The isolation parameter $\Upsilon$ is a [*strong*]{} function of group radius. Figure \[fig:isovrad\] shows $\log(\Upsilon)$ as a function of projected group radius in kpc. The horizontal line is $\Upsilon = 3$. Groups with large angular radii are not isolated simply because their isolation annuli are larger. Because of this dependence, $\Upsilon$ alone does not specify the physical environment of a particular RSCG. In fact, there is evidence that most HCG’s are also embedded in larger systems (de Carvalho et al.  1994; Ramella et al.  1994).

The correlation of $\Upsilon$ with radius results in a correlation of $\Upsilon$ with group density. Figures \[fig:isodens\]a and \[fig:isodens\]b show the density distributions of the two subsamples (isolated and not isolated) for groups with $N=3$ and with $N \geq 4$, respectively. We apply a K-S test to the density distributions of the two subsamples in each case. The null hypothesis that the density values are drawn from the same distribution is acceptable only at the 3.6% significance level for groups with $N=3$ and the 0.46% level for groups with $N \geq 4$. Thus isolation does imply higher density, as expected. The correlation is not physical; it is a result of the correlation of $\Upsilon$ with 