Hostname: page-component-78c5997874-j824f Total loading time: 0 Render date: 2024-11-05T21:19:45.176Z Has data issue: false hasContentIssue false
  • English
  • Français

Factor Analysis, Random Data, and Patterned Results

Published online by Cambridge University Press:  20 January 2017

Robert K. Vierra  and
David L. Carlson
Robert K. Vierra
Affiliation:
Department of Anthropology, Northwestern University, Evanston, IL 60201
David L. Carlson
Affiliation:
Department of Anthropology, Illinois State University, Normal, IL 61761
Get access Rights & Permissions [Opens in a new window]

Abstract

Multivariate statistical techniques such as factor analysis are capable of producing patterned results with most, if not all, data matrices. This paper demonstrates that patterned results are obtainable when principal component analysis is applied to a random data set. It is suggested that Bartlett's test for the statistical significance of a correlation matrix be employed in deciding whether a factor analysis of the matrix is justified.

Type
Research Article
Information
American Antiquity , Volume 46 , Issue 2 , April 1981 , pp. 272 - 283
Copyright
Copyright © Society for American Archaeology 1981

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Ahler, Stanley 1971 Projectile point form and function at Rodgers Shelter, Missouri. Missouri Archaeologicol Society, flesearch Series 8.Google Scholar
Ahler, Stanley 1973 Post-Pleistocene depositional change at Rodgers Shelter, Missouri. Plains Anthropoiogist 18:1–26.Google Scholar
Armstrong, J. S., and Soelberg, P. 1968 On the interpretation of factor analysis. Psychological Bulletin 70:361–364.Google Scholar
Azoury, I., and Hodson, F. R. 1973 Comparing Paleolithic assemblages: Ksar Akil, a case study. World Archaeology 4:292–306.Google Scholar
Bartlett, M. S. 1950 Tests of significance in factor analysis. British Journal of Psychology, Statistical Section 3:77–85.CrossRefGoogle Scholar
Benfer, Robert A. 1967 A design for the study of archaeological characteristics. American Anthropologist 69:719–730.Google Scholar
Benfer, Robert A. 1972 Factor analysis as numerical induction: how to judge a book by its cover. American Anthropologist 74:530–554.Google Scholar
Binford, Lewis R. 1972 Model building—paradigms and the current state of Paleolithic research. In An archaeological perspective, edited by Binford, L. R., pp. 244–294. Seminar Press, New York.Google Scholar
Binford, Lewis R., and Binford, Sally R. 1966 A preliminary analysis of functional variability in the Mousterian of Levallois Facies. American Anthropologist 68:238–295.Google Scholar
Christenson, Andrew, and Read, Dwight 1977 Numerical taxonomy, R-mode factor analysis, and archaeological classification. American Antiquity 42:163–179.CrossRefGoogle Scholar
Doran, J. E., and Hodson, F. R. 1975 Mathematics and computers in archaeology. Harvard University Press, Cambridge, Mass.Google Scholar
Downer, Alan S. 1977 Activity areas, surface collection and factor analysis at the Phillips Spring site (23H1216), Missouri. Plains Anthropologist 22:299–311.CrossRefGoogle Scholar
Driver, Harold E., and Sanday, Peggy R. 1966 Factors and clusters of kin avoidances and related variables. Current Anthropology 7:169–176.Google Scholar
Driver, Harold E., and Schuessler, Karl F. 1957 Factor analysis of ethnographic data. American Anthropologist 59:655–663.Google Scholar
Driver, Harold E., and Schuessler, Karl F. 1967 Correlational analysis of Murdoch's 1957 ethnographic sample. American Anthropologist 69:332–352.Google Scholar
Dumond, Don E. 1974 Some uses of R-mode analysis in archaeology. American Antiquity 39:253–270.Google Scholar
Frankel, David 1974 Inter-site relationships from the Middle Bronze age of Cyprus. World Archaeology 6:190–208.Google Scholar
Freeman, Leslie G. 1973 The analysis of some occupation /Joor distributions from earlier and Middle Paleolithic sites in Spain. Paper presented at the IXth International Congress of Anthropological and Ethnological Sciences, Chicago.Google Scholar
Geier, Clarence R. 1974 Notes on a lithic micro-tool industry from the Plains periphery. Plains Anthropologist 19:272–286.Google Scholar
Glover, I. C. 1969 The use of factor analysis for the discovery of artifact types. Mankind 7:36–51.Google Scholar
Gunn, Joel 1975 An envirotechnological system for Hogup Cave. American Antiquity 40:3–21.Google Scholar
Gunn, Joel, and Weir, Frank 1976 Tool kit hypotheses: a case of numerical induction. Newsletter of Lithic Technology V(3):31–40.CrossRefGoogle Scholar
Healan, Dan M. 1972 Surface delineation of functional areas at a Mississippian ceremonial center. Missouri Archaeological Society, Memoir 10.Google Scholar
