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To examine how peculiar velocities can affect the 2-, 3-, and 4-pointredshift correlation functions, we evaluate volume-average correlations forconfigurations that emphasize and minimize redshift distortions for fourdifferent volume-limited samples from each of the CfA, SSRS, and IRAS redshiftcatalogs. We find a characteristic distortion for the 2-point correlation,$\xibar_2$: the slope $\gamma$ is flatter and the correlation length is largerin 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. Higherorder correlations $\xibar_3$ and $\xibar_4$ suffer similar redshiftdistortions, but in such a way that, within the accuracy of our analysis, thenormalized amplitudes $S_3$ and $S_4$ are insensitive to this effect. Thehierarchical amplitudes $S_3$ and $S_4$ are constant as a function of scalebetween 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 $S_4$Comment: 20 pages (12 figues available on request), LaTeX,  FERMILAB-Pub-93-097-

Redshift distortions of galaxy correlation functions