A basic indicator for relative contributions and a remarkable difference between a ratio of averages and an average of ratios - Leo, Egghe; Ronald, Rousseau; Egghe, Leo; Rousseau, Ronald (Malaysian Journal of Library and Information Science, 2017)
Egghe, L., & Rousseau, R. (2014). A basic indicator for relative contributions and a remarkable difference between a ratio of averages and an average of ratios. Malaysian Journal of Library & Information Science, Vol.19, no. 1: 17-22. This article has been inspired by the activity index and problems in its proper understanding. It studies a basic relative contribution index which is placed in the context of countries’ publication contributions. Two versions are proposed: one being an average of ratios (AoR) and the other one a ratio of averages (RoA). A Lotkaian-Zipfian framework is used to model the two versions of the proposed indicator. A remarkable difference between the two approaches (RoA vs. AoR) is found when determining the fraction of units (countries) that have a value larger than one. This observation contributes to the understanding of the differences between these two approaches.