By:  Michael Sperazza, University of Montana

This paper is the result of an exploratory statistical analysis on the Ainu peoples. I desired to investigate if sexual dimorphism can be identified in the nasal and orbital cranial measurements? The data set utilized is a subset of the W. W. Howells Raw Data Files of Cranial Measurements. The statistical reports run for this analysis included; all statistical measures on the variables, correlation matrix of the individuals and variables, discriminant analysis on the individuals, cluster analysis of both the individuals and variables, and a factor analysis of the variables. The statistical calculations were setup to test the cranial measurements for variation due to size and shape of the measured areas. So what can be learned from this initial analysis? It can be said of this test sample that using a discriminant analysis on the raw data is a good predictor of sex. However, when focusing on nasal and orbital variability, size is the determining variable, not the shape. Although shape does describe some of the variability, it dose not in a significant manner. It can also be said for this sample group that size accounts for so much variability, that it was our best measure.

Introduction

This paper is the result of an exploratory statistical analysis on the Ainu peoples. I desired to investigate if sexual dimorphism can be identified in nasal and orbital cranial measurements? The data set utilized is a subset of the W. W. Howells Raw Data Files of Cranial Measurements.

The Ainu people of northern Japan are fairly Caucasoid looking with light skin. Their origins are still in question, however they are believed to be a relic population of the Palearctic or Nearctic. The Ainu are recent people, with the oldest skulls dating to no more than about 7500 B.C. (Coon 1962). Recent studies suggest the Ainu are related to the Jomon peoples, whom 12,000 years ago founded Japan's first major civilization. Today many places in Japan have names formed from Ainu words (Kristof 1996).

To start this study, a set of only Ainu cranial data was isolated from the rest of the Howells data set. The full Ainu data set contained measurements from 25 females and 48 males. Contained within this data set was a total of the 82 different cranial measurements. Since this was an initial study, the next step was to reduce the size of the data set to a manageable sample. Arbitrarily, the first 15 females and males were selected for the study. Then the Howells data measurements were restricted to the first of four measurement records. The first record contains the first 30 cranial measurements in the Howells Data Set.

I decided to look for sexual dimorphism within a narrowly defined region, the nasal and orbital regions of the face. The study utilized a total of 18 cranial measurements, containing 14 nasal and orbital measurements and three cranial measurements which cover the three directional plans of the skull (see Figures 1 & 2, and Table 1). In addition, the individual's sex was selected as part of the data set. Each individual was given a marker tag having either an 'M' or 'F' flag to identify sex and a number 1 through 15.
 
 

Figure 1  Location of Cranial Measurements  Front View    (Howells 1973, Skelton 1996, Dienhart 1979)

Figure 2  Location of Cranial Measurements  Lateral View    (Howells 1973, Skelton 1996, Dienhart 1979)

Table 1: Codes and Descriptions of Measurements

Code                         Measurement Name Description

NOL	Nasio-Occipital Length	Greatest cranial length in the median sagittal plane, measured from nasion.
BNL	Basion-Nasion Length	Direct length between nasion and basion.
BBH	Basion-Bregma Height	Distance from bregma to basion.
XCB	Max. Cranial Breadth	The maximum cranial breadth perpendicular to the median sagittal plane.
STB	Bistephanic Breadth	Breadth between the intersections, on either side, of the coronal suture and the inferior temporal line.
ZYB	Bizygomatic Breadth	The maximum breadth across the zygomatic arches, wherever found, perpendicular to the median plane.
AUB	Biauricular Breadth	The least exterior breath across the roots of the zygomatic processes (arches).
NPH	Nasion-Prosthion Height	Upper facial height from nasion to prosthion.
NLH	Nasal Height	The average height from nasion to lowest point on the border of the nasal aperture on either side.
OBH	Orbit Height	The height between the upper and lower borders of the left orbit.
OBB	Orbit Breadth	Breadth from ectoconchion to dacryon.
NLB	Nasal Breadth	The greatest breadth across the alveolar borders.
SSS	Bimaxillary Subtense	The projection or subtense from the subspinale to the bimaxillary breadth.
NAS	Nasio-Front Subtense	The subtense from nasion to the bifrontal breadth.
EKB	Biorbital Breadth	The breadth across the orbits from the ectoconchion to ectoconchion.
DKB	Interorbital Breadth	The breadth across the nasal space from dacryon to dacryon.
NDS	Naso-Dacryal Substense	The subtense from the deepest point in the profile of the nasal bones to the interorbital breadth.
Sex	Sex

(Howells 1973)

Analysis

The statistical analysis was performed using SPSSX software run on a Digital VAX computer at the University of Montana. The statistical reports run for this analysis included; all statistical measures on the variables, correlation matrix of the individuals and variables, discriminant analysis on the individuals, cluster analysis of both the individuals and variables, and a factor analysis of the variables.

The statistical calculations used were set up to test the cranial measurements for variation due to size and shape of the measured areas. In the first part of the project the cranial measurements, or variables, were compared to each other using the correlation similarity measure. The similarity coefficient reports create a matrix of the variables showing the similarity of one object or variable to the other, while each of the individuals were run through a Euclidean dissimilarity analysis.

The next step was to group the similarity and dissimilarity matrixes. These procedures are run to group the individuals and variables in homogenous classes, based on either their similarity or dissimilarity (Bailey 1994). The difference between the two analyses is that cluster analysis defines groups by measuring within-group variance. While discriminate analysis knows before hand to which group an object belongs. It determines an individual's mean score and resolves the individual's closeness to the one of the sex group means (Bailey 1994).

