bright ($S_{3.6~\muup \rm m} = 1.07 \times 10^{4} ~\muup \rm Jy$) source so is not included in the SERVS catalogue. The 3.6 $\muup$m-flux density for this source was estimated from the image, and although we do not have enough information to calculate a photometric redshift for this source, this value is used in Section \[section:R\] when calculating radio-to-infrared ratios.

The spectral index and flux density distributions of the sources with and without a counterpart are compared in Fig. \[fig:alpha\_matched\]. The spectral index distributions of the two groups of sources (those with and without a match) are broadly similar, except that a higher proportion of the very steep ($\alpha^{15.7}_{1.4} > 0.8$) sources are unmatched (32 percent of sources with $\alpha^{15.7}_{1.4} > 0.8$ are unmatched compared to 11 percent of sources with $\alpha^{15.7}_{1.4} < 0.8$). This is probably because these very steep sources tend to be significantly extended (all of the sources with $\alpha > 1$ have angular sizes $> 20$ arcsec, Section \[section:sizes\]) and are therefore more likely to be classified as confused when matching. The 15.7-GHz flux density distributions of the two groups of sources are similar, although all six of the brightest 10C sources have counterparts in the multi-wavelength 