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Rules for Random Aggregation

Author

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  • D G Steel

    (Department of Applied Statistics, University of Wollongong, Northfields Avenue, Wollongong, NSW 2522, Australia)

  • D Holt

    (Department of Social Statistics, University of Southampton, Highfield, Southampton SO17 1BJ, England)

Abstract

In this paper we derive the effect of aggregation on common statistics when the geographic areas used in the analysis are equivalent to randomly formed groups of individuals. Simple rules of aggregation are provided for use when analysis of such groups is performed. The expectations of common statistics such as means, variances, regression and correlation coefficients, are not affected by aggregation. However, the variation of these statistics is affected, mainly as a result of changes in the number of groups. This variation is related solely to random fluctuations associated with the generation of variate values. Weighting by the group population sizes is shown to be important in the calculation of statistics. Generally, unweighted statistics have larger variation than the corresponding weighted version, and the variation depends not only on the number of groups but also on the distribution of group population sizes. Methods for conducting statistical analysis of aggregate data in this situation are described and statistical inferences based on unweighted statistics are shown to be invalid.

Suggested Citation

  • D G Steel & D Holt, 1996. "Rules for Random Aggregation," Environment and Planning A, , vol. 28(6), pages 957-978, June.
    • Handle: RePEc:sae:envira:v:28:y:1996:i:6:p:957-978
    DOI: 10.1068/a280957
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    Cited by:

    1. Irene L. Hudson & Linda Moore & Eric J. Beh & David G. Steel, 2010. "Ecological inference techniques: an empirical evaluation using data describing gender and voter turnout at New Zealand elections, 1893–1919," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 173(1), pages 185-213, January.
    2. Jan Ubøe & Jens Petter Gitlesen & Inge Thorsen, 2008. "Laboratory Testing of Spurious Spatial Structure in Trip Distribution Models," Spatial Economic Analysis, Taylor & Francis Journals, vol. 3(3), pages 361-372.
    3. Ortega, Emilio & López, Elena & Monzón, Andrés, 2012. "Territorial cohesion impacts of high-speed rail at different planning levels," Journal of Transport Geography, Elsevier, vol. 24(C), pages 130-141.
    4. Jens Petter Gitlesen & Inge Thorsen & Jan Ubøe, 2004. "Misspecifications in modelling journeys to work," ERSA conference papers ersa04p420, European Regional Science Association.
    5. Gitlesen, Jens Petter & Thorsen, Inge & Ubøe, Jan, 2004. "Misspecifications due to aggregation of data in models for journeys-to-work," Discussion Papers 2004/13, Norwegian School of Economics, Department of Business and Management Science.

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