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tokens: f from the MCMC analyses at z = 0.5 and z = 1. We utilize the monopole and quadrupole up to the k max given in Table 1 , and the hexadecapole up to for TNS and for EFTofLSS at z = 0.5, while for TNS and for EFTofLSS at z = 1. In contrast to the exploratory, full P ( k , μ) Fisher matrix analysis performed in Section 4 , at z = 0.5 we find that the EFTofLSS model does significantly better than the TNS model and the gain from the inclusion of the hexadecapole in the EFTofLSS model is also larger with respect to the TNS case. At z = 1, where the models have the same range of validity, the improvement is less dramatic. An important point we wish to reemphasize is that taking the hexadecapole up to too high a k max (the ones found in Table 1 ) produces biased estimates of the growth rate f for both models, with the exception of the EFTofLSS case at z = 0.5 where indeed we can take k max = k max,4 . This is what has been done in the Fisher analysis in Section 4 , which uses the full P ( k , μ) up to the same k max from Table 1 . As we have already stated, the MCMC analysis resembles what is done in a real data analysis procedure, and is therefore more robust and reliable. To reiterate the point above, we have also performed checks to see what happens if we set the same k max = k max, 4 for TNS at z = 0.5. We found that including the hexadecapole at the same k max results in for TNS giving a (barely) unbiased result for f . This results to a larger error of , compared to our default case with error. We have also checked that increasing k max = k max,4 beyond results in a biased recovery of f . A similar test can be found in fig. 4 of Paper I . Further, we note that in earlier work by Taruya, Saito Nishimichi ( 2011 ), Fisher matrix forecasts using the multipole expansion were performed for the TNS model equipped with a linear bias prescription, taking the same k max for monopole, quadrupole, and hexadecapole. The authors showed that the monopole and quadrupole contain most of the constraining power, but the hexadecapole can somewhat help to further decrease the errors. While the model considered in Taruya et al. ( 2011 ) is not the same as the one we consider in this work, the main result is general: it is preferable to include the monopole and quadrupole at a derived common k max and then add the hexadecapole for as long as the constraints are not biased. 5.1 The effect of positivity priors on the EFTofLSS constraints It is important to comment on the effect of the positivity priors imposed on the EFTofLSS parameters ; these can have a non-negligible effect on the EFTofLSS f constraints. More specifically, we have found that if the fiducial values for these parameters are sufficiently away from zero so that no positivity priors are needed, the f constraints can increase substantially. This explains the apparent inconsistency between our MCMC results and some of the MCMC results in Paper III . In this paper a different set of simulations, cosmology,