Sampling variation of principal components
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The convenience of reducing the dimension of a data matrix by principal component analysis invites substantive interpretation of the coefficients of the components. To test the consistency of component coefficients, 10 samples of approximately 25, 50, 100, and 200 items each were randomly drawn, with replacement, from a source sample consisting of 2086 subalkaline asalt analyses. From each sample principal components were calculated using 9 major oxides as variables. Although the eigenvalues are remarkably consistent, both across and within sample size groups, the coefficients of the eigenvectors are subject to considerable sample variance. It is sometimes assumed that the coefficients of the components calculated from small samples are well enough known to be used in detailed petrological interpretation. Our results indicate that the validity of this assumption should be tested in each specific research even when rather large samples are used. The testing procedure used here is suitable of a sufficiently large reservoir of sample items is available; in the absence of such a reservoir complete simulation could be used.
Key wordsprincipal components sampling simulation
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- Chayes, F., 1975, On distinguishing alkaline from other basalts: Carnegie Institution Yearbook 1974–1975, p. 546–547.Google Scholar
- Chayes, F., 1976, Characterizing the consistency of current usage of rock names by means of discriminant functions: Carnegie Institution Yearbook 75, p. 782–784.Google Scholar
- LeMaitre, R. W., 1968, Chemical variation within and between volcanic rock series—A statistical approach: J. Petrol., v. 9, part 2, p. 220–252.Google Scholar
- Middleton, G. V., 1964, Statistical studies on scapolites: Can. J. Earth Sciences, v. 1, no. 1, p. 23–24.Google Scholar