Statistics calculated using the means of geographic areas can differ substantially from the corresponding statistics based on data from individuals. Analysts who base their conclusions about individual-level relationships on area-level analyses run the risk of committing the ecological fallacy. Statistical models are proposed that capture the essential features of the structure of a population composed of geographically defined groups and can encompass grouping processes and contextual effects. These models are used to show how small effects in the analysis of individual-level data can be magnified substantially when the corresponding analysis based on aggregated data is carried out. Thus the source of aggregation effects is exposed. While aggregation effects have been studied by many authors, no general approach has been offered to the problem of adjusting an area-level analysis so as to correct for aggregation effects and hence remove, or at least reduce, the bias that leads to the ecological fallacy. The statistical models proposed are used to provide an approach to this problem. Data from the 1991 U.K. Census of Housing and Population are used to illustrate the size of the aggregation effects and the extent to which the proposed adjustments succeed in their objective.