  In the first part of this study (Paper I), we introduced the systematic
improvement probability (SIP) as a tool to assess the level of improvement on
absolute errors to be expected when switching between two computational
chemistry methods. We developed also two indicators based on robust statistics
to address the uncertainty of ranking in computational chemistry benchmarks:
Pinv , the inversion probability between two values of a statistic, and Pr ,
the ranking probability matrix. In this second part, these indicators are
applied to nine data sets extracted from the recent benchmarking literature. We
illustrate also how the correlation between the error sets might contain useful
information on the benchmark dataset quality, notably when experimental data
are used as reference.
