  We propose a principled Bayesian method for quantifying tension between
correlated datasets with wide uninformative parameter priors. This is achieved
by extending the Suspiciousness statistic, which is insensitive to priors. Our
method uses global summary statistics, and as such it can be used as a
diagnostic for internal consistency. We show how our approach can be combined
with methods that use parameter space and data space to identify the existing
internal discrepancies. As an example, we use it to test the internal
consistency of the KiDS-450 data in 4 photometric redshift bins, and to recover
controlled internal discrepancies in simulated KiDS data. We propose this as a
diagnostic of internal consistency for present and future cosmological surveys,
and as a tension metric for data sets that have non-negligible correlation,
such as LSST and Euclid.
