collection; NHM, Natural History Museum, London, UK; MH, Musée de
l’Homme, Paris, France, MAPSE, Museo Antropológico Padre Sabastián Englert, Rapa Nui.
TABLE 6. Average imputed dataset significance1
Museum sample
AANMW
MNHN-KB
MNHN-NAE
NHM
MH
AMNH
MAPSE
Sex
D-statistic
df
Male
Female
Male
Female
Male
Female
Male
Female
Male
Female
Male
Female
Male
Female
0.041
0.003
0.047
0.013
0.035
0.029
0.032
0.054
0.020
0.015
0.017
0.096
0.010
0.017
30,
30,
30,
30,
30,
30,
30,
30,
30,
30,
30,
30,
30,
30,
2
⬁
⬁
⬁
⬁
⬁
⬁
⬁
⬁
⬁
⬁
⬁
⬁
⬁
⬁
P-value
⬎0.9999
⬎0.9999
⬎0.9999
⬎0.9999
⬎0.9999
⬎0.9999
⬎0.9999
⬎0.9999
⬎0.9999
⬎0.9999
⬎0.9999
⬎0.9999
⬎0.9999
⬎0.9999
1
AANMW, Anthropologische Abteilung, Naturhistorisches Museum Wien, Vienna, Austria; MNHN-KB, Museo Nacional de
Historia Natural (MNHN), Santiago, Chile, Knoche/Bienvenido
collection; MNHN-NAE, Museo Nacional de Historia Natural
(MNHN), Santiago, Chile, Norwegian Archaeological Expedition
collection; NHM, Natural History Museum, London, UK; MH,
Musée de l’Homme, Paris, France; AMNH, American Museum of
Natural History, New York, NY; MAPSE, Museo Antropológico
Padre Sabastián Englert, Rapa Nui.
2
Critical value: 1.46.
more likely a result of sample size (n ⫽ 11) or of an
individual outlier.
ANTHROPOLOGISCHE ABTEILUNG,
NATURHISTORISCHES MUSEUM WIEN
VARIABILITY ASSESSMENT
In order to determine if the excessive variability
observed in the Anthropologische Abteilung,
Naturhistorisches Museum Wien (AANMW) male
and female samples was due to temporal changes or
sample size, I added to the samples data from Rapa
Nui crania curated in the Bioanthropology Collection at Indiana University (IU, Bloomington, IN;
male, n ⫽ 5; female, n ⫽ 1). During data collection,
the word “Cooke” was observed written on each cranium, a possible reference to G.H. Cooke. The cura-
tors of the Bioanthropology Collection were unaware
of the identity and provenience of the crania, and
had no knowledge of the meaning of the word
“Cooke” inscribed on them. The collection containing
the Rapa Nui crania also contains skeletal material
from Peruvian individuals, collected in 1887 during
a voyage of the U.S.S. Mohican. Upon further investigation by the collection curators, it was discovered
that the entire collection had been donated to the
university by the great, great grandson of Dr. G.H.
Cooke.
Additionally, three Rapa Nui crania (male, n ⫽ 2;
female, n ⫽ 1) curated by the Smithsonian Institution (SI, Washington, DC), collected by either paymaster William J. Thomson or ship’s surgeon G.H.
Cooke of the U.S.S. Mohican in December 1886
(Cooke, 1899; Thomson, 1891), will be added to the
AANMW sample. Though collected by different individuals, the justification for adding these two collections to the AANMW samples is the similar time
period in which crania were collected.
The results from the ␹2-test and F-test statistics
and their associated P-values for the comparisons
between the combined AANMW/IU/SI male and female samples and the Museo Antropológico Padre
Sabastián Englert male and female samples are presented in Table 9. As is evident, the combined male
sample (n ⫽ 13) does not have any variability significantly greater than the baseline male sample.
For the combined female sample (n ⫽ 9), only the
␹2-test indicated variability significantly greater
than the baseline female sample, and no significantly greater variability after removing the first
latent root/eigenvalue. Clearly these statistical procedures are highly sensitive to sample size, and the
results of the first analyses of the AANMW revealed
significantly greater levels of variability due to
small sample size, not due to temporal changes. If
there had been temporal changes in the Rapa Nui
54
V.H. STEFAN
TABLE 7. Male intrasample variability vs. baseline sample results1
Museum collection
AANMW
MNHN-KB
MNHN-NAE
NHM
MH
AMNH
Root/eigenvalue no.
