The 'h' Index – A Measure of Quality of Scientific Research

The index is designed to improve upon simple measures such as the total number of citations or publications to distinguish truly influential physicists from those who simply publish large number of low quality papers. The index works best for comparing scientists working in the same field, as different fields often have differing citation conventions. (Wikipedia)

If a scientist has received a Nobel Prize, he doesn’t need any other measure for the quality of his/her research work. The Nobel is a measure in itself. It is however desirable to have a convenient measure to describe and quantify the quality of research of other lesser scientists. Such a measure was devised by J.E. Hirsch (An index to quantify an individual’s scientific research output, September 2005) who called it h index. A high value of h indicates a high quality of research. Hirsch developed his index for assessing the quality of primarily the physicists but suggested that can be used for the life scientists also.

In Hirsch’s own words, “A scientist has index h if h of his/her Np papers have at least h citations each, and the other (Np – h) papers have no more than h citations each.” For example, if a scientist is rated to have h = 20, it means that 20 of his papers (out of, say, total of 50) were cited at least 20 times each. The remaining 30 were cited less than 20 times each.

There are other, single numbers, measures also that can possibly be used to show any individual scientist’s output or quality of work. One of these is the number of total publications that a scientist published in reputed refereed journals. While it shows productivity of the given author, it doesn’t indicate the quality of his/her work. Another measure can be the highest number of citations that a paper received. It shows the quality of the given paper but doesn’t show the productivity of the scientist. If an average number of citations per paper is used instead, it rewards low productivity and penalizes high productivity.

While the h index is not flawless, it is arguably a better measure than most others. Evaluation of h becomes complex for papers of multiple authors and group work. Similarly, self-citations are liable to skew the h index in favor of the author. In spite of these drawbacks, h index is a convenient measure that can be used in evaluating the quality and quantity of the published work of a scientist. This index can be used in evaluating a science teacher for the award of tenure, promotion and advancement in his/her career. Hirsch argued that “..for faculty at major research universities h ~ 10 to 12 might be a typical value for advancement to tenure (associate professor), and h ~ 18 for advancement to full professor. Fellowship in the American Physical Society might occur typically for h ~ 15 to 20. Membership in the US National Academy of Sciences may typically be associated with h ~ 45 and higher except in exceptional circumstances.”

According to Wikipedia, “Edward Witten, among the physicists, has the highest h of 110 which is increased to 132 as of December 2005. Witten is the string theorist who propounded the M-theory. Steven Weinberg (a co-winner of Nobel Prize for unification of the weak and electromagnetic interactions, with Salam and Glashow (h=53)) has h = 88 while Salam has only h = 58. Weinberg diversified his work making contributions in cosmology while Salam was mainly confined to particle physics. Stephen Hawkings’ h is 62 while that of Leonard Susskind (one of the founders of string theory) is 68. Michio Kaku, author of several popular books on physics, a quantum mechanistic, has h = 22. Lee Smolin who is active in loop quantum gravity and author of Three Roads to Quantum Gravity and The Life of the Cosmos, among several others, has h =33. Brian Greene (author of The Elegant Universe) has h =32.

In the life sciences, the highest h of 191 is scored by S.H. Snyder and the lowest of the 10 scientists recorded by Wikipedia goes to A. Ulrich with h = 120. That the h values can be very different in one field from the other is shown by the above numbers.