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A problem that can arise when inferring characteristics of individuals from aggregate data referring to a population of which they are members. Such aggregate data are frequently used in geographical work, referring to the populations of defined areas (hence they are often termed ecological data), so the problem is potentially serious for some forms of geographical analysis.
The fallacy was initially highlighted by W.S. Robinson (1950). Using 1930 US census data, he obtained a high correlation coefficient of 0.773 from a regression of the percentage of each state\'s population who were illiterate on the percentage who were black. It could be inferred from this that blacks were much more likely to be illiterate than were non-blacks but using data on individuals from the same source, he found a correlation of only 0.203: there was a higher level of illiteracy among blacks than non-blacks, but much less than the state-level (ecological) analysis suggested. The lesson was clear: just because blacks were concentrated in the states with the highest levels of illiteracy did not necessarily mean a much higher level of illiteracy among blacks.
Alker (1969) extended the ecological fallacy (of identifying spurious individual-level correlations from analyses of aggregate data) by identifying five others:
{img src=show_image.php?name=2022.gif } the individualistic fallacy which assumes that the whole is no more than the sum of its parts (see regionalism) — many societies are more than mere aggregations of their individual members; {img src=show_image.php?name=2022.gif } the cross-level fallacy assumes that a relationship observed in one aggregation of a population — i.e. one set of spatial units — applies to all others, and is thus a universal feature of that population: research on the modifiable areal unit problem has demonstrated that this is invalid; {img src=show_image.php?name=2022.gif } the universal fallacy assumes that the pattern observed in a selection of individuals — often not randomly selected according to the principles of sampling — holds for its population; {img src=show_image.php?name=2022.gif } the selective fallacy in which data from carefully chosen cases are used to \'prove\' a point; and {img src=show_image.php?name=2022.gif } the cross-sectional fallacy is the assumption that what is observed at one point in time applies to other times.Recognition of these fallacies and their associated pitfalls indicates a need for careful interpretation of the results of studies based on aggregate data. An observed relationship may be consistent with a hypothesis, but a causal relationship should never be assumed: as Robinson\'s example showed, wrong conclusions can be drawn by attempts to move from the particular to the general.
The problem of drawing conclusions about individual-level correlations from aggregate data has long concerned social statisticians. Most attempts to resolve it have failed, because they cannot avoid the possibility of producing \'nonsense\' answers, such as a population in which 120 per cent of the members are illiterate. King (1997) has solved it for a particular situation, however. If one has information on, for example, the number of black people and the number of illiterates in each sub-area of a larger area for which the inference is to be drawn, then using the \'method of bounds\' it is possible to produce robust estimates of the number of blacks who are illiterate, the number of non-blacks who are literate etc. in that larger area as well as in each of the sub-areas. (RJJ)
References Alker, H.R. 1969: A typology of ecological fallacies. In M. Dogan, and S. Rokkan, eds, Quantitative ecological analysis in the social sciences. Cambridge, MA and London: The MIT Press, 69-86. King, G. 1997: A solution to the ecological inference problem: reconstructing individual behavior from aggregate data. Princeton, NJ: Princeton University Press. Robinson, W.S. 1950: Ecological correlations and the behavior of individuals. American Sociological Review 15: 351-7.
Suggested Reading Duncan, O.D., Cuzzort, R.P. and Duncan, B. 1961: Statistical geography. Glencoe, IL: The Free Press. |
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