Aggregation Bias, Local Estimates and the Devil

When faced with a big problem, it is natural to summarize the data en route to a solution. But accepting summary as fact gives up evidence for convenience. Statistical measures from aggregate data may only be capable of indication or trends over time. Only consistency provides a mathematical basis for compiling data into a model; otherwise, the assumptions that turn actual data into indexes are subjective and biased. This paper recommends models of elements but not aggregate models. The proof of empiricism is control of micro variables representing the heterogeneity of individuals – these are the “critical details.” Imputation adds bias and variance to measurement, post weighting only complicates results arbitrarily, and allocation of sums by crude ratios is unjustified.