Chi square
df
P-value
F-statistic
df
P-value
Overall
12
23
34
Overall
Overall
Overall
Overall
Overall
12
329.18
270.41
225.05
187.90
651.90
303.65
822.00
1,087.76
414.14
349.91
180
180
180
180
660
270
840
1200
330
330
7.8279E-11
1.4874E-05
0.0127
0.3279
0.5814
0.0778
⬎0.9999
0.9907
0.0011
0.2160
3.4217
1.9179
1.2034
180, 31.1
180, 31.1
180, 31.1
7.4789E-05
0.0170
0.2771
0.9073
1.1060
0.8910
0.7875
1.3154
1.0085
660, 572.8
270, 151.8
840, 717.8
1,200, 919.5
330, 224.2
330, 224.2
0.8863
0.2471
0.9461
⬎0.9999
0.0137
0.4757
1
Baseline sample: MAPSE, Museo Antropológico Padre Sabastián Englert, Rapa Nui; AANMW, Anthropologische Abteilung,
Naturhistorisches Museum Wien, Vienna, Austria; MNHN-KB, Museo Nacional de Historia Natural (MNHN), Santiago, Chile,
Knoche/Bienvenido collection; MNHN-NAE, Museo Nacional de Historia Natural (MNHN), Santiago, Chile, Norwegian Archaeological
Expedition collection; NHM, Natural History Museum, London, UK; MH, Musée de l’Homme, Paris, France; AMNH, American
Museum of Natural History, New York, NY.
2
First latent root/eigenvalue removed.
3
Second latent root/eigenvalue removed.
4
Third latent root/eigenvalue removed.
E (exponent), value raised to the power of the given negative number.
TABLE 8. Female intrasample variability vs. baseline sample results1
Museum collection
Root/eigenvalue no.
Chi square
df
P-value
F-statistic
df
P-value
Overall
12
23
Overall
Overall
Overall
Overall
Overall
340.93
271.37
227.45
534.31
331.51
689.99
746.48
318.45
210
210
210
540
300
750
780
330
2.7854E-08
0.0028
0.1945
0.5609
0.1019
0.9424
0.8007
0.6660
2.0059
1.0724
210, 26.7
210, 26.7
0.0187
0.4371
0.8345
0.9552
0.7499
0.7957
0.7664
540, 269.5
300, 96.2
750, 399.6
780, 416.0
330, 118.6
0.9592
0.6212
0.9996
0.9965
0.9649
AANMW
MNHN-KB
MNHN-NAE
NHM
MH
AMNH
1
Baseline sample: MAPSE, Museo Antropológico Padre Sabastián Englert, Rapa Nui; AANMW, Anthropologische Abteilung,
Naturhistoisches Museum Wien, Vienna, Austria; MNHN-KB, Museo Nacional de Historia Natural (MNHN), Santiago, Chile,
Knoche/Bienvenido collection; MNHN-NAE, Museo Nacional de Historia Natural (MNHN), Santiago, Chile, Norwegian Archaeological
Expedition collection; NHM, Natural History Museum, London, UK; MH, Musée de l’Homme, Paris, France; AMNH, American
Museum of Natural History, New York, NY.
2
First latent root/eigenvalue removed.
3
Second latent root/eigenvalue removed.
E (exponent), value raised to the power of the given negative number.
TABLE 9. AANMW/IU/SI sample variability vs. baseline sample results
Museum
collection
Male
Female
Root/eigenvalue no.
Chi square
df
P-value
F-statistic
df
P-value
Overall
Overall
12
249.92
342.42
278.60
390
270
270
⬎0.9999
0.0018
0.3464
0.5055
1.2253
390, 294.2
270, 73.6
⬎0.9999
0.1515
1
Baseline sample; MAPSE, Museo Antropológico Padre Sabastián Englert, Rapa Nui; AANMW, Anthropologische Abteilung,
Naturhistorisches Museum Wien, Vienna, Austria; IU, Indiana University, Bloomington, IN; SI, Smithsonian Institution, Washington, DC.
2
First latent root/eigenvalue removed.
crania, by adding data to the AANMW samples from
additional crania collected during the sample period
(1880s), one would expect the level of excess variability to have remained the same or to have become
greater. This was not the case.
These results provide support for the conclusions
reached regarding the male American Museum of
Natural History sample discussed above. The excessive variability observed was likely an artifact of
sample size, and not temporal changes or the true
existence of excess variability. The results of any
␹2-test and F-test of intrasample variability must be
interpreted with caution and with consideration of
the size of the hypothesis sample.
