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The use of principal components analysis in physical anthropology
Author(s) -
Andrews Peter,
Williams David B.
Publication year - 1973
Publication title -
american journal of physical anthropology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.146
H-Index - 119
eISSN - 1096-8644
pISSN - 0002-9483
DOI - 10.1002/ajpa.1330390220
Subject(s) - principal component analysis , matrix (chemical analysis) , multivariate statistics , analogy , data matrix , variance (accounting) , representation (politics) , data set , mathematics , product (mathematics) , sample (material) , set (abstract data type) , function (biology) , statistics , principal (computer security) , sample size determination , computer science , law , geometry , evolutionary biology , epistemology , philosophy , materials science , business , chemistry , composite material , biology , operating system , biochemistry , accounting , chromatography , political science , programming language , clade , politics , gene , phylogenetic tree
Abstract A principal components analysis of eighty fossil and modern hominid skulls employing a total of 25 measurements is presented. The results are discussed briefly, but the central concern of this paper is to examine how the multivariate functions are arrived at and what they show in terms of biological function. A number of sources of error are discussed deriving from the method of calculating the cross‐products matrix, the incomplete representation of sample variance, the use of data sets involving more than one biological function, and the use of samples that are unevenly constructed. It is concluded that more than one kind of cross‐product matrix should be used in principal components analysis so that distortions that arise from the method of normalizing the cross‐product matrix and the position of the origin of the new set of axes counter‐balance each other; that data sets should never encompass more than one functional complex; and that constituent samples in the total sample matrix should be of equal size as far as possible. It is also concluded that the number of variables that can be usefully employed in one data set is limited, by analogy with the law of diminishing returns.