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Finally, a environmental correction was applied to the local group data. If we split the known local group galaxies into groups based on their location - satellites of the Milky Way, satellites of M31 (Andromeda) and those attached to neither of these two - we find that the \cite{Weisz_2014} data, which contains only a subset of approximately half of all galaxies, does not sample evenly from these three groups. To correct for this, we weight galaxies to ensure that at each mass and redshift the different environments are correctly weighted.  A significant analysis was also performed on the errors on the local group data reported by \cite{Weisz_2014}. These errors were calculated using methods defined in \cite{Dolphin_2012} (systematic) and \cite{Dolphin_2013} (random) but are considered extremely conservative. A method to determine a more reasonable set of uncertainties was not found and so we adopt the convention used in a later paper by Weisz,  The main analysis of the local group data was to do with the error bars reported by \cite{Weisz_2014}. These errors follow the conventions specified in \cite{Dolphin_2012} for systematic uncertainties and \cite{Dolphin_2013} for random. However, these uncertainties are extremely conservative and so instead we use the same convention as in Weisz  \cite{Weisz__2014} \cite{Weisz_2014} which conservatively and simply apply  a relative 50\% fractional  uncertainty of 50\%. to all masses. This method is also considered conservative but significantly improves on the original.