Hill, James N. 1970 Broken K Pueblo: prehistoric social organization in the American Southwest. Anthropological Papers of the University of Arizona 18.Google Scholar
Hodson, F. Roy 1969 Searching for structure within multivariate data. World Archaeology 1:90–105.Google Scholar
House, John H., Klinger, T. C., and Schiffer, M. B. 1975 A test of the Dalton settlement pattern hypothesis using Cache project survey data. In The Cache River archaeological project, edited by Schiffer, M. B. and House, J. H.. Arkansas Archeological Survey, Research Series 8:93–101.Google Scholar
Johnson, Craig M. 1977 Factor analysis as a technique for exploring patterned variability in archaeological remains. In Trends in Middle Missouri prehistory: a festschrift honoring the contributions of Donald J. Lehmer, edited by Raymond Wood. Memoir of the Plains Anthropologist 13:38–52.Google Scholar
Judge, W. James 1973 Paleoindian occupation of the central JRio Grande Valley in New Mexico. University of New Mexico Press, Albuquerque. Leblanc, Steven Google Scholar
Leblanc, Steven 1975 Micro-seriation: a method for fine chronologic differentiation. American Antiquity 40:22–38.Google Scholar
Lischka, Joseph J. 1975 Broken K revisited: a short discussion of factor analysis. American Antiquity 40:220–227.Google Scholar
Lord, Kenneth J. 1977 Numerical analysis of faunal remains of the Little Bethlehem (41AU38) and Leonard K [41AU37) sites. Plains Anthropologist 22:291–298.Google Scholar
Marquardt, William H. 1974 A statistical analysis of constituents in human paleofecal specimens from Mammoth Cave. In Archeology of the Mammoth Cave area, edited by Watson, Patty Jo, pp. 193–202. Academic Press, New York.Google Scholar
McMillan, R. Bruce 1976 The dynamics of cultural and environmental change at Rodgers Shelter, Missouri. In Prehistoric man and his environments, edited by Wood, W. R. and McMillan, R. B., pp. 211–232. Academic Press, New York.Google Scholar
Montet-White, Anta 1973 Le Malpas rockshelter: a study of Late Paleolithic technology in its environmental setting. University of Kansas Publications in Anthropology No. 4. Lawrence, Kansas.Google Scholar
Montet-White, Anta 1974 Significance of variability in Archaic point assemblages. Plains Anthropologist 19:14–24.Google Scholar
Nie, N. H., Hull, C. H., Jenkins, J. G., Steinbrenner, K., and Bent, D. H. 1975 Statistical package for the social sciences (second ed.). McGraw-Hill, New York.Google Scholar
Roper, Donna C. 1974 The distribution of Middle Woodland sites within the environment of the lower Sangamon River, Illinois. Illinois State Museum, Reports of Investigations 30.Google Scholar
Rowlett, R. M. and Pollnac, R. B. 1971 Multivariate analysis of Marnian La Tene cultural groups. In Mathematics in the archaeological and historical sciences, edited by Hodson, F. R., Kendall, D. G., and Tautu, P., pp. 46–58. Aldine, Chicago.Google Scholar
Rummel, R. J. 1970 Applied factor analysis. Northwestern University Press, Evanston.Google Scholar
Sawyer, Jack, and Robert A., Levine 1966 Cultural dimensions: a factor analysis of the world ethnographic sample. American Anthropologist 68:708–731.Google Scholar
Schiffer, Michael B. 1975 Factors and “toolkits“: evaluating multivariate analyses in archaeology. Plains Anthropologist 20:61–70.CrossRefGoogle Scholar
Schiffer, Michael B. 1976 Behavioral archeology. Academic Press, New York.Google Scholar
Sneath, P. H. A., and Sokal, R. R. 1973 Numerical taxonomy. Freeman, San Francisco.Google Scholar
Thurstone, L. L. 1947 Multiple-factor analysis. University of Chicago Press, Chicago.Google Scholar
Tiffany, Joseph A. 1974 An application of eigenvector techniques to the seed analysis of the Borgley Rockshelter (47-GT- 156). Wisconsin Archeologist 55:2–41.Google Scholar
Turpin, Solveig, Rabinowitz, Joel, Henderson, Jerry, and Patterson, Patience E. 1976 A statistical examination of Caddoan vessel design and shape from the Ben McKinney site, Marion County, Texas. Plains Anthropologist 21:165–179.Google Scholar
Vehik, Rain 1977 A multivariate analysis of the Fristoe burial complex in southwestern Missouri. Plains Anthropologist 22:123–132.Google Scholar
Vierra, Robert K. 1975 Structure versus /unction in the archaeological record. Ph.D. dissertation, University of New Mexico. University Microfilms, Ann Arbor.Google Scholar
Vierra, Robert K., and Taylor, R. L. 1977 Dummy data distributions and quantitative methods: an example applied to overlapping spatial distributions. In For theory building in archaeology, edited by Binford, Lewis R., pp. 317–324. Academic Press, New York.Google Scholar