Braun Tibor, Glänzel Wolfgang, Schubert András: Országok, szakterületek, folyóiratok tudománymetriai mutatószámai 1981-1985 (A MTAK Informatikai És Tudományelemzési Sorozata 6., 1992)
Indicators - Citation scores and scales
A. SCHUBERT, W. GLÄNZEL, T. BRAUN : SCIENTOMETRIC DATAFILES As a result of this skewness, average citation rates inform only about one aspect of the underlying distribution, namely, about its location. For this purpose, however, the average seems to be irreplaceable. The median, this "robust" location estimator of very skew and discrete citation distributions almost surely results in a value of either 0 or 1, therefore, it is totally uninformative. To supplement the average, at least one more indicator characterizing the dispersion of citations and defining thereby a proper citation scale should be determined. The most commonly used such indicator, the standard deviation, is, in a sense, counterindicated in the case of veiy skew, long tailed distributions, since it is overly sensitive to very small changes in the tail values. The usual "robust" measures (e.g. the interquartile range) have the same flaw as the median. Our choice was an unusual but easily appreciable indicator: the average citation rate to papers cited higher than average. Together with the average citation rate itself, this indicator is an element of a series of statistics: z. = E(x\x> =z.J ,0=1,2,3,...). Here x denotes a random variable (in our case the number of citations), E(x\.) is its conditional expectation. This series of statistics has already been used for scaling citation rates and named citation scores in some of our recent papers 14,1 5. In the present study, the average citation rate, z 1 is supplemented by the second element of this series, z 2 = E(x\x> =z t). Since, therefore, this value represents the average of citation rates higher than the average, it deserves to be named the outstanding citation rate. Using the samples of citation distributions collected in this study, it was interesting to observe that the difference z 2-z, is a very close proxy for the standard deviation of the distribution (the larger the sample, the better the approximation). Without attempting to give any theoretical explanation to this empirical finding, the following standardization of citation rates suggests itself: u = (x - z l)/(z 1 - Zj) . The u value so obtained will be called unified citation score, and, as an alternative to the relative citation rate (RCR ), can be used as a measure of relative eminence in various sets of publications (journals, fields, countries, etc.). Scienlomelrics 16 (1989) 11
