What bases do the other interpretations of average provide for evaluating the twoNAEP results by comparing means? Consider the data reduction interpretation: Dataare distilled to a single value, presumably because of our inability to consider all thevalues together. We argue that nothing in this interpretation suggests that any new
information emerges from this process; indeed, a considerable loss of information
seems to be the price paid for reducing complexity. By this logic, it would seem that