Defining population diversity to be the distribution of population elements along
a continuum of homogeneity to heterogeneity with respect to one or more variables, measures are described with variance-based interpretations which can be
applied to qualitative data. A significant contribution is that the measures are not
restricted to the analysis of univariate distributions. Rather, it is possible to use
these statistics to define relationships in bivariate and multivariate distributions.
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References
1.
Agresti, A. and B.F. Agresti (1977) "Statistical analysis of qualitative variation ," pp. 204-237 in K. F. Schuessler (ed.) Sociological Methodology 1978. San Francisco: J ossey-Bass.
2.
Blau, P. (1970) "A formal theory of differentiation in organizations ." Amer. Soc. Rev.35: 201-218.
3.
Childers, G.W., B.H. Mayhew, and L.N. Gray (1971) "System size and structural differentiation in military organizations: testing a baseline model of the division of labor ." Amer. J. of Sociology76: 813-830.
4.
Gibbs, J. and H. Browning (1966) "The division of labor, technology, and the organization of production in twelve countries." Amer. Soc. Rev.31: 81-92.
5.
Gibbs, J. and W. Martin (1962) "Urbanization, technology, and the division of labor: international patterns." Amer. Soc. Rev.27. 667-677
6.
Gini, C. (1912) "Variabilita e mutabilita, contributo allo studio delle distribuzioni: relazione statische," in Studi Economico-Giuridici della R. Universita di Cagliari.
7.
Goodman, L.A. and W.H. Kruskal (1954) "Measures of association for cross-classifications ." J of Amer. Statistical Assn.49: 732-764.
8.
Greenberg, J.H. (1956) "The measurement of linguistic diversity." Language32: 109-115.
9.
Khinchin, A.I. (1957) Mathematical Foundations of Information Theory . New York. Dover.
10.
Labovitz, S. and J. Gibbs (1964) "Urbanization, technology, and the division of labor: further evidence " Pacific Soc. Rev7: 3-9.
11.
Lieberson, S. ( 1969) "Measuring population diversity." Amer Soc. Rev34850-862.
12.
Light, R.J. and B.H. Margolin (1971) "An analysis of variance for categorical data." J. of Amer Statistical Assn66. 534-544.
13.
Margolin, B.H. and R.J. Light (1974) "An analysis of variance for categorical data 11: small sample comparisons with chi square and other competitors." J. of Amer Statistical Assn.69. 755-764.
14.
Mayhew, B., R. Levinger, J. McPherson, and T. James (1972) "System size and structural differentiation in formal organizations a baseline generator for two major theoretical propositions ." Amer. Soc. Rev.37: 629-633.
15.
McFarland, D. (1969) "Measuring the permeability of occupational structures: an information-theoretic approach." Amer. J. of Sociology75: 41-61.
16.
Mueller, J.H., K.F. Schuessler, and H.L. Costner (1977) Statistical Reasoning in Sociology. Boston: Houghton Mifflin.
17.
Pielou, E.C. (1969) An Introduction to Mathematical Ecology. New York: John Wiley.
18.
——— (1967) "The use of information theory in the study of the diversity of biological populations." Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability 4: 163-177.
19.
Rushing, W. (1976) "Profit and nonprofit orientations and the differentiation coordination hypothesis for organizations: a study of small general hospitals ." Amer. Soc. Rev.41: 676-691.
20.
——— (1968) "Hardness of material as related to division of labor in manufactunng industries." Admin. Sci. Q.13: 225-245.
21.
Sammuel, Y. and B. Mannheim (1970) "A multidimensional approach toward a typology of bureaucracy." Admin. Sci. Q.15: 216-228
22.
Shannon, C. (1948) "A mathematical theory of communications." Bell System Technical J.27: 397-423, 623-656.
23.
Simpson, E.H. (1949) "Measurement of diversity." Nature163: 688.
24.
Smith, D.L. and R.E. Snow ( 1976) "The division of labor: conceptual and methodological issues." Social Forces55: 520-528.
25.
Smith, R.B. (1977) "A proportional reduction in error interpretation for Danials' ρ2 and its special cases." Social Forces55. 1067-1075.
26.
Theil, H. (1967) Economics and Information Theory. Skokie, IL. Rand McNally.