DISCUSSION AND CONCLUSIONS
The results of this study show the ability of the
multiple imputation and variance comparison methodologies to predict missing variables while maintaining the inherent variance/covariance structure
and to discriminate among groups in artificially assembled samples. It is evident that the Anthropologische Abteilung, Naturhistorisches Museum Wien,
Austria, Weisser collection; the Museo Nacional de
ASSESSING INTRASAMPLE VARIATION
Historia Natural, Santiago, Chile, Knoche/Bienvenido and Norwegian Archaeological Expedition
collections; the Natural History Museum, London,
Lord Crawford/Katherine Scoresby Routledge collection; the Musée de l’Homme, Paris, Alphonse Pinart/
Alfred Métraux collection; and the American Museum of Natural History, New York, Shapiro
collection male and female samples exhibit little
excess intrasample variability due to the different
time periods from which the various museum samples were collected. It is therefore evident that the
hypothesis samples represent subsamples of the underlying Rapa Nui population represented by the
baseline sample, and are from the same chronological periods. The baseline sample (Museo Antropológico Padre Sabastián Englert, Rapa Nui Gill collection) appears to encompass the range of
variability expressed by the hypothesis samples.
A critical consideration for any study assessing
museum sample variation remains the selection of
W, the baseline sample (Key and Jantz, 1990a,b).
The sample utilized to estimate baseline variability
would have a profound effect on all subsequent analyses. The use of the Museo Antropológico Padre Sabastián Englert, Rapa Nui Gill collection to estimate
W is justifiable, as it represents individuals from all
regions of the island and spans the time periods
during which ahu and cave burials were practiced
(the Late Prehistoric (AD 1680 –1722) through the
Protohistoric (AD 1722–1868) periods; Gill and Owsley, 1993; Gill et al., 1983; Owsley et al., 1994;
Shaw, 1996; Stevenson, 1984). The results of this
research indicate that it is not unwarranted to pool
the various Rapa Nui museum cranial samples for
further analyses. The methodologies utilized for this
research will be incorporated to investigate intrasample variability among other prehistoric
Polynesian cranial collections, in order to ensure the
accurate assessment of Polynesian prehistory
through the use of craniometrics.
Though this study utilized Rapa Nui cranial samples from around the world, a number of methodological issues were addressed which are important
for all research using skeletal samples. Among these
issues are intra- and interobserver error, sampling
bias, missing data estimation, and intrasample variation. One ultimate goal of many physical anthropology studies is the assessment of morphological/
phenotypic variation. However, embedded in all
morphological data is environmental variation, creating bias and error within the data. One recognizable source of environmental variance is intra- and
interobserver variation (error) in the measuring and
recording of morphological dimensions. Differences
in measuring techniques and equipment can lead to
excessive variation when data from multiple sources
are pooled together for an analysis. Standardization
in techniques, equipment, and periodic assessment
of intra- and interobserver error could significantly
minimize a source of environmental variation (Utermohle and Zegura, 1982).
55
Sampling bias is a source of environmental variation that may or may not be within the control of
the individual researcher. Collection and sampling
bias with regards to sample size, physical condition
of skeletal elements, accessibility of elements, biological age, sex, and race of specimens can lead to
bias in the morphological variation of the sample.
The demographic/age cohort structure of samples
representing a single population might not be a concern when assessing intrasample variation, as was
the case for this study. However, knowledge of the
demographic/age cohort structure of a sample might
be of vital concern when comparing samples from
different populations. Researchers need to assess
the composition of their samples to insure they are
appropriate for the research question under investigation.
The estimation of missing data can also contribute
to the environmental variation present within sample data. It was discussed above how various missing data estimation techniques produce different
types of bias within sample morphological variation.
Each technique has its advantages and disadvantages, and the most appropriate method for the research question under investigation needs to be utilized. In many case this is a judgment call by the
individual researcher, but that decision needs to be
addressed and justified. Additionally, interpretation
of results obtained from estimated data have to take
into account the method utilized and the biases that
the technique embeds in the data.
All the factors discussed above can greatly influence intrasample variation. This study should encourage other physical anthropologists to assess the
degree of intrasample variability produced when: 1)
data from various museum skeletal samples are
pooled to represent a single population (i.e., Rapa
Nui), or a related group of populations (i.e., Polynesians); and 2) when independent data from two or
more researchers are pooled. This type of assessment is far too little practiced.
