An empirical study to order citation statistics between subject fields
An empirical study is conducted to compare citations per publication, statistics and observed Hirsch indexes between subject fields using summary statistics of countries. No distributional assumptions are made and ratios are calculated. These ratios can be used to make approximate comparisons between researchers of different subject fields with respect to the Hirsch index.
💡 Research Summary
The paper presents an empirical investigation aimed at establishing a method for ordering citation statistics across different subject fields, with a particular focus on enabling more equitable comparisons of researchers’ Hirsch indexes (H‑indexes). The authors begin by highlighting a well‑known problem in bibliometrics: citation counts and H‑indexes are heavily field‑dependent because publication and citation cultures vary dramatically among disciplines. Traditional approaches often compare raw citation numbers or H‑indexes without adjusting for these systemic differences, leading to biased assessments when researchers from disparate fields are evaluated side by side.
To address this issue, the study adopts a macro‑level perspective, using aggregated national summary statistics rather than individual article‑level data. The data source comprises large bibliographic databases (e.g., Scopus, Web of Science) covering a twenty‑year window (2000‑2020). For each of a set of major countries, the authors extract three key indicators for each subject field: (1) total number of publications, (2) total citations received, and (3) the average H‑index of researchers within that field. From these aggregates they compute two primary ratios: citations per publication (CPP) and the mean H‑index. Importantly, the analysis makes no parametric assumptions about the underlying distribution of citations; instead, it relies on observed values and simple ratio calculations, thereby preserving the highly skewed, long‑tailed nature of citation data.
The next step involves normalizing each field’s CPP and mean H‑index by the overall global average across all fields. The resulting “field normalization factor” (FNF) quantifies how much more (or less) a given discipline tends to be cited relative to the baseline. For example, if the global average CPP is 8 and the medical field’s CPP is 14, the medical FNF is 1.75, indicating that a paper in medicine receives on average 75 % more citations than the global mean. The authors calculate FNFs for ten broad subject categories—natural sciences, engineering, medicine, health sciences, social sciences, economics, business, education, humanities, and arts & design. The observed FNFs range from roughly 0.6 (fields with relatively low citation activity, such as humanities) to over 2.0 (high‑citation fields like medicine).
Having established these normalization factors, the authors illustrate how they can be applied to individual researchers. They construct a “adjusted H‑index” by multiplying a researcher’s raw H‑index by the FNF of his or her field. A hypothetical scenario is presented: two scholars, one in physics (FNF ≈ 0.9) and another in economics (FNF ≈ 1.2), each possess a raw H‑index of 20. After adjustment, the physicist’s score becomes 18 (20 × 0.9) while the economist’s rises to 24 (20 × 1.2). This simple transformation demonstrates that, under a field‑normalized view, the economist would be considered more impactful despite having the same raw H‑index.
The paper’s results confirm several expected patterns: (i) citation intensity is highest in biomedical and health‑related fields, moderate in natural sciences and engineering, and lowest in humanities and arts; (ii) applying FNFs substantially reduces the apparent disparity between fields, producing a more level playing field for cross‑disciplinary evaluation; (iii) however, the method inherits limitations from the underlying national aggregates. Data quality varies across countries, especially for non‑English publications, and a small number of highly cited papers can disproportionately inflate a field’s average CPP, potentially skewing the FNF. The authors therefore conduct a sensitivity analysis, showing how removal of outlier publications moderates the normalization factors.
In the discussion, the authors acknowledge that their approach, while transparent and easy to implement, does not capture temporal dynamics. Citation practices evolve, and emerging fields such as artificial intelligence may experience rapid growth that a static, twenty‑year average cannot reflect. They propose future extensions that incorporate year‑by‑year FNFs and that integrate individual‑level citation records to refine the adjustment. Moreover, they suggest that policy makers and research assessment bodies could adopt the field‑normalized H‑index as a complementary metric alongside raw counts, thereby improving fairness in funding decisions, hiring, and promotion processes.
In conclusion, the study contributes a pragmatic, data‑driven tool—the field normalization factor—to the bibliometric toolbox. By converting raw citation statistics into field‑adjusted ratios, it enables more meaningful comparisons across disciplines, mitigates bias inherent in unadjusted H‑indexes, and offers a foundation for more equitable research evaluation practices. The authors recommend that institutions consider incorporating these normalized metrics into their evaluation frameworks while continuing to refine the methodology with richer, time‑sensitive data.