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In the Pearson--Readhead (PR) and Caltech--Jodrell (CJ1) surveys we have made milliarcsecond-resolution images at $\lambda6$ and $\lambda18$~cm of the cores of 127 radio sources from a complete sample of 200 objects with total $\lambda6$~cm flux density $\ge 0.7$~Jy. This large sample is suitable for a variety of statistical studies, including the following.\par (1)~The distribution of $\Delta$PA, the difference in position angle between parsec-scale and kiloparsec-scale structure, is bimodal with peaks at $0^\circ$ and $90^\circ$, confirming the result found in a smaller subsample by Pearson and Readhead. We discuss the differences in properties of the two types of object, and interpret the distribution in terms of relativistic beaming of helical jets (cf.~Conway \& Murphy 1993, ApJ, 411, 89).\par (2)~We present the $\theta$--$z$ (angular size--redshift) diagram for this sample, and compare it with the results of Kellermann (1993, Nature, 361, 134) which showed evidence for a deceleration parameter $q_0=0.5$. In contrast to Kellermann, we find that the the angular displacement between the unresolved nucleus and the 2\% contour in the jet does not depend on redshift in the way expected for a standard measuring rod, and that most parsec-scale jets have a self-similar, scale-free structure that cannot be used for cosmological inferences.
