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modifiable areal unit problem |
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A particular form of ecological fallacy associated with the aggregation of data into areal units for geographical analysis.
Most geographical data refer to points in space — such as individual dwellings and workplaces — but many censuses and other sources aggregate these into spatial units (such as census tracts) in order to preserve anonymity. Those spatial units form the \'individuals\' used in geographical analysis, from which inferences may be drawn about the individuals within the units: Robinson\'s classic exposé of the ecological fallacy, for example, showed that a high correlation between two variables at a particular spatial aggregation (in his case, between percentage black and percentage illiterate at the State scale in the US) should not imply a similar correlation at the individual level (that blacks are more likely to be illiterate).
Openshaw (1977, 1984) extended Robinson\'s work by showing that when data are aggregated spatially the ecological fallacy can be decomposed into two effects. With the scale effect, the larger the unit of aggregation the larger on average is the correlation between two variables. There is also an aggregation effect because of the very large number of different ways in which, for example, the 500,000 or so residents of the city of Sheffield could be grouped into 29 wards, each comprising a contiguous block of territory and containing about 17,000 residents. Openshaw has shown that if you construct a large number of the possible aggregations for such a situation, you obtain a frequency distribution for the correlation between two variables across those aggregation units which, although it may be leptokurtic and have most of its values around the distribution mean, could cover the full range of possible values from -1.00 to +1.00 (hence the title of Openshaw and Taylor, 1987).
Openshaw\'s arguments regarding scale and aggregation effects caution against inferring individual relationships from one aggregation only. To the extent that the spatial division used is arbitrary and unrelated to the nature of the phenomena being analysed, therefore, Openshaw\'s findings counsel care in data analysis and interpretation. (They also suggest that researchers wanting to produce a particular result could do so by evaluating the many possible optional aggregations open to them until they find one that \'fits\'!)
The development of computer programs for assessing the extent of the modifiable areal unit problem (i.e. by generating the frequency distribution for the correlation under consideration) has also allowed advances in the evaluation of procedures for aggregating smaller areal units into larger ones. In the UK, for example, Parliamentary constituencies are constructed by grouping contiguous electoral wards. Johnston and Rossiter (1982) showed that in many parts of England the relative success of the two main political parties can be substantially influenced by the particular aggregation selected by the neutral Parliamentary Boundary Commission whereas in the USA Cirincione and Gurrieri (1997) have suggested the use of similar computer-intensive methods as a means of evaluating allegations of racial gerrymandering in the definition of Congressional Districts. (RJJ)
References Cirincione, C. and Gurrieri, G. 1997: Computer-intensive methods in the social sciences. Social Science Computer Review 15: 83-97. Johnston, R.J. and Rossiter, D.J. 1982: Constituency building, political representation and electoral bias in urban England. In D.T. Herbert and R.J. Johnston, eds, Geography and the urban environment: progress in research and applications, volume 5. Chichester and New York: John Wiley, 113-55. Openshaw, S. 1977: A geographical study of scale and aggregation problems in region-building, partitioning and spatial modelling. Transactions, Institute of British Geographers. NS 2: 459-72. Openshaw, S. 1984: The modifiable areal unit problem. Concepts and techniques in modern geography 38. Norwich: Geo Books. Openshaw, S. and Taylor, P.J. 1979: A million or so correlation coefficients: three experiments on the modifiable areal unit problem. In R.J. Bennett, N.J. Thrift and N. Wrigley, eds, Statistical applications in the spatial sciences. London: Pion Ltd.
Suggested Reading Duncan, O.D., Cuzzort, R.P. and Duncan, B. 1961: Statistical geography. Glencoe, IL: The Free Press; King, G. 1997: A solution to the ecological inference problem: reconstructing individual behavior from aggregate data. Princeton, NJ: Princeton University Press. |
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