ACKNOWLEDGMENTS
This research project would not have been possible without the well-documented Rapa Nui skeletal
sample established by Dr. George W. Gill, Scientific
Leader of the 1981 Easter Island Anthropological
Expedition, and the efforts of his University of Wyoming students, and Chilean and American colleagues. Dr. Douglas W. Owsley, of the Smithsonian
Institution, computerized the craniometric data
from that project. I thank Dr. Gill and Dr. Owsley
for providing me the opportunity to conduct research
on these Rapa Nui craniometrics. Their field efforts
were supported by the National Geographic Society,
the Center for Field Research-Earthwatch, the Government of Chile, the University of Chile, the University of Wyoming, the Kon-Tiki Museum, the
Smithsonian Institution, and the World Monuments
Fund. This particular research project would not
have been possible without the additional assistance
56
V.H. STEFAN
Porion-nasion3 H-NAR*‡
Porion-subnasale4 H-SSR*‡
Porion-prosthion5 H-PRR*‡
Basion-porion height B-BPH†
Maxillofrontal breadth GH-MXB†
Maxillofrontal subtense GH-MXS†
Zygoorbital breadth GH-ZOB†
Zygoorbital subtense GH-ZOS†
Alpha chord GH-ALB†
Alpha subtense GH-ALS†
Simotic cord H-WNB*
Bimaxillary breadth H-ZMB*
Bimaxillary subtense H-SSS*
Mastoid length H-MDH*
Mastoid width H-MDB*
Cheek height H-WMH*
Malar length, inferior H-IML*
Malar length, maximum H-XML*
Palatal depth M-PAD
Maxilloalveolar breadth6 H-MAB*
Maxilloalveolar length B-MAL
provided by Dra. Silvia Quevedo K. and Dra. Marı́a
Eliana Ramı́rez of the Museo Nacional de Historia
Natural (Santiago, Chile), Professeur André Langaney, Philippe Mennecier, and Simone Jousse of the
Laboratoire d’Anthropologie Biologique, Musée de
l’Homme (Paris, France), Professeur Henry de Lumley of the Muséum d’Histoire Naturelle (Paris,
France), Domimique Grimaud-Hervé of the Institut
de Paléontologie Humaine (Paris, France), Dr. Robert Kruszynski of the Human Origins Group, Natural History Museum (London, UK), Dr. Ian Tattersall and Dr. Kenneth M. Mowbray of the American
Museum of Natural History (New York, NY), Dr.
Della C. Cook, Indiana University (Bloomington,
IN), and Dr. Douglas W. Owsley, Smithsonian Institution (Washington, DC) during my data collection
in the United States, Chile, and Europe. I thank Dr.
Richard L. Jantz, Dr. Hans C. Petersen, and Dr.
John W. Graham for their helpful discussions regarding the methodologies employed in the research.
APPENDIX
Standardized craniofacial measurements1
Maximum cranial length H-GOL*
Nasion-occipital length H-NOL*
Maximum cranial breadth H-XCB*
Maximum frontal breadth H-XFB*
Minimum frontal breadth B-WFB
Bizygomatic breadth H-ZYB*
Basion-bregma height H-BBH*
Basion-nasion length H-BNL*
Nasion-bregma chord H-FRC*
Bregma-lambda chord H-PAC*
Nasion-prosthion height H-NPH*
Nasion-alveolare2 B-NAL
Biasterionic breadth H-ASB*
Basion-prosthion length H-BPL*
Bistephanic breadth H-STB*
Bijugal breadth H-JUB*
Foramen magnum length H-FOL*
L. orbital height H-OBH*
L. orbital breadth, dacrion B-OBD
L. orbital breadth, max-f H-OBB*
Biorbital breadth H-EKB*
Nasal height H-NLH*
Nasal breadth H-NLB*
Bifrontal breadth H-FMB*
Biauricular breadth H-AUB*
Minimum cranial breadth H-WCB*
Auricular height B-AUR‡
Porion-bregma height B-PBH‡
1
B, Bass (1995); GH, Gill et al. (1988); H, Howells (1973); M, Martin
and Saller (1957). *Measurement abbreviations from Howells (1989).
Other abbreviations developed by author for easy of data handling
and analysis. †Measurement taken with a simometer. ‡Measurement
taken with a head spanner. Palate depth measurement taken with a
palatometer. All other measurements taken with a sliding or spreading caliper.
2
Upper facial height.
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