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And just a little later in the journal, as far as the relationship is concerned, as the aggregation bias and the ecological error are related (fat is mine): This is hardly a serious problem for me, since I was planning to do multi-level modeling anyway, as I think, both the aggregation will break down the semi-segregator bias and ecological error. But I`m curious to know what the aggregation bias really means. There is no article on Wikipedia that talks about it, and googling provides all kinds of definitions. However, I think the classic quote in this area is James (1982). The context refers to a situation where I am interested in predicting the results of class size tests. I have each other`s test results and class sizes. I was warned not to calculate the test result for each class (i.e. create a new variable class_test_average, and then use class_size to predict class_test_average. I was told that if I did, I could have a problem with “aggregation bias” and “ecological error.” But these concepts have been expressed to me in a somewhat depressive way. I understood that ecological error is linked to conclusions that relationships at the macro level are translated into the same relationships at the micro level.

However, I did not understand the aggregation bias at all. The main drawback of using aggregated data is probably the inherent difficulty in drawing conclusions in several valid steps on the basis of a single level of analysis [1]. Alker has identified three types of erroneous conclusions that can occur if a researcher tries to generalize from one level of study to another. The individualistic error is the attempt to establish macro-level relationships (aggregates) from micro-levels (individuals). This is the classic problem of aggregation that was first studied by economists, and according to Hannan [15, p. 5], it is an attempt to group observations on “behavioural units” to study the economic relationships that exist for sectors or economies as a whole.¬†Flat-level sections may occur if, at the same level of analysis, conclusions are drawn from one subpopulation to another. The ecological illusion, named by Robinson`s work [18], is the opposite of the individualistic illusion and involves conclusions ranging from higher levels of analysis to lower levels of analysis. Robinson showed that there was not necessarily an equivalent between individual and ecological correlations, and that the latter would generally be greater than the former. Although the ecological illusion has been widely debated and made public, it remains a common error in studies of cause-and-effect findings. Clark, W. A., Avery, K. L.

(1976). The impact of data aggregation in statistical analysis.

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