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We used 5487 star-forming galaxies at redshift z~0.63 extracted from theVIPERS and 143774 comparison galaxies in the local Universe from the GSWLCcatalog. We employed two families of methods: parametric and non-parametric. Inthe former approaches, we compared the FMR projections plagued by observationalbiases on differently constructed control samples at various redshifts. Then,the metallicity difference between different redshifts in M*-SFR bins. In thelatter approach, we related the metallicity and the normalized sSFR. Themethodologies implemented to construct fair, complete samples for studying theMZR and the FMR produced consistent results showing a small, but stillstatistically significant evolution of both relations up to z~0.63. Inparticular, we observed a systematic trend where the median metallicity of thesample at z=0.63 is lower than that of the local sample at the same M* and SFR.The average difference in the metallicity of the low and intermediate redshiftsis approximately 1.8 times the metallicity standard deviation of the median, ofthe intermediate redshift sample, in M*-SFR bins. We confirmed this resultusing the Kolmogorov-Smirnov test. When we applied the M*-completenesscriterion to catalogs, the metallicity difference in redshifts decreased toapproximately 0.96 times the metallicity standard deviation of the median, thusnot statistically significant. This result may be dominated by the limitedparameter space, being the lower M* galaxies where the difference is larger outfrom the analysis. A careful reading of the results, and their underlyingselection criteria, are crucial in studies of the mass-metallicity and FMRs.

A comparative study of the fundamental metallicity relation: the impact of methodology on its observed evolution