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The Hirsch index, or h-index is a widely used citation statistic that, arguably, accurately reflects the impact of a scientist. It takes into account the number of publications as well as how often those papers are cited. For example, an author with 4 publications each with at least 4 citations, has a h-index of 4. Another author with 200 publications, each cited only once, has a Hirsch index of just 1, simply because the papers are not cited more than once. A possible confounding factor in this index are self-citations. If the latter fictional author would have cited all his previous work in his latter 100 papers, their h-index would sky rocket to 100.

Google Scholar nicely provides the h-index and at my institution they use Google Scholar to calculate the h-index for every researcher. However, Google Scholar includes self-citations, while I have heard colleagues from other institutions say that a h-index should not include self-citations, for reasons illustrated above.

Interestingly, the widely used journal impact factor (JIF) from Thomson Reuters does include self-citations (Shema, 2012).

My question is: should the h-index include or exclude self-citations? Is there a consensus reached on this topic? If there is no consensus, should the h-index then not be accompanied by an identifier to clarify which of the two methods was adopted to calculate it?

Reference
- Shema, Sci Am blogs, 2012

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    I think your example is incorrect ("...with one publication cited 4 times, one cited 3 times, one 2 times and one 1 time has a h-index of 4..."). He has 2 papers that are cited 2 times or more, thus h = 2. – damian Sep 29 '15 at 11:56
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    What do they then use that h-index for? Your description that it accurately reflects the impact of the scientist is not at all widely accepted (and as far as I recall, it is mathematically only barely better than pure citation count on average). – Tobias Kildetoft Sep 29 '15 at 11:58
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    @AliceD: Indexed by who? In CS, for instance, DBLP is often considered the authoritative database of indexed works, but even that doesn't always cover everything that is considered relevant and worthy work by specific subfields. Note that the page you linked to lists the statement "It only includes citations in journals that are listed in the ISI Thomson database" as a disadvantage. – O. R. Mapper Sep 29 '15 at 12:21
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    Requiring an impact factor would be a bad idea, as it would exclude arXiv citations, and those should (at least for most purposes) be treated the same as citations to anything with an impact factor. – Tobias Kildetoft Sep 29 '15 at 12:25
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    @O.R.Mapper indeed. It's not unknown IME for an h-index calculated using Google Scholar to be ten points or more higher than one calculated using Web of Science (etc), because of the difference in what's included both as a publication and as a citation in the various databases. – Andrew Sep 29 '15 at 12:42
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There's no firm consensus on whether to include self-citations. (For example, the original paper by Hirsch discusses how one could correct for self-citations but doesn't include this as part of the definition of the h-index.) The reason is that it doesn't matter: the h-index is a crude tool, and if your decisions make delicate enough use of it that the outcome may change depending on whether self-citations are included, then you are using it wrong.

For example, you mention a hypothetical case of someone whose high h-index comes primarily from self-citations. In a case like this, someone on the hiring/tenure committee should ask "Gee, why does this candidate have such a high h-index when the rest of the file gives little or no evidence that their work is influential or important?" Then a few minutes of investigation will reveal the truth.

There's nothing special about self-citations here. I know a case of an eccentric researcher in mathematics who gets a lot of citations from followers of his publishing in marginal places. The total number looks impressive, but if you look at where the citations are coming from, you find only rather weird-looking papers published in places you've never heard of. To keep from being misled by cases like this, you have to do some due diligence when you see a surprising number, and if you're doing that already then skewed h-indices from self-citation are not such a great threat. (In practice the skew is generally pretty small, too.)

The net effect is that if the hiring or tenure committee is just paying attention to numbers like the h-index, without any perspective or further investigation, then that's a major problem with their methodology. If they do notice oddities but feel compelled to give credit for a high h-index anyway, then that's an even worse problem.

In practice, different websites for computing h-indices can give substantially different values, depending on which sources they count citations from. If you care about specifying a well-defined number, then you need to tell exactly how the h-index was computed (which goes far beyond just whether self-citations are included).

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First and foremost, I recommend reading the related question: "Why is it said that judging a paper by citation count is a bad idea?" That question may help relieve some of your concern about the importance of having an answer for this question.

Now, turning to H-index: to the best of my knowledge, there is no consensus as to whether self-citations should count or not count. Saying whether self-citations are included might be useful, but then it would also be useful to know quite a bit more about how the database for computing an H-index is being constructed.

My own thinking on pros and cons goes as follows:

Given all of these things, I personally think the best thing to do is to count self-citation in H-index and mark it clearly as such.

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    On top of that, there is also the practical issue that all the common tools for calculating the h-index (as far as I know) are unable to detect self-citations. As such, it would be very annoying to calculate an h-index value without self-citations. – xLeitix Sep 29 '15 at 12:57
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    @xLeitix - Scopus does it with and without – AliceD Sep 29 '15 at 13:00
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Self citing is a common thing in medicine where good number of the papers are simply case reports and reviews. A faculty can co-author with large number of students and trainees and keep citing his/her previous papers. The publication numbers can be unreal, citations become mathematically multiplied and h-index will be high. I came across authors with average 3 papers per week and most of papers cited their own previous papers.
I agree that bibliometrics do not reflect scientific impact, it simply bedazzle those who look at volume rather than quality. How many times NIH reviewers count publications as a measure of candidate. Jobs in academia is the same.

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