In the December 2012 issue of Significance, a monthly magazine now published jointly by the American Statistical Association and the Royal Statistical Society, there's an interesting article titled, "Statistics of Statisticians: Critical Masses for Research Groups".
In this article, Ralph Kenna and Beretrand Berche discuss the idea of critical mass when it comes to the size of research groups in various disciplines. They explain how the so-called "Ringelmann effect" in sociology can be tested, and how this leads to measures of an upper bound on group sizes, "... above which research quality either tends not to improve or the rate of improvement starts to level out."
Let Nc is the number of researchers in a group, above which quality improvement starts to decline. Kenna and Berche report values for the following disciplines, among others:
Pure Mathematics: Nc ≤ 4
Economics/Econometrics: 8 ≤ Nc ≤ 14
Statistics & Operational Research: 11 ≤ Nc ≤ 23
Physics: 20 ≤ Nc ≤ 30
Law: 27 ≤ Nc ≤ 35
Chemistry: 23 ≤ Nc ≤ 49
Medical Sciences: 33 ≤ Nc ≤ 49
Business/Management: 40 ≤ Nc ≤ 56
O.K., so now we now why we have Business Schools that are highly inflated in more ways than one!
The Economics/ Econometrics numbers are interesting.
The authors' take-away message? "... there is no threshold group size beyond which research quality significantly improves. On the other hand, there is a measurable upper critical mass, beyond which the Ringelmann effect kicks in." Moreover, this critical mass varies considerably by discipline.
There are some obvious implications here for academic administrators and policy-makers alike.
Pure Mathematics: Nc ≤ 4
Economics/Econometrics: 8 ≤ Nc ≤ 14
Statistics & Operational Research: 11 ≤ Nc ≤ 23
Physics: 20 ≤ Nc ≤ 30
Law: 27 ≤ Nc ≤ 35
Chemistry: 23 ≤ Nc ≤ 49
Medical Sciences: 33 ≤ Nc ≤ 49
Business/Management: 40 ≤ Nc ≤ 56
O.K., so now we now why we have Business Schools that are highly inflated in more ways than one!
The Economics/ Econometrics numbers are interesting.
The authors' take-away message? "... there is no threshold group size beyond which research quality significantly improves. On the other hand, there is a measurable upper critical mass, beyond which the Ringelmann effect kicks in." Moreover, this critical mass varies considerably by discipline.
There are some obvious implications here for academic administrators and policy-makers alike.
© 2013, David E. Giles
Hi Professor Giles,
ReplyDeleteIt is not clear from this post what is meant by a "group". Do they mean a group of academics collaborating on a paper?
It is also not clear what is meant by "... above which ... the rate of improvement starts to level out." So they're saying that the first derivative of the research quality function (not that this function exists; I'm strictly talking about the rate of change concept) starts to become constant after a certain number of researchers? This doesn't convey useful information because the marginal rate of improvement in research quality for every additional researcher could still be massive.
Hi - my understanding of a group in this context is (say) an academic department or a resarch unit. Beyond that, I guess you'd need to read their work for more details. :-)
ReplyDeleteHi Professor Giles,
ReplyDelete23/01/2013 was the 100th anniversary of Markov chains and the 300th of the law of large numbers, I think it deserved a post :-)