We have presented an alternative interpretation for the absence of correlation in the relationship between the core radio power (𝑃_C) and core-dominance parameter (𝑅) for a sample of BL Lacs and radio galaxies found in Fan & Zhang (Astron. Astrophys. 407, 899 (2003)). This is contrary to the predictions of the relativistic beaming and radio source orientation models in which the core luminosity is expected to be Doppler-boosted relative to the extended luminosity which is generally assumed to be isotropic. Our analysis of the 𝑃_C - 𝑅 data indicates a strong luminosity selection effect (reminiscent of bright source samples due to Malmquist bias) in the sample. In particular, we showed that a strong 𝑃_C - 𝑅 correlation exists above some redshift cut-off which may correspond to the flux limit of the sample used.

In this paper, we use the distributions of luminosity ($P$) and radio size ($D$) to re-examine the consistency of the unified scheme of high-excitation radio galaxies and quasars in the recently updated 3CRR sample. Based on a standard cosmology, we derive theoretically and show from observed data, the luminosity limit above which the 3CRR objects are well-sampled. We find, on average, a quasar fraction $\sim$0.44 and galaxy-to-quasar size ratio $\approx$2. Assuming a relativistic outflow of jet materials, we find a mean angle to the line of sight in the range 35$^{\circ} \leq \phi \leq 44^{\circ}$ for the quasars. On supposition of luminosity and orientation-dependent linear size evolution, expressed in a general functional form $D_{\rm (P,z,\phi)} \approx P^{\pm q}(1+z)^{−w} \sin \phi$, we show that above the flux detection threshold of the 3CRR sample, high-excitation galaxies and quasars undergo similar evolutionwith $q = −0.5$; $w = −0.27$ and luminosity independent evolution parameter $x = 2.27$, when orientation effect is accounted for. The results are consistent with orientation-based unified scheme for radio galaxies and quasars.