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The continuous progress toward more precise cosmological surveys andexperiments has galvanized recent interest into consistency tests oncosmological parameters and models. At the heart of this effort is quantifyingthe degree of inconsistency between two or more cosmological data sets. Weintroduce an intuitive moment-based measure we call the \textit{index ofinconsistency} (IOI) and show that it is sensitive to the separation of themeans, the size of the constraint ellipsoids, and their orientations in theparameter space. We find that it tracks accurately the inconsistencies whenpresent. Next, we show that parameter marginalization can cause a loss ofinformation on the inconsistency between two experiments and we quantify such aloss using the drop in IOI. In order to zoom on a given parameter, we definethe relative residual IOI and the relative drop in IOI. While these twoquantities can provide insights on the parameters that are most responsible forinconsistencies, we find that the full IOI applied to the whole parameterspaces is what must be used to correctly reflect the degree of inconsistencybetween two experiments. We discuss various properties of IOI, provide itseigenmode decomposition, and compare it to other measures of discordance.Finally, we apply IOI to current geometry data sets (i.e. an improvedSupernovae Type Ia compilation, baryon acoustic oscillations from 6dF, SDSS MGSand Lyman-$\alpha$ forest, and high-$\ell$ CMB temperature data fromPlanck-2015) versus growth data sets (i.e. Redshift Space Distortions fromWiggleZ and SDSS, Weak Lensing from CFHTLenS, CMB Lensing, Sunyav-Zeldovicheffect, and low-$\ell$ CMB temperature and polarization data from Planck-2015).We find that a persistent inconsistency is present between the two data sets.This could reflect the presence of systematics in the data or inconsistenciesin the underlying model.

Cosmological discordances: a new measure, marginalization effects, and application to geometry vs growth current data sets