Metrics: hI,norm and hIa

Note: This tutorial was originally written for Publish or Perish version 4 and all screenshots come from this version. However, the information as such is also applicable for the latest Publish or Perish version 5.

In the last decade, the h-index has become a very popular tool to compare academics. Unfortunately, it has two major drawbacks.

1. Large differences in h-index between disciplines

First, there are large differences in typical h-values between disciplines. Part of these disciplinary differences are caused by the fact that academics in the Life Sciences and Sciences typically publish more (and shorter) articles. They also typically publish with a larger number of co-authors than academics in the Social Sciences and Humanities.

2. Large differences in h-index between junior and senior academics

Second, the h-index is a less appropriate measure of academic achievement for junior academics, as their papers have not yet had the time to accumulate citations. Especially in the Social Sciences and Humanities it might take more than five years before a paper acquires a significant number of citations.

Introducing two new metrics: hI,norm and hIa

The two remaining statistics in the most right-hand column of the Publish or Perish results section - hI,norm and hIa - are metrics that I introduced to address the problem of disciplinary and career stage differences. These two metrics "correct" for differences in the number of co-authorships and for differences in academic age. As such they are more suitable for comparisons across disciplines and career stages.

hI,norm

The hI,norm is an individual h-index. The hI,norm is calculated as follows:

  • normalize the number of citations for each paper by dividing the number of citations by the number of authors for that paper, and then calculate the h-index of the normalized citation counts

Those with co-authors can achieve the same hI,norm

Someone who co-publishes with others will not need to publish more articles to achieve the same hI,norm as an academic who publishes single-authored articles. However, the co-authored articles will need to gather more citations to become part of the hI,norm, as the article’s citations will be divided by the number of co-authors.

Illustrating the hI,norm

The example below shows how academics with the same h-index can have very different individual h-indices (hI,norm). The first screenshot shows my own record, an academic in the Social Sciences with a substantial number of single-authored articles.

tip18a tip18b tip18c tip18d

The second screenshot presents a Professor in Physics at the University of Melbourne, with a similar h-index, but a much lower hI,norm as most of his articles were co-authored with at least three other academics. The third and fourth screenshot show two other Professors at the same University (in the Social Sciences and Humanities) who had a similar hI,norm as the Physics Professor with much lower h-indices as their work was largely (or solely) single-authored.

hI,annual (hIa)

The hI,annual (hIa for short) addresses the problem of comparing academics at different career stages. It is calculated as follows:

  • hIa: hI,norm/academic age, where:
    • academic age: number of years elapsed since first publication

hI, annual = number single-author equivalent impactful articles per year

The hIa-index thus measures the average number of single-author equivalent h-index points that an academic has accumulated in each year of their academic career. A hIa of 1.0 means that an academic has consistently published one article per year that, when corrected for the number of co-authors, has accumulated enough citations to be included in the h-index. The three last academics in the hI,norm example above have very different hI,annual indices, despite having similar hI,norm indices because their academic age runs from 22 to 40.

Illustrating the hI,annual

Below, I have reproduced the metrics of four high-performing individuals at different career stages. They have respectively been publishing for 9, 20, 29 and 40 years. As is immediately obvious, the h, g and hI,norm indices for these four academics differ very substantially. However, their hI,annual indices are very similar indeed. Using the hIa might thus be useful to “spot” high performers early in their career.

9 years
20 years
29 years
40 years
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Obviously, there is no guarantee that the academically younger academics will continue to grow their h-index (and thus hI,norm) during the next 10, 20 or 30 years time. Unless academics keep on publishing high-impact work or their current publications acquire substantially more citations, their hIa will decline naturally with age. Hence, maintaining a high hIa for more than 20 years is indicative of very productive and impactful academics.

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