light of the redshift information in Section \[section:properties\_z\]. The 10C sample is compared to the S$^3$ simulation in Section \[section:s3\_z\] and to other observational studies in Section \[section:other-studies\].

Data used {#section:multi-data}
=========

Radio data {#section:radio-data}
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The work in Paper I is based on a sample of sources selected from the 10C survey at 15.7 GHz. The 10C survey was observed with the Arcminute Microkelvin Imager (AMI; @2008MNRAS.391.1545Z) which has a resolution of 30 arcsec. Full details of the 10C survey can be found in @2011MNRAS.415.2708D and @2011MNRAS.415.2699F. This work uses the Lockman Hole field of the survey, which consists of 4.64 deg$^2$ complete to 1 mJy and 1.73 deg$^2$ complete to 0.5 mJy. In Paper I we investigated the radio properties of this sample by matching the catalogue to several lower-frequency catalogues available in the field; a deep Giant Meterwave Radio Telescope (GMRT) survey at 610 MHz [@2008MNRAS.387.1037G; @2010BASI...38..103G], a Westerbork Synthesis Radio Telescope (WSRT) survey at 1.4 GHz [@2012rsri.confE..22G], two deep Very Large Array (VLA) surveys at 1.4 GHz by @2006MNRAS.371..963B (BI2006) and @2008AJ....136.1889O (OM2008), the National Radio Astronomy Observatory (NRAO) VLA Sky Survey (NVSS; @1998AJ....115.1693C) and Faint Images of the Radio Sky at Twenty centimetres (FIRST; @1997ApJ...475..479W). 