  We investigate the properties of photometrically-selected compact groups
(CGs) in the Sloan Digital Sky Survey. In this paper, the fourth in a series,
we focus on understanding the characteristics of our observed CG sample with
particular attention paid to quantifying and removing contamination from
projected foreground or background galaxies. Based on a simple comparison of
pairwise redshift likelihoods, we find that approximately half of compact
groups in the parent sample contain one or more projected (interloping)
members; our final clean sample contains 4566 galaxies in 1086 compact groups.
We show that half of the remaining CGs are associated with rich groups (or
clusters), i.e. they are embedded sub-structure. The other half have spatial
distributions and number-density profiles consistent with the interpretation
that they are either independently distributed structures within the field
(i.e. they are isolated) or associated with relatively poor structures.
Comparisons of late-type and red-sequence fractions in radial annuli show that
galaxies around apparently isolated compact groups resemble the field
population by 300 to 500 kpc from the group centre. In contrast, the galaxy
population surrounding embedded compact groups appears to remain distinct from
the field out beyond 1 to 2 Mpc, consistent with results for rich groups. We
take this as additional evidence that the observed distinction between compact
groups, i.e. isolated vs. embedded, is a separation between different host
environments.
