Quality Research Follows the Power Law

Abstract

Research output can be evaluated with productivity and impact, which are quantified by the numbers of publications ( N ) and citations N c , 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 N and Q C ) 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 1 = Q N / Q C ) and a reduced index ( Q 2 =( Q N Q C ) 0.5 ) to evaluate research quality over time. We rationalized that the power law dependency of quality research is due to its heterogeneous production pathways that require extra effort with respect to “regular” research output. We found that research quality for the top 2% scientists is maximized with ~100 citations/paper and with about ~100 publications. A major advantage of these indices is that they are relative to the academic peers with similar accomplishments in publications and citations, and therefore, are independent of career stages. Since Q indices are positively correlated with H/N ratios, the research quality can also be quickly and conveniently estimated by the readily accessible values calculated using the equation H/ (N)^(2/3) or H/(Nc)^(1/2) .