  Purpose: We address the question of whether differences are statistically
significant in the rankings of universities. We propose methods measuring the
statistical significance among different universities and illustrate the
results by empirical data. Design/methodology/approach: Based on z-testing and
overlapping confidence intervals, and using data about 205 Chinese universities
included in the Leiden Rankings 2020, we argue that three main groups of
Chinese research universities can be distinguished.
  Findings: When the sample of 205 Chinese universities is merged with the 197
US universities included in Leiden Rankings 2020, the results similarly
indicate three main groups: high, middle, low. Using this data (Leiden Rankings
and Web-of-Science), the z-scores of the Chinese universities are significantly
below those of the US universities albeit with some overlap.
  Research limitations: We show empirically that differences in ranking may be
due to changes in the data, the models, or the modeling effects on the data.
The scientometric groupings are not always stable when we use different
methods.
  R&D policy implications: Differences among universities can be tested for
their statistical significance. The statistics relativize the values of
decimals in the rankings. One can operate with a scheme of low/middle/high in
policy debates and leave the more fine-grained rankings of individual
universities to operational management and local settings.
  Originality/value: In the discussion about the rankings of universities, the
question of whether differences are statistically significant, is, in our
opinion, insufficiently addressed.
