values of $D_{0}$. Figure \[fig:pairsep\] shows that the value $D_{0}$ = 50 kpc yields the best match between CfAnorth (solid line) and the HCG’s (dashed line). A K-S test indicates that the null hypothesis that the density values are drawn from the same distribution is acceptable at the 19% confidence level. On the basis of this match, the catalog with $V_{0}$ = 1000 km s$^{-1}$ and $D_{0}$ = 50 kpc is our objectively selected catalog of compact groups, the RSCG’s. Table \[tab:sepdist\] lists the median, first and third quartiles of the separation distributions for the HCG catalog and the CfAnorth catalog of compact groups. Table \[tab:sepdist\] also includes physical parameters for the RSCG’s we extract from CfAsouth, SSRS2 and CfA2+SSRS2 using $D_{0}=50$ kpc and $V_{0}=1000$ km s$^{-1}$. Note that the third quartile value for the SSRS2 sample (and for the CfA + SSRS2 sample) is inflated by the presence of a single group of 13 galaxies.

The physical properties of RSCG’s are similar to the HCG’s, even though we do not implement all of Hickson’s selection criteria directly. First, we do not take galaxy magnitudes into account in the group selection; some of our systems have fewer than three galaxies 