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Handy tip: Consider the coverage and sources for each citation database to help you decide which database to use, the h-index and other metrics will vary depending on how suitable the database is to your discipline and research area.
Citation metrics, such as the h-index, are derived from Scopus, Web of Science and Google Scholar.
For Pros and Cons of each see http://myri.conul.ie/wp-content/uploads/2016/04/H-index-datasheet-2016.pdf
Note: SciVal, which is based on Scopus citation data, is used by the Institutional Research Office to generate reports. See http://www.nuigalway.ie/institutionalresearchoffice/research-metrics/research-metric-tools/scopus-&-scival-overview/ for more information and SciVal training videos.
The essay, The Thomson Scientific Database: The Journal Selection Process, describes the selection process used.
In this blog post, Anne-Wil Harzing who created the Publish or Perish software, outlines how Google Scholar is more inclusive than other citation databases for Social Sciences, Humanities, and Engineering & Computer Science:
This datasheet from MvRI provides a single sheet summary on Google Scholar (GS) for bibliometrics through the use of the Publish or Perish (PoP) software. It includes the pros and cons of GS as a data source and an overview of the key metrics provided by PoP.
A video recording of "Google Scholar, Scopus and the Web of Science: A longitudinal and cross-disciplinary comparison", a presentation given at a seminar organised by the Spanish Journal of Psychology at the Universidad Complutense, Madrid, 16 November 2015. - Presentation slides