  To examine how peculiar velocities can affect the 2-, 3-, and 4-point
redshift correlation functions, we evaluate volume-average correlations for
configurations that emphasize and minimize redshift distortions for four
different volume-limited samples from each of the CfA, SSRS, and IRAS redshift
catalogs. We find a characteristic distortion for the 2-point correlation,
$\xibar_2$: the slope $\gamma$ is flatter and the correlation length is larger
in redshift space than in real space; that is, redshift distortions ``move''
correlations from small to large scales. At the largest scales (up to $12
\Mpc$), the extra power in the redshift distribution is compatible with
$\Omega^{4/7}/b \approx 1$. We estimate $\Omega^{4/7}/b$ to be $0.53 \pm 0.15$,
$1.10 \pm 0.16$ and $0.84 \pm 0.45$ for the CfA, SSRS and IRAS catalogs. Higher
order correlations $\xibar_3$ and $\xibar_4$ suffer similar redshift
distortions, but in such a way that, within the accuracy of our analysis, the
normalized amplitudes $S_3$ and $S_4$ are insensitive to this effect. The
hierarchical amplitudes $S_3$ and $S_4$ are constant as a function of scale
between 1--$12 \Mpc$ and have similar values in all samples and catalogues,
$S_3 \approx 2$ and $S_4 \approx 6$, despite the fact that $\xibar_2$,
$\xibar_3$, and $\xibar_4$ differ from one sample to another by large factors
(up to a factor of 4 in $\xibar_2$, 8 for $\xibar_3$, and 12 for $\xibar_4$).
The agreement between the independent estimations of $S_3$ and $S_4$
