Comparison of the citation distribution and h-index between groups of different sizes

Evaluating the performance of institutions with different resources is not easy, any citation distribution comparisons are strongly affected by the differences in the number of articles published. The paper introduces a method for comparing citation distributions of research groups that differ in size. The citation distribution of a larger group is reduced by a certain factor and compared with the original distribution of a smaller group. Expected values and tolerance intervals of the reduced set of citations are calculated. A comparison of both distributions can be conveniently viewed in a graph. The size-independent reduced Hirsch index – a function of reducing factor that allows the comparison of groups within a scientific field – is calculated in the same way. The method can be used for comparing groups or units differing in full-time equivalent, funding or the number of researchers, for comparing countries by population, gross domestic product, etc. It is shown that for the calculation of the reduced Hirsch index, the upper part of the original citation distribution is sufficient. The method is illustrated through several case comparisons.