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tokens: with the SPT cluster cosmology analysis of Bocquet et al. ( 2015 ), when it is combined with the first release of the Planck primary CMB cosmology results (Planck Collaboration et al. 2014 ). The combination of the velocity-dispersion-based MOR normalization constraints of Bocquet et al. ( 2015 ) with CMB data leads to a shift in Ω m – σ 8 orthogonal to the cluster SPT cosmology constraints on these parameters. As a result the normalization of the mass–SZE MOR shifts accordingly, to account for the implied different cluster mass scale, leading to the difference seen in Fig. 9 . For a quantitative comparison, we follow Bocquet et al. ( 2015 ) to compute the significance of the difference of two distributions. We randomly draw points from two distributions and compute the difference δ between pairs of points. We use this to estimate the probability distribution P δ of these differences and compute the likelihood that zero is within this distribution. Assuming a normal distribution, this likelihood is then converted to a significance. The lower normalization parameter A SZ , corresponding to higher cluster masses, inferred from a joint cosmological analysis of the SPT cluster sample and Planck CMB data sets (Bocquet et al. 2015 ) disagrees with our result at the 2.6 σ level. We emphasize that the change in normalization in Bocquet et al. ( 2015 , yellow to cyan line in Fig. 9 ) when the underlying cosmology shifts is caused by the self-calibration of the scaling relations from cluster number counts. In this work, we adopt a cosmology with Ω m , σ 8 and H 0 close to the results of Bocquet et al. ( 2015 ) without the Planck data added. Because we use the cluster mass function only for Eddington bias correction and not for self-calibration of the MOR, small changes in the cosmological parameters do not have any big impact on our recovered normalization A SZ . In particular, changing the cosmological parameters to the ones obtained from SPT clusters with Planck data (Bocquet et al. 2015 ) changes our normalization by less than 1 per cent and does not bring it into better agreement with their lower A SZ value. Also used in the SPT–SZ cosmology analysis is the mass– Y X scaling relation. As for the mass– ζ relation, our marginalized posterior for the normalization is in very good agreement with the prior utilized in the cosmology analysis (de Haan et al. 2016 ). This is an important result, as the prior was based on an external calibration of the normalization of the mass– Y X scaling relation, namely the Vikhlinin et al. ( 2009 ) scaling relation updated with the weak lensing mass calibration of the Weighing the Giants (WtG) and CCCP projects (von der Linden et al. 2014 ; Applegate et al. 2014 ; Hoekstra et al. 2015 ). We are now able to confirm that these priors were appropriate for cosmology analysis based on an internal calibration . Fig. 10 shows a comparison of the marginalized and joint posterior probability distributions for the normalizations A