skewed citation distributions should not be averaged

Loet Leydesdorff loet at LEYDESDORFF.NET
Thu Sep 1 05:43:00 EDT 2011

```Dear Wolfgang:

Let's try to take this further. I have two questions:

1. You formulate:

"According to the central limit theorem, the distribution of the means of
random samples is approximately normal for a large sample size, provided the
underlying distribution of the population is in the domain of attraction of
the Gaussian distri-bution."

What is a "large" as different from a "huge" sample size? In Pajek, one
calls networks "huge" with more than 100,000 nodes. Do you mean that order
of magnitude? (10^5)

2. Are samples such as all citable items of a specific journal random
samples? The same in the case of performance measurement: can the sample of
all papers of the University of Louvain in 2010 be considered as a random
sample? Can samples based on specific selection criteria (such as search
strings) or stratified samples equally be considered as random?

Perhaps, I learned wrongly how to draw a random sample. :-)

Best wishes,
Loet

-----Original Message-----
From: ASIS&T Special Interest Group on Metrics
[mailto:SIGMETRICS at LISTSERV.UTK.EDU] On Behalf Of Glanzel, Wolfgang
Sent: Thursday, September 01, 2011 9:55 AM
To: SIGMETRICS at LISTSERV.UTK.EDU
Subject: Re: [SIGMETRICS] skewed citation distributions should not be
averaged

Dear Colleagues,

distribution itself but about the distribution of the mean value.
Furthermore, the text is not a statement but based on a proven theorem in
probability theorem. One needs large however not huge data sets for
empirical application.
I would also like to stress that the mean value is still an efficient and
unbiased estimator of the expected value of the underlying random variable.
This applies to all (continuous, discrete, symmetrical, skewed or
whatsoever) distributions  as long as the latter one is finite.
Best regards,

Wolfgang
-----Original Message-----
From: ASIS&T Special Interest Group on Metrics
[mailto:SIGMETRICS at LISTSERV.UTK.EDU] On Behalf Of Sylvan Katz
Sent: Mittwoch, 31. August 2011 23:24
To: SIGMETRICS at LISTSERV.UTK.EDU
Subject: Re: [SIGMETRICS] skewed citation distributions should not be
averaged

Loet,

Yes - perhaps something in the order of 20-30 years of Scopus or WoS data
might be large enough.

Sylvan

--On Wednesday, August 31, 2011 11:08 PM +0200 Loet Leydesdorff
<loet at LEYDESDORFF.NET> wrote:

> Adminstrative info for SIGMETRICS (for example unsubscribe):
> http://web.utk.edu/~gwhitney/sigmetrics.html
>
>> A closer look at the evolution of the citation distributions over a
>> long
> period of time maybe necessary before a definitive answer can be given
> to the question of whether "Citation distributions are so skewed that
> using the mean or any other central tendency measure is ill-advised."
>
> Dear Silvan,
>
> Wouldn't one need very large samples (N > 10^6) to test this?
> Typically, IFs, for example, are computed over 10^2 - 10^3 citable items.
>
> Best,
> Loet
>

Dr. J. Sylvan Katz, Visiting Fellow
SPRU, University of Sussex
http://www.sussex.ac.uk/Users/sylvank

```