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Two Solutions to Galton's Problem

Published online by Cambridge University Press:  14 March 2022

Raoul Naroll
Raoul Naroll*
Affiliation:
San Fernando Valley State College
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Abstract

Two solutions are offered to the problem of distinguishing “historical” from “functional” associations in cross-cultural surveys. The underlying logic of the mathematical model is discussed and three kinds of association distinguished: hyperdiffusional or purely “historical” association, undiffusional or purely “functional” association, and semidiffusional or mixed “historical-functional” association. Two overland diffusion arcs constitute the test sample; the relationship of social stratification to political complexity constitutes the test problem. A sifting test establishes a bimodal distribution of interval lengths between like types and sifts out repetitions with a lesser interval length than the second mode. A cluster test shows that for the test problem, the “hits” cluster more than the “misses”.

Type
Research Article
Information
Philosophy of Science , Volume 28 , Issue 1 , January 1961 , pp. 15 - 39
Copyright
Copyright © Philosophy of Science Association 1961

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References

1 George P. Murdock, Social Structure (New York: Macmillan, 1949).

2 John W. M. Whiting and Irving L. Child, Child Training and Personality (New Haven : Yale University Press, 1953).

3 M. J. Levy, Jr., and L. A. Fallers, “The Family: Some Comparative Considerations,” American Anthropologist 61 (1959) 648.

4 Francis Galton in Edward B. Tylor, “On a Method of Investigating the Development of Institutions applied to the Laws of Marriage and Descent,” Journal of the Royal Anthropological Institute, 18 (1889) 272.

5 Robert H. Lowie, “Evolution in Cultural Anthropology: a Reply to Leslie White,” American Anthropologist 48 (1946) 227, 230.

6 L. T. Hobhouse, G. C. Wheeler and M. Ginsburg, The Material Culture and Social Institutions of the Simpler Peoples (London: Chapman and Hall, 1930).

7 Andre J. Köbben, “New Ways of Presenting an Old Idea: The Statistical Method in Social Anthropology,” Journal of the Royal Anthropological Institute, 82(1952) 129-146; John W. M. Whiting, “The Cross-Cultural Method,” Handbook of Social Psychology, Gardner Lindzey, ed. (Cambridge, Mass.: Addison-Wesley, 1954 1: 525-31.)

8 For a review of the many studies of this kind see Clyde Kluckhohn, “On certain recent applications of association coefficients to ethnological data,” American Anthropologist 41 (1939) 345-377; Harold E. Driver, “Statistics in Anthropology”, American Anthropologist, 55 (1953) 50 f.

9 Galton in Tylor, loc. cit., Lowie, loc. cit.; Franz Boas, “Anthropology and Statistics,” The Social Science and their Interrelations, W. F. Ogburn and A. Goldenweiser, eds., (Boston: Houghton Mifflin, 1927) 120 f.

10 Wilson D. Wallis, “Probability and the Diffusion of Culture Traits,” American Anthropologist 30 (1928) 94-106.

11 Clyde Kluckhohn, op. cit., 259 f.

12 A. L. Kroeber, “Culture Element Distributions: III Area and Climax,” University of California Publications in American Archeology and Ethnology 37 (1936) 111 f.

13 Beatrice Whiting, Paiute Sorcery, Viking Fund Publications in Anthropology, No. 15 (New York: Wenner-Gren Foundation, 1950) pp. 88 f.

14 John W. M. Whiting and Irving L. Child, Child Training and Personality (New Haven: Yale University Press, 1953), pp. 184-7.

15 Thurlow R. Wilson, “Randomness of the distribution of social organization forms: a note on Murdock's Social Structure,” American Anthropologist, 54 (1952) 134-138.

16 Harold E. Driver, “An Integration of functional, evolutionary and historical theory by means of correlations,” Indiana University Publications in Anthropology and Linguistics, Memoir 12, (Bloomington, 1956); Harold E. Driver and William C. Massey, Comparative Studies of North American Indians, Transactions of the American Philiosophical Society, Vol. 47, Part 2 (Philadelphia, 1957) pp. 421-439.

17 Raoul Naroll, “A Preliminary Index of Social Development,” American Anthropologist, 58 (1956) 711 f.

18 Kluckhohn, op. cit., p. 359.

19 Ibid.

20 John F. Kenney and E. S. Keeping, Mathematics of Statistics, Part Two (2nd Edition, New York: Van Nostrand, 1951) pp. 2-5,

21 Raoul Naroll, “Controlling Data Quality,” Series Research in Social Psychology, Symposia Studies Series, Volume 4, National Institute of Social and Behavioral Sciences, September, 1960. Raoul Naroll, Data Quality Control, Chicago: The Free Press of Glencoe, in press.

22 George Peter Murdock, “World Ethnographic Sample,” American Anthropologist 59 (1597) 664-487.

23 U. S. Air Force navigation and planning charts, 1:5,000,000, Lambert Conformai Conic Projection; two series of these were used, as available, the AP series and the GNC series. Great circle routes were worked out through the use of the Great Circle Sailing Charts of the U. S. Hydrographic Office; these furnish convenient gnomonic projections which can be applied to any land area simply by substituting any convenient meridian of longitude for the central meridian of the chart and relabeling the other meridians accordingly.

24 Frederick Mosteller and Robert R. Bush, “Selected Quantitative Techniques,” Handbook of Social Psychology, op. cit. 1: 321 f; Abraham Wald and J. Wolfowitz, “On a test whether two samples are from the same populations,” Annals of Mathematical Statistics, 11 (1940) 147-162; Frieda S. Swed and C. Eisenhart, “Tables for Testing the Randomness of grouping in a sequence of alternatives,” Annals of Mathematical Statistics, 14 (1943) 66-87.

25 Mosteller and Bush, op. cit., pp. 315-7; Colin White, “The Use of Ranks in a Test of Significance for Comparing Two Treatments,” Biometrics, 8 (1952) 33-41, gives tables at two-sided .05, .01 and .001 significance levels for N = 30 and provides an empirical check on the closeness of the normal approximation and an alternative method of extending his tables.