ble. This comparability is sometimes lost when the empirical results 

 are derived from aggregated (or disaggregated) observations on the 

 variables. For example, a theory may imply a linear relationship 

 between a set of independent variables, one of which may be sto- 

 chastic, and a dependent variable; the relationship may be esti- 

 mated by minimizing the sum of squared residuals. If aggregated 

 observations are used in the estimation, the regression coefficients 

 may suffer from bias, that is, their expectations may differ from 

 their theoretical counterparts. Therefore, when county data is used 

 to test a community hypothesis, aggregation bias is a potential 

 problem. This problem evaporates if the county and the community 

 are coincident, and if this is not a viable assumption then the prob- 

 lem would evaporate if the county averages are uncorrelated with 

 the stochastic elements of the community observations (cf. Fire- 

 baugh, 1978). 



Aggregation bias has long been recognized as a problem. More 

 recently it has been shown that aggregation interferes with the 

 application of the t test of these coefficients, and furthermore may 

 play havoc with the measure known as R 2 (Greenwood and Luloff, 

 1979). These impacts do not necessarily require the preconditions for 

 bias. Therefore, if the comparability between theoretical and empir- 

 ical findings is assumed incorrectly, unsupportable hypotheses may 

 find support, and the confidence in the predictive power of the 

 theory may be falsely bolstered. That these are among the conse- 

 quences of aggregation may be shown theoretically, but the practi- 

 cal significance can, perhaps, be best indicated by example. 



Two approaches to demonstrating the confounding impact of 

 aggregation suggest themselves. The first is an arbitrary approach 

 in which a set of observations is transformed by arbitrary rules into 

 sets of aggregated observations. Each set of transformed observa- 

 tions could be used to estimate the regression coefficients, the t 

 values, and the value of R 2 . The major advantage with this 

 approach is that it would be inexpensive to implement; the draw- 

 back is that the transformation rules are arbitrary. In practice, 

 transformation rules are not arbitrary. County data, for example, 

 aggregates minor civil divisions which have something in common; 

 they are contained within the same county. A second approach 

 would be to look at real data and transform it into aggregated 

 observations using accepted aggregate concepts. This is relatively 

 more expensive since a large data base is needed. Moreover, the 

 number of aggregations is restricted. Another difficulty is that there 

 is no clear benchmark with this approach. Arbitrary data may be 

 determined with known coefficients and stochastic parameters. 

 Since the reason for the examples is to demonstrate the confounding 



