Specialization indicators in scientometrics: Understanding the Activity Index and the F-measure through their underlying components

This study provides a conceptual and analytical clarification of the Activity Index (AI) and the F-measure by identifying the structural relationships with their underlying share components and explaining their context-dependent properties. We conduct both an algebraic and empirical analysis of the relation among these indicators in two analytical contexts: Countries Specialization Comparison (comparing the specialization of multiple countries within a fixed domain) and Domains Comparison (comparing specialization across multiple domains within a fixed country). To examine the indicators’ dependencies, we compute Pearson and Spearman correlation coefficients between the indicators and their underlying share components, DShareC (a domain’s share of a country’s output) and CShareD (a country’s share of world output in that domain), using bibliometric data from InCites and OpenAlex covering >200 countries across 22 and 26 research fields over the period 1980–2024. We show that the AI and the F-measure exhibit a mirrored asymmetrical association with their underlying share components across the two analytical contexts. For Countries Comparison, the AI is rank-equivalent to DShareC for comparing countries within a fixed domain, whereas the F-measure operates as a proxy for CShareD. In the Domains Comparison, this pattern reverses: the AI becomes rank-equivalent to CShareD for comparing domains within a fixed country, whereas the F-measure is modulated by the volume of national output, correlating with DShareC in high-output countries and with CShareD in low-output countries. These findings clarify that the interpretation of specialization indicators depends on the analytical context in which they are applied. These results provide a conceptual framework for interpreting specialization indicators in scientometric evaluations and clear criteria for indicator selection, distinguishing between measures of internal research prioritization and global participation in scientific output.