Page 79 - Becoming Metric Wise

70 Becoming Metric-Wise

from each of the four countries, but show exactly how many publications
there are resulting from inter-country collaborative work (Fig. 4.2).

4.2.2 Ordinal Scales

In a set of chemistry journals some may belong to the top 10% of their
field (in the Web of Science), they can be indexed in the Web of Science,
but not belong to the top 10% of its category, or they cannot be indexed
in the Web of Science. In this example, one may say that there is a natural
ranking between these three categories of journals, but nothing more can
be said based on this information. Also, in such cases, one uses bar dia-
grams, but now the order in which categories are placed on the horizontal
axis is fixed in a natural way and before data are collected. Data collected
over time or time series have a natural order (time) and are usually repre-
sented following this natural order, leading to visualizations of time series.

4.2.3 Interval Scales

Suppose one considers a scientist and collects all their publications and for
each of these, the number of received citations. One could consider this a
measurement (counting the number of received citations) on nominal cat-
egories, namely the different publications, and represent them by bar dia-
grams. Yet, this would not be very illuminating. A better approach would
be to show how many publications (or the relative frequency of publica-
tions) that are cited zero times, once, twice and so on. Yet, when citations
are counted fractionally (for details on fractional counting we refer the
reader to Chapter 5: Publication and Citation Analysis) this approach
makes no sense and one has to collect how many publications receive a
fractional count result lying in the intervals [0, 1[, [1,2[, and so on, end-
ing with one or more intervals with lengths larger than one. In other
applications, intervals have other widths and do not have to start with
zero. The main point is that these intervals may not overlap. Bringing
data together in classes is sometimes called binning and the resulting clas-
ses or intervals are then referred to as bins. The difference between the
smallest value (in the previous example dealing with citations this would
probably be zero) and the largest one is called the range (R) of the
observations.
If there are k classes of equal width, denoted as W, and the first class
begins at the smallest observation minus W/2, while the last one ends at
the largest observation 1 W/2, then the class width is equal to R/(k 2 1).