Bibliometrics

1.  Relative Growth Rate (RGR)
 Doubling Time (Dt)
 Collaborative Coefficient (CC)
 Activity Index (AI)
 Co-authorship Index(CAI)
 Author Productivity
 Degree of Collaboration
 Bradford Law of Scattering and
Lotka’s Law
 Priority Index (RPI)
Contents

2. Relative Growth Rate (RGR)
The mean relative growth rate R-(1-2) over a specified period of interval can be calculated
from the following equation.
W2-W1
R(1-2) = -----------
T2-T1
Where,
R (1-2) = Mean relative growth rate over the specified period interval;
W1 = log w1 (Natural log of initial number of publications)
W2 = log w2 (Natural log of initial number of publications)
T2-T1 = the unit difference between the initial time and final time.

3. DOUBLING TIME
Doubling time (Dt) = 0.693/R(a)
Therefore,
Doubling time for publications Dt(a) = 0.693 / R (a)

4. The pattern of co-authorship among different countries have been examined by
making use of Collaborative Coefficient (CC) suggested by Ajiferuke e.tal (1988).
The formula used for calculating CC is as follows. Where
k
CC=1-[∑ (1/j)Fj/N]
J=1
Fj=the number of authored papers
N=total number of research published; and
k=the greatest number of authors per paper
COLLABORATIVE COEFFICIENT (CC)

5. According to Ajiferuke, CC tends to zero as single-authored papers dominate, and to 1-1/j as
j-authored papers dominate. This implies that higher the value of CC, higher the probability of
multi-authored papers.
COLLABORATIVE COEFFICIENT (CC)…

6. To study how the patterns of co-authorship have changed during a period use of Co-
authorship index has been applied in this study. For calculating CAI the entire data set was
divided into four blocks.
CAI={(Nij/Nio)/(Noj/Noo)}*100
Nij : Number of papers having j authors in block I
Nio : Total Output of Block I
Noj : Number of papers having j authors for all blocks;
Noo : Total number of papers for all authors and all blocks
J=1, 2, 3, > 4
CO-AUTHORSHIP INDEX (CAI)

7. CO-AUTHORSHIP INDEX (CAI) …

8. Activity Index characterises the relative research effort of a country toa given field. It is defined
as
AI =(given field’s share in the country’s publication output) / (given field’s share in the world’s
publication output) } x 100
AI =100 indicates that the country’s research effort in the given field
Corresponds precisely to the world’s average. AI>100 reflects higher activity than the world’s
average, and AI<100 indicates lower than average effort dedicated to the field under study.
In this study, Activity Index for India has been calculated for different years to see how India’s
research activity changed during different years using the above formula.
Activity Index characterizes the relative research effort of a country to a given field.
ACTIVITY INDEX (AI)

9. AI = {(Ii / Io ) / (W i / Wo )} x 100
Where
Ii=India’s output in the year i
Io=Total Indian output
wi=world output in the year i
wo=Total world output
ACTIVITY INDEX (AI) …

10. In order to identify the degree of collaboration, the
research or has adopted K. Subramanyam’s
formula3.
The formula is C = Nm/(Nm+Ns)
Where,
C = Degree of collaboration in a discipline
Nm = Number of multiple authored papers
Ns = Number of the single authored papers
DEGREE OF COLLABORATION

11. Research priority Index is a statistical tool for applying cross-national comparisons. Priority index
(PI) is computed by the following formula
nij/nio
PI=________ x 100
noj/noo
Where as
nij = the number of publications of country i in sub-field j.
nio = the number of publications of country i in all sub-field
noj = the number of publications of all countries in sub-field j, and
noo = the number of publications of all countries in all sub-fields.
RESEARCH PRIORITY INDEX (RPI)

12. The sum was used as deviser for 1/n 4.65 to determine the proportion of the total number of
authors expected to produce ‘n’ paper (in the case of present study n=1,2,3,4,… 10), the following
formula was used to find the proportions.
S = Σ 1/n 4.65
For present study S is the sum of Lotka’s modified rations for the value a= 4.65.
The formula
An = 1/n 4.65 T/S (n = 1,2,3, ……..10)
Where T is total number of authors in the sampling and ‘An’ is the total number of expected
authors producing ‘n’ papers.
LOTKA’S LAW OF AUTHOR’S PRODUCTIVITY

13. LOTKA’S LAW OF AUTHOR’S PRODUCTIVITY …
The Lotka’s law also tested with the application of scientific productivity chi-square model in
relation to a number of authors who contributed ‘n’ number of publication.
It can be expressed by the equation an = a1/n2, n =1,2,3
The chi-square can be computed as (F-p) 2/p.
F = observed number of authors with ‘n’ publications
P = expected number of authors.

14. TABLE7: SHOWING PRODUCTIVITY OF AUTHOR BASED ON LOTKA’S LAW
No. of
authors
Observed
Number of
authors with ‘n’
or (an) or (f)
Observed
percentage of
authors 100 x an /
a1
Expected
number of
authors
(an=an/n2
)or(p)
(F-
P)^2/P
1 1131 100.00 1131.00 0.00
2 1395 123.34 348.75 3138.75
3 1183 104.60 131.44 8412.44
4 793 70.11 49.56 11151.56
5 491 43.41 19.64 11312.64
6 273 24.14 7.58 9289.58
7 130 11.49 2.65 6112.65
8 78 6.90 1.22 4837.22
9 46 4.07 0.57 3634.57
10+ 72 6.37 0.72 7056.72
Total 5592 1693.13 64946.14

15. Price's Square Root law, which states that half (50%) of the literature on a subject will
be contributed by the square root of total number of authors publishing in that area.
PRICE’S SQUARE ROOT LAW

16. Pareto Principle (80/20 Rule) states that, for many events, roughly 80% of
the effects come from 20% of the causes. The original observation was in
connection with income and wealth. Pareto noticed that 80% of Italy's wealth was
owned by 20% of the population. He then carried out surveys on a variety of
other countries and found to his surprise that a similar distribution applied.
PARETO PRINCIPLE (80/20 RULE) AND COLLABORATIVE INDEX

17. Bradford’s law is to explain that a group of journals could be arranged in an order of
decreasing productivity and showed that journals which field most productive articles are
coming first and the most unproductively in the last. According to this journals are to be
grouped into a number of zones each producing a similar number of articles. However the
number of journals in each zone well be increasing rapidly. Then the relationship between
the zones is 1:n:n2 . According to Bradford’s distribution, the relationship between the zone
is 1:n:n2 contrastingly the relationship in each of the present study.
BRADFORD’S LAW OF SCATTERING JOURNALS

18. ZIPF's LAW OF WORD OCCURRENCE
RANKING OF WORD OCCURRENCE