Quality Research Follows the Power Law.
Research output can be evaluated with productivity and impact, which are quantified by the numbers of publications (N) and citations N<sub>c</sub>, respectively. The h-index (H) unifies both factors. However, as an extensive variable, it grows with quantity of research output and favors senior researchers over juniors. In this report, by analyzing the data of the world top 2% scientists (n = 179,597) from an online database, we found that h-index follows power laws and proposes a different model from what Hirsch has originally proposed. We propose intensive indices (Q<sub>N</sub> and Q<sub>C</sub>) to measure quality research by comparing the actual h-index of a researcher with the power-law fitted h-indices from the top 2% scientists with the same numbers of publications and citations respectively. We further calculated a dynamic research quality (Q<sub>1</sub>=Q<sub>N</sub>/Q<sub>C</sub>) and a reduced index (Q<sub>2</sub>=(Q<sub>N</sub>Q<sub>C</sub>)<sup>0.5</sup>) to evaluate rese
Added 2026-04-21