For the variables, a similarity coefficient matrix was utilized, then run in a cluster analysis. A dendrogram charting the linkage between variables was then plotted. Finally, a factor analysis was run to investigate the size and shape components of the variables. The factor analysis groups the variables, or measurements, based on inter-correlated relationships, which allows a variable to belong to more than one group. Each significant factor is composed of a group of variables which together explains a percentage of the variation in the individuals.

In the factor analysis, the Eigenvalue reflects total variability and how much of that variability can be explained by the data (Foor 1996). The factor analysis ranks groupings by Eigenvalue, to which a value over 1.0 is significant (Foor 1996). In this analysis four groupings of variables received Eigenvalues above 1.0, which represents 77.2 percent of the variability. The first group represents 49.9 percent of the variability, the second 12.2 percent, the third 8.2 percent and the fourth 7 percent. The remaining 22.8 percent is represented in 13 additional groups, these are considered insignificant groupings.

The scores for each individual on the first four factors were utilized to create an adjusted data matrix. I could now test the factored discriminate groups for the effects of size and shape against the known sex of the individuals. The overall goal of all these reports and manipulations, was an attempt to find groupings of variables, if any, which would show patterns from which sexual dimorphism could be recognized.

It is typical in this type of analysis that the first grouping of variables will represent overall size variation. This study was no exception, for 15 of the 17 variables were significant in the first factor group. This tells us that most cranial measurements vary with respect to each other as skull size changes. The two exceptions are OBH and SSS.

I had suspected that size differences would distinguish between the sexes but what about the shape? Grouped in the second factor are OBH, SSS and NLH. These three measurements are all facial heights, so this factor reflects facial height as independent from facial breadth and overall size. However, this may be an example of structural correlation, since OBH and SSS over lap part of the NLH. The third and fourth factors each contain one significant variable, OBH and NAS respectively. Interestingly, these are again both height measurements. I am tempted to conclude that height of the nasal and orbital apertures are somehow independent of the variability in other cranial measurements, but more research is needed. To test these factors as predictors of sexual dimorphism, I used the scores of the four significant factors for each individual as data for a cluster and discriminant analysis.

Results

The results of the statistical reports are based on my interpretation of the numerical groups. I now present my observed patterns and interruption of those patterns.

The Euclidean dissimilarity matrix reported on the individuals, then clustered them into groups based on the dissimilarity of one individual to another. These clusters were then plotted in a dendrogram to visually show the cluster results. This dendrogram of the unadjusted individuals reveals two main groupings. In one group only females are present. The other group contains all the males and 3 females. The females grouped with the males represent 20 percent of the female population. This leads to the speculation that the female Ainu have a greater amount of variation than the males. The remaining dissimilarity of 80 percent of the females showed that it may be possible to use sexual dimorphism in cranial measurements as an indication of sex.

In an attempt to refine the predictive power of the model, I than ran a discriminant analysis. The discriminant function refined the separation by sexes so that only one female was incorrectly categorized. This means the discriminate function was 96.6 percent accurate.

In the first discriminant analysis utilizing the raw measurement data, the analysis could separate all but 1 female. But how much of that predictive power was represented by size and how much by shape? When the data matrix was discriminated without the first factor the factor related to size, the separation deteriorated. Now, 6 females and 5 males were incorrectly grouped. This seemed as though the shape factors could separate out some of the variation, but not a significant portion. Using shape alone only 63% of the cases were properly grouped, which is slightly better than guessing which would be about 50%.

I then tested the new data matrix for the size factor was it still as accurate a predictor as the unadjusted factor? This time the size factor could discriminate all but one of the females. This means that after factoring for size and shape the size factor on its own was 96.7 percent accurate. This is the same predictability as when using only the raw data.

Conclusions

So what can be learned from this initial analysis? It can be said of this test sample that using a discriminant analysis on the raw data is a good predictor of sex. However, when focusing on nasal and orbital variability, size is the determining variable, not the shape. Although shape does describe some of the variability, it does not in a significant manner. It can also be said for this sample group that size accounts for so much variability, that it was our best measure.

These conclusions are supported by a study published by Skelton, were he found in a study of over 13,000 individuals that size was the primary factor in discriminating sex. Although the discriminate function works well for sexing skeletal remains, the principal component is size.
 

Bailey, Kenneth D.
1994  Typologies and Taxonomies: An Introduction to Classification Techniques. Sage University Paper series on Quantitative Applications in the Social Sciences, Series no. 07-102. Thousand Oaks, California: Sage.

Coon, Carleton S.
1962  The Origin of Races. New York: Alfred A. Knopf

Dienhart, Charlotte M.
1979  Basic Human Anatomy and Physiology. Philadelphia: W. B. Saunders Company

Foor, Thomas
1996  Class Lectures in Anthropological Research Methods. Missoula, Montana: University of Montana.

Howells, W. W.
1973  Cranial Variation in Man: A Study by Multivariate Analysis of Patterns of Difference Among Recent human Populations. Cambridge, Massachusetts: Harvard University, Peabody Museum of Archaeology and Ethnology.

Kristof, Nicholas D.
1996  Japans forgotten people, are trying to be heard; the Ainu have started a campaign to preserve their ancient culture. New York Times 5 October:A4

Skelton, Randall R.
1996  Skull Graphics in jpg and bmp formats. Missoula, Montana: University of Montana.
1997  How Children Score on Discriminant Functions Designed for Adults. Intermountain Journal of Science, 3(1):47-53.
 

Michael Sperazza is in his second year of the Masters program at University of Montana, majoring in Physical Anthropology. His areas of interest include hominid morphologic change, sexual dimorphism and phylogenetic relationships.  He is currently conducting research on molar cusp patterns of Australopithecines for his thesis.

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