Aggregation in Data Tables: Implications for Evaluating Criminal Justice Statistics

Data collected on a set of objects (cities, for instance) over a set of attributes (time points, for instance) can be subjected to a variety of aggregation schemes. For example, if a hypothesized pattern over the attributes is to be confirmed (a temporal increase in homicide rate, for instance), the data could be first aggregated over cities and then compared to the hypothesized pattern. Alternatively, the correspondence for each city could be separately assessed and the individual city indices aggregated. The stage at which aggregation takes place affects the size of the final measure of confirmation as well as its significance, but, unfortunately, in opposite ways. Preliminary data aggregation typically leads to larger summary statistics and larger significance levels. The conflicting notions of size and significance are first formalized in detail when the basic data are single numerical values obtained for each object-attribute pair. Extensions are presented to multigroup concordance, hierarchical aggregation schemes, and to object data defined by pairwise proximities between the attributes.