Fw: [SIGMETRICS] Towards a new crown indicator: an empirical analysis

Loet Leydesdorff loet at LEYDESDORFF.NET
Sun Apr 18 04:31:28 EDT 2010

Dear Ton and colleagues,

Let's assume now that we agree about the normalizations in the old and
new crown indicators, and move this discussion further. What continues
to puzzle me in both normalizations is that the expected values are
themselves statistics. Usually (for example, in the case of
chi-square) one uses the statistics of observed over expected. But in
this case, this observed over expected is the statistics of a
statistics.

It works a bit differently for the two normalizations.

First, there is the question whether one should use the means. In the
denominator of equation 1 (the old crown indicator) one took the means
over these means and that can probably be justified because the means
of the sets are more normally distributed than the underlying sets.
Because of the distributions in the underlying sets, however, one
could make an argument for taking the medians. This argument holds
equally for the normalization in the new crown indicator. (You may
react.)

An interesting aspect of the old crown indicator was that one had two
dimensions when taking the means over the means, namely the
distributions over the fields (or journals) and the distributions
within each case. This might allow for developing an expected value on
the basis of the uncertainty contained in these two dimensions which
is more sophisticated than taking the means over the means. The size
of the set is in this case not n, but n x m. I am not suggesting that
one should take the mean over (n x m) -- that would be silly -- but
someone may be able to suggest another statistics which could be used
as an expected value (in the denominator) at the level of the group in
the numerator.

Best wishes,

Loet

On Fri, Apr 16, 2010 at 6:54 PM, T. van Raan <vanraan at xs4all.nl> wrote:
> Adminstrative info for SIGMETRICS (for example unsubscribe):
> http://web.utk.edu/~gwhitney/sigmetrics.html
>
> Dear Colleagues,
>
> To remove any misunderstanding concerning the point raised by Loet (see
> below), the following short comment. In Eq. 1 of our paper the elements (i)
> in the summation in the numerator obviously concern the same elements as in
> the denomitator, by definition. The elements are the publications of any
> kind of entity (e.g., group, institute, university, country). In the
> numerator the number of citations received by each of the elements i are
> totalled, and in the nominator we have the sum of the expected values of the
> same elements i. So both summations concern exactly the same set, and thus
> the total size of the summation is the same for the denominator and the
> nominator, which is n.
>
> Best regards,
> Ton van Raan
>
>
> ----- Original Message ----- From: "Loet Leydesdorff" <loet at LEYDESDORFF.NET>
> To: <SIGMETRICS at LISTSERV.UTK.EDU>
> Sent: Friday, April 16, 2010 12:39 PM
> Subject: Re: [SIGMETRICS] Towards a new crown indicator: an empirical
> analysis
>
>
>> Adminstrative info for SIGMETRICS (for example unsubscribe):
>> http://web.utk.edu/~gwhitney/sigmetrics.html
>>
>> Dear Ton,
>>
>> I read the paper with interest.
>>
>> It seems to me that the value of n in the numerator and denominator of
>> Equation 1 are different, aren't they? Would it then not be better to
>> use different symbols, (fore example, m and n)?
>>
>> Perhaps, I misunderstand. In that case, please, clarify.
>>
>> Best wishes,
>>
>> Loet
>>
>>
>> On Wed, Apr 14, 2010 at 2:29 PM, Anthony F.J. van Raan
>> <vanraan at xs4all.nl> wrote:
>>>
>>> Adminstrative info for SIGMETRICS (for example unsubscribe):
>>> http://web.utk.edu/~gwhitney/sigmetrics.html
>>>
>>> Dear Colleagues, we have the following contribution to the discussion on
>>> new bibliometric performance indicators: http://arxiv.org/abs/1004.1632v1
>>> .
>>>
>>> Best wishes,
>>> Ton van Raan
>>>
>>
>>
>>
>> --
>> Loet Leydesdorff
>> Amsterdam School of Communications Research (ASCoR)
>> Kloveniersburgwal 48, 1012 CX Amsterdam
>> Tel.: +31-20- 525 6598; fax: +31-20- 525 3681
>> loet at leydesdorff.net ; http://www.leydesdorff.net/
>> ---------------------------------------
>> Now available: The Knowledge-Based Economy: Modeled, Measured,
>> Simulated, 385 pp.; US\$ 18.95;
>

--
Loet Leydesdorff
Amsterdam School of Communications Research (ASCoR)
Kloveniersburgwal 48, 1012 CX Amsterdam
Tel.: +31-20- 525 6598; fax: +31-20- 525 3681
loet at leydesdorff.net ; http://www.leydesdorff.net/
---------------------------------------
Now available: The Knowledge-Based Economy: Modeled, Measured,
Simulated, 385 pp.; US\$ 18.95;