the other HCG’s because the physical or velocity separation of member galaxies exceeds our limits, or because of magnitude errors.

Both our selection procedure and Hickson’s introduce biases as a function of redshift or distance. The most important bias is the dependence of density on distance. At large distances, any magnitude-limited survey samples only the bright end of the luminosity function. Both our sample of galaxies and Hickson’s are magnitude-limited; Hickson’s limit is fainter. Because our selection criteria do not vary with redshift to compensate for the magnitude limit, the systems we detect at large distances are generally denser than the average nearby system. Hickson’s sample suffers from a similar bias. His distant groups are more likely to have larger total populations because of the magnitude limit, but there is no fixed upper limit to the physical inter-galaxy separations. We model these effects in Section 8.2.

Nearby groups with large angular radii are absent from the HCG catalog because of the large probability of interlopers within the annulus $\theta_{G} \leq \theta \leq 3 \theta_{G}$. These nearby groups are also more difficult to spot by eye. Figure \[fig:n\_of\_z\] shows the redshift distribution of HCG’s (dotted line) and RSCG’s (solid line). We 