A CRITICAL COMMENTARY ON LEIMKUHLER'S ‘EXACT’ FORMULATION OF THE BRADFORD LAW
| Published date | 01 February 1981 |
| Pages | 77-88 |
| DOI | https://doi.org/10.1108/eb026708 |
| Date | 01 February 1981 |
| Author | B.C. BROOKES |
| Subject Matter | Information & knowledge management,Library & information science |
A CRITICAL COMMENTARY ON LEIMKUHLER'S
'EXACT' FORMULATION OF THE BRADFORD LAW
B.
C. BROOKES
It is argued that the powerful techniques of OR operate on only a small
fraction of the statistical information that the social sciences usually provide.
This argument is illustrated by Leimkuhler's recent claim to have found an
'exact' fit to the Bradford law. An elementary theorem of Shannon informa-
tion theory shows that his new function is applied to only 2·3% of the
statistical information inherent in the bibliography he chooses and that
Bradford's original simple formulation not only fits this segment but also
the whole bibliography more closely than the new formulation.
As
every loss
of statistical information can be measured, it can be shown that sophisticated
mathematical techniques cannot compensate for the information they
squander.
I. THE PROBLEMS POSED BY LEIMKUHLER'S PAPER
IN A RECENT paper (1981), Leinikuhler1 claims to have found an exact formu-
lation of the Bradford law. But the fit he claims for his new formulation can be
shown to be less exact than his own earlier (1967)2 formulation in which he
captured, in very precise analytical terms, Bradford's own notoriously ambiguous
verbal formulation. Because of this earlier contribution, however, Leimkuhler's
recent paper deserves careful consideration.
Leinikuhler first reduces Bradford's unconventional frequency-rank distribu-
tion to a conventional
frequency
distribution. This step has the great advantage of
enabling all the sophisticated techniques of operational research to be focused on
the problem. This same step, however, has the still greater disadvantage of
squandering more than 90% of the statistical information inherent in the
bibliography.
There is a further discarding of information when, after an analysis in which
the x2-function is minimized to yield the parameters Leinikuhler seeks for his
formula, he applies the x2-test for goodness of fit but selects only the central
segment of the distribution for his goodness-of-fit criterion. He thus omits the
two tails of his distribution from consideration. As the problem of fitting the
Bradford law to data lies mostly in the tails of the distribution (which, in this case,
embrace more than half of the bibliography) it seems to me that the new tech-
nique fails to justify the claims made for it.
Moreover, the form of the frequency distribution Leinikuhler works with is so
different from that of the frequency-rank distribution which gave rise to Brad-
ford's law that it is difficult to accept the idea that the new function he fits to a
small part of the bibliography can legitimately be called Bradford's law. Nor does
he show that his adoption of Morse's 'Bradford function' has improved the fit.
What difference does it make? He sees no need to justify any of these steps.
So I question Leimkuhler's present claim. More seriously, however, I question
his methodology which I regard as typical of the operational research approach
Journal
of
Documentation,
Vol. 37, No.
2,
June
1981,
pp. 77-88.
77
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