1 It is important to note that the biases, introduced from either inclusion of non-peer-reviewed articles or preferential inclusion of English-language journals, cannot be statistically measured nor 100% removed. The publication database contains administrative data that are collected for purposes of cataloging research output, as opposed to a statistical population survey in which errors could be specified and measured.

2 Publication output only includes those indexed in the Scopus database. The publication output discussion uses fractional counting, which credits coauthored publications according to the collaborating institutions or countries based on the proportion of their participating authors. Country assignments refer to the institutional address of authors, with partial credit given for each international coauthorship. As part of our data analysis, we employ filters on the raw Scopus S&E publication data to remove publications with questionable quality, which appear in what are sometimes called predatory journals (NSB Indicators 2018: Bibliometric Data Filters sidebar).

3 This report uses the World Bank (2021) country income classifications accessed in March 2021. The World Bank updates the classifications each year on 1 July. The World Bank income classifications are assigned using the gross national income per capita as measured in current U.S. dollars. This report uses the rankings. More information is available at https://datahelpdesk.worldbank.org/knowledgebase/articles/906519-world-bank-country-and-lending-groups.

4 It is possible that the growth rates could be influenced by fractional counting. For example, the compound annual growth rate for France using whole counting is 1%. Publication output using whole counting is available in Table SPBS-17.

5 The proportion of output attributable to the large producers is consistent whether using fractional counting, as in Figure PBS-2 and Table PBS-1, or whole counting, as in Table SPBS-17. There is a slight difference between the United States and China when looking at the whole counting total production numbers. Using whole counting for 2020, the United States had 600,053 articles, while China had 742,431. A whole counting measure allocates one full count to each country with an author contributing to the article; in fractional counting, each country receives a proportion of the count based on the number of authors from that country. For example, if an article had four authors—with two from the United States, one from China, and one from Brazil—the fractional scores would be 2/4 for the United States, 1/4 for China, and 1/4 for Brazil. In this example, the difference between whole and fractional counting indicates that the United States had more authors on the example paper, compared to the number of authors in China or Brazil.

6 There is little difference between whole or fractional counting of publications for the large producing countries. Whole counting shows a difference for small countries with high collaboration rates because they only receive a fraction of a point for each article, while whole counting awards them a full point (Table SPBS-17 through Table SPBS-31).

7 European Commission, Horizon Europe, https://ec.europa.eu/info/research-and-innovation/funding/funding-opportunities/funding-programmes-and-open-calls/horizon-europe_en.

8 The total international collaboration rate differs from the co-publications of individual countries. Individual country scores use whole counting in which each country, with an institutional address on the paper, receives one point. Therefore, the basis count for individual countries will be larger than the number of papers that have authors with institutional addresses from two or more countries, which is the basis for computing the total international collaboration rate.

9 Countries contributing less than 1% of all internationally coauthored papers in 2020 are not included in the analysis.

10 Relative citation index is a citation-based measure of scientific influence. It is calculated from a country’s share of all cited S&E publications divided by the other country’s share of all cited S&E publications; an index less than 1.00 means a lower-than-expected tendency to cite the other country.

11 Publications include some peer-reviewed journal articles that receive citations as examples of poor or outdated research, but often the articles refuting the low-quality article receive many more citations (Wallin 2005).

12 The share of S&E articles in the top 1% of cited articles is computed by field because different fields of science have different rates of citation. Details provided in Science-Metrix (2021a).

13 Table SPBS-73 and Table SPBS-89 provide the data to compare the computer and information sciences publications in the top 1% for both journal articles and conference proceedings with the HCA scores with only journal articles. For the large producing countries, the HCA that include conference proceedings show the same trend but with slightly higher HCA scores as the HCA with only journal articles. This comparison is made for computer and information sciences because conference proceedings are close to 20% of the references in which proceedings are much less cited (Lisée, Larivière, and Archambault 2008).

14 The share of top 1% articles produced by a country is computed as follows: Sx = HCAx / Ax, where Sx is the share of output from country x in the top 1% most-cited articles; HCAx is the number of articles from country x that are among the top 1% of most-cited articles; and Ax is the total number of articles from country x with a relative citation (RC) score. Both HCAx and Ax are based on whole counting. The RC score is a normalized citation score assigned to a paper and used to rank articles into the top 1%. The RC score takes into consideration the citation behavior between fields and years of publication.

15 Computing the HCA score using fractionally counted publications gives a more exact view of performance for countries with relatively fewer articles.