Biology Reference
In-Depth Information
mean after
Darroch and Mosimann (1985)
to the data, males and females must be analyzed
separately. Without a size correction, both within- and between-group shape variation can be
obscured by size differences and many morphometric researchers are more interested in
shape variation alone. While traditional morphometric variables can be scaled or size cor-
rected through the approaches mentioned above, there is no consensus on which method
works best and different techniques for size removal may mean that the results of studies
are not comparable.
Traditional Multivariate Statistics
The range of statistical methods available for answering anthropological questions adds to
the allure of traditional morphometrics with techniques for investigating patterns of morpho-
logical variation as well as procedures that assess the validity of a statistical hypothesis.
While
Marcus (1990)
includes a wide range of multivariate statistical methods employed
in morphometric studies in many different disciplines, only a subset of these are regularly
used in human skeletal biology. Methods such as principal component analysis, canonical
variates analysis, discriminant function analysis, regression, multivariate analysis of vari-
ance, and the related multivariate analysis of covariance provide statistical tools for
exploring variation and accepting (or not accepting) hypotheses.
Principal components analysis (PCA) allows the exploration of the range of variation and
interrelationships present in the entire dataset. PCA transforms intercorrelated variables into
uncorrelated variables known as principal components (PC). Each PC is a linear combina-
tion of the original variables that maximize the variance (think variation) represented (
Ren-
cher, 1995; Afifi and Clark, 1996
). The principal components are organized such that the first
component contains the greatest variance with the remaining components ordered by
decreasing variance. Since most of the sample variation is usually explained by the first
few components, individual specimen PC scores or group mean scores can be plotted in
two or three dimensions to explore the variation present between groups or individuals.
PCA can also be used to reduce the dimensionality of a dataset for further analysis. This
can be useful in anthropological morphometrics, as sometimes sample sizes are smaller
than the number of variables available (which results in a singular covariance matrix making
certain analyses, such as canonical variates analysis and discriminant function analysis,
impossible).
Further, PCA resolves
multicollinearity
(correlation among multiple variables) by gener-
ating uncorrelated variables. In morphometrics, principal components can sometimes be
interpreted in terms of morphology based on the correlation between the principal compo-
nent coefficients and the original variables. These properties make PCA an attractive explor-
atory method for assessing the distribution of overall sample variation and the
intercorrelation of variables as well as a useful tool for reducing the dimensionality of the
original dataset without losing significant information.
An exploratory method for grouped data,
canonical variates analysis
(CVA), generates
Mahalanobis distances
between groups based on sample centroids. It also produces canonical
variates (CV) from rotation and scaling of the centroids (
Marcus 1990
). In morphometrics,
Mahalanobis distances (D
2
) can be interpreted in terms of similarity or dissimilarity between
groups. The canonical variates are linear combinations of the original variables that
