How to standardize (if you must)

Abstract

In many situations we are interested in appraising the value of a certain characteristic for a given individual relative to the context in which this value is observed. In recent years this problem has become prominent in the evaluation of scientific productivity and impact. A popular approach to such relative valuations consists in using percentile ranks. This is a purely ordinal method that may sometimes lead to counterintuitive appraisals, in that it discards all information about the distance between the raw values within a given context. By contrast, this information is partly preserved by using standardization, i.e., by transforming the absolute values in such a way that, within the same context, the distance between the relative values is monotonically related to the distance between the absolute ones. While there are many practically useful alternatives for standardizing a given characteristic across different contexts, the general problem seems to have never been addressed from a theoretical and normative viewpoint. The main aim of this paper is to fill this gap and provide a conceptual framework that allows for this kind of systematic investigation. We then use this framework to prove that, under some rather weak assumptions, the general format of a standardization function can be determined quite sharply.