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

Loet Leydesdorff loet at LEYDESDORFF.NET
Sun Apr 18 08:01:35 EDT 2010

```PS. I am sorry: the size of the set remains n, but the number of
categories is n x m (in the denominator, while n in the numerator).
L.

On Sun, Apr 18, 2010 at 10:31 AM, Loet Leydesdorff <loet at leydesdorff.net> wrote:
> 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
> wish to add a reflection about this issue to the preprint to which I
> 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;
>

--
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;

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