  The size-dependent nature of the so-called group or departmental h-index is
reconsidered in this paper. While the influence of unit size on such collective
measures was already demonstrated a decade ago, institutional ratings based on
this metric can still be found and still impact on the reputations and funding
of many research institutions. The aim of this paper is to demonstrate the
fallacy of this approach to collective research-quality assessment in a simple
way, focusing on the h-index in its original form. We show that randomly
reshuffling real scientometric data (varying numbers of citations) amongst
institutions of varying size, while maintaining the volume of their research
outputs, has little effect on their departmental h-index. This suggests that
the relative position in ratings based on the collective h-index is determined
not only by quality (impact) of particular research outputs but by their
volume. Therefore, the application of the collective h-index in its original
form is disputable as a basement for comparison at aggregated levels such as to
research groups, institutions or journals. We suggest a possible remedy for
this failing which is implementable in a manner that is as simple and
understandable as the h-index itself.
