Statistical and Historical Analyses of Nations Which Deviate From the Size-Density Law


We examine nations which deviate significantly from the −2/3 sizedensity slope previously observed for the aggregated political subdivisions of 98 modern nations and previously derived from the theory of timeminimization. We correct Stephan’s original list of deviant nations, demonstrate that all slopes more negative than −2/3 were due to the erroneous inclusion of cities in the original data sets, develop a theory to account for the less negative deviant slopes, and test the theory both through statistical manipulation of current data and through analysis of available historical data.

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  1. Bogue, Donald J. 1969. Principles of Demography. New York: Wiley.

    Google Scholar 

  2. Breunig, Charles. 1970. The Age of Revolution and Reaction: 1789–1850. New York: Norton.

    Google Scholar 

  3. Lehmann, E. L. 1959. Testing Statistical Hypotheses. New York: Wiley.

    Google Scholar 

  4. Massey, Douglas S., and G. Edward Stephan. 1977. The Size-Density Hypothesis in Great Britain: Analysis of a Deviant Case. Demography 14:351–361.

    Article  Google Scholar 

  5. Massey, Douglas S., Lucky M. Tedrow, and G. Edward Stephan. 1980. Regional Population Density and County Size: A Note on the Problem of Tautology in Size-Density Relationships. Geographical Analysis 12:184–188.

    Article  Google Scholar 

  6. Mitchell, B. R. 1975. European Historical Statistics. New York: Columbia University.

    Google Scholar 

  7. Sachs, Moshe Y. (ed.). 1976. Worldmark Encyclopedia of the Nations (4 vols.). New York: World mark.

    Google Scholar 

  8. Stephan, G. Edward. 1971. Variation in County Size: A Theory of Segmental Growth. American Sociological Review 36:451–461.

    Article  Google Scholar 

  9. —. 1972. International Tests of the Size Density Hypothesis. American Sociological Review 37:365–368.

    Article  Google Scholar 

  10. —. 1977. Territorial Division: The Least Time Constraint Behind the Formation of Subnational Boundaries. Science 196:523–524.

    Article  Google Scholar 

  11. —. 1979. Derivation of Some Social-Demographic Regularities from the Theory of Time Minimization. Social Forces 53:812–823.

    Article  Google Scholar 

  12. Stephan, G. Edward, and Douglas R. McMullin. 1981. The Historical Distribution of County Seats in the United States: A Review, Critique and Test of Time-Minimization Theory. American Sociological Review 46:907–917.

    Article  Google Scholar 

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Stephan, G.E., McMullin, D.R. & Stephan, K.H. Statistical and Historical Analyses of Nations Which Deviate From the Size-Density Law. Demography 19, 567–576 (1982).

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  • Historical Analysis
  • Dominican Republic
  • Deviant Case
  • Central African Republic
  • Proper Unit