\label{sec:distance}
The distance is degenerate with the inclination \citep{Cutler_1994,Aasi_2013}, and the inclination can be better constrained for precessing systems \citep{van_der_Sluys_2008,Vitale_2014}. Because we are considering a population with low spins, precession is minimal, and there should be little effect from including spin in the analysis.
The absolute size of the distance credible interval \(\mathrm{CI}_p^{D}\) approximately scales with the distance; hence, we divide the credible interval by the true (injected) distance \(D_\star\); this gives an approximate analogue of twice the fractional uncertainty \citep{Berry_2014}. The cumulative distribution of the scaled credible intervals is plotted in Figure \ref{fig:distance}. The mean (median) values of \(\mathrm{CI}_{0.5}^{D}/D_\star\) for the spinning and non-spinning analyses are \(0.436\) (\(0.376\)) and \(0.426\) (\(0.363\)), respectively; the values of \(\mathrm{CI}_{0.9}^{D}/D_\star\) are \(0.981\) (\(0.845\)) and \(0.951\) (\(0.819\)), and the fractional uncertainties \(\sigma_D/\langle D\rangle\) are \(0.302\) (\(0.262\)) and \(0.245\) (\(0.239\)). There is negligible difference between the spinning and non-spinning analyses, as expected.