  In our chapter we address the statistical analysis of percentiles: How should
the citation impact of institutions be compared? In educational and
psychological testing, percentiles are already used widely as a standard to
evaluate an individual's test scores - intelligence tests for example - by
comparing them with the percentiles of a calibrated sample. Percentiles, or
percentile rank classes, are also a very suitable method for bibliometrics to
normalize citations of publications in terms of the subject category and the
publication year and, unlike the mean-based indicators (the relative citation
rates), percentiles are scarcely affected by skewed distributions of citations.
The percentile of a certain publication provides information about the citation
impact this publication has achieved in comparison to other similar
publications in the same subject category and publication year. Analyses of
percentiles, however, have not always been presented in the most effective and
meaningful way. New APA guidelines (American Psychological Association, 2010)
suggest a lesser emphasis on significance tests and a greater emphasis on the
substantive and practical significance of findings. Drawing on work by Cumming
(2012) we show how examinations of effect sizes (e.g. Cohen's d statistic) and
confidence intervals can lead to a clear understanding of citation impact
